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Extrusion behaviour of cohesive potato starch pastes: I. Rheological characterisation
Journal of Food Engineering 66 (2005) 1–12 www.elsevier.com/locate/jfoodeng
Extrusion behaviour of cohesive potato starch pastes: I. Rheological characterisation A. Cheyne a, J. Barnes b, D.I. Wilson a
a,*
Department of Chemical Engineering, University of Cambridge, Pembroke Street, Cambridge CB2 3RA, UK b United Biscuits Research and Development, Lane End Road, High Wycombe, UK Received 12 September 2003; accepted 21 February 2004
Abstract The extrusion behaviour of a cohesive mixture of hydrated potato starch solids was characterised using capillary rheometry. Data were collected from isothermal ram extrusion tests and were modelled using (i) the modified plasticity approach described by Benbow and Bridgwater, and (ii) standard fluid mechanics approaches for power law and Herschel–Bulkley fluids. Neither approach proved to be entirely satisfactory, with particle size effects strongly manifested in the Benbow–Bridgwater parameters, and problems with the Mooney analysis for describing the materials as a fluid. Shear-thinning behaviour, as reported elsewhere other starch doughs/mixtures, was evident, while both wall slip and extensional shear contributions were important. The utility of the Benbow– Bridgwater approach was demonstrated by its application to modelling of annular dies, where it provided reasonably accurate predictions once particle size effects were accounted for. 2004 Elsevier Ltd. All rights reserved. Keywords: Starch; Potato; Extrusion; Rheology; Annulus; Plastic
1. Introduction Extrusion is widely used in the food industry to generate solid or semi-solid products with particular product shapes and textures. Indeed, certain shapes and microstructures are only achievable via extrusion routes. The effect of shear, temperature, and local temperature changes induced by shear during extrusion, are frequently critical parameters in modifying the microstructure of the food materials being processed (Matz, 1991). Understanding the interactions between ingredients, process parameters and equipment design and operation is therefore essential in order to achieve product quality targets and develop new products. Key mechanical parameters required for equipment design and operation principally involve the response of the material to deformation via extensional and simple shear, while key product quality parameters are related to the microstructure of the final form. Linking these two groups of data is not straightforward, owing to difficulties in quantifying the rheology and in measuring appropriate *
Corresponding author. Tel.: +44-1223-334-791; fax: +44-1223-331796. E-mail address: [email protected] (D.I. Wilson). 0260-8774/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2004.02.028
microstructural features. These links have been studied for many applications (Aguilera & Stanley, 1990; Noel, Ring, & Whittam, 1990); however the physical and chemical complexity of many biomaterials, such as the starches used in foods, means that such relationships can rarely be predicted in advance (Meuser, Manners, & Seibel, 1995). Today, starchy foods comprise 58% of total world food production and represent the major source of carbohydrate in the human diet (estimated to comprise 80% of the global average calorie intake (FAO, 1999)). Starch must be processed to promote conversion (i.e. structural disordering) before it has nutritive value. Conversion processes such as gelatinisation, involving the application of heat, moisture and possibly mechanical disruption, feature microstructural changes over length scales between 109 and 104 m. The microstructural changes occurring during conversion vary with the processing route, and have been studied extensively for certain applications (Hulleman, Janssen, & Feil, 1998; Mitchell et al., 1997; Senouci & Smith, 1986; Svegmark & Hermansson, 1991; van Soest, 1996). Extrusion of starch–water pastes enables products to be formed with controlled conversion at a large scale. There is a significant body of work in the literature on
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Nomenclature die land flow cross-sectional area (capillary die) Af die land flow cross-sectional area (annular die) A0 barrel flow cross-sectional area Aw total die wall area (annular die) C circumference of die cross-section D die land diameter D0 barrel diameter E extensional shear consistency factor in Eq. (9) k bulk shear consistency factor in Eq. (6a) K wall slip consistency factor in Eq. (7a) L die land length j extensional shear index in Eq. (9) m bulk yield stress index in Eq. (2) n wall shear stress index in Eq. (4) NTr Trouton ratio Pdie entry extrusion pressure across die entry Pdie land extrusion pressure through die land Pextrusion total extrusion pressure Pj joining pressure Pextensional the pressure drop associated with extensional flow at die entry Pshear the pressure drop associated with shear flow at die entry p bulk shear strain rate index in Eq. (6a) A
relationships between process parameters and non-food starch characteristics, e.g. shear and temperature on starch microstructures during extrusion cooking (Senouci & Smith, 1986). Similarly, the rheology and microstructural development during shear of dilute starch suspensions at lower temperatures has been studied extensively (Hermansson & Svegmark, 1996). There is little reported work, however, on extrusion of starch pastes with intermediate water contents below the gelatinisation temperature range, or mixtures of native and pre-processed starches, despite their common use in the food industry. This work is concerned with the extrusion behaviour of a mixture of potato solids, containing native and gelatinised starches, used in the manufacture of snack food products. The key processing stage is ram extrusion at ambient temperatures, such that extrusion cooking does not occur (Cheyne, Wilson, Barnes, & Sala€ un, 2001).. The products are cooked following the extrusion forming step. The use of potato solids means that visco-elastic effects associated with gluten hydration and network development are minimal. This paper describes mechanical (rheological) characterisation and extrusion modelling of a model industrial starch paste.
Qtotal q R V Vplug Vs
total volumetric paste flow rate wall slip velocity index in Eq. (6b) die radius (capillary die) extrudate velocity velocity for pure slip (plug flow) wall slip velocity
Greek symbols a shear rate dependency factor in Eq. (2) b wall shear rate dependency factor in Eq. (4) C apparent shear rate c_ shear rate extensional shear rate c_ e e strain ge apparent extensional viscosity gs apparent shear viscosity h paste flow entry angle in Eq. (11) r0 bulk yield stress at zero flow rate in Eq. (2) ry yield stress s shear stress se extensional shear stress s0 wall yield stress at zero flow rate in Eq. (4) sw , swy wall shear stress, wall yield shear stress sy bulk yield shear stress U die exit effect integral from Eq. (12) w die entry angle (conical dies)
An accompanying paper (Cheyne, Barnes, Gedney, & Wilson, 2004) reports associated studies of microstructure development during extrusion.
2. Modelling pastes undergoing extrusion Pastes, along with concentrated suspensions, are often termed ‘soft solids’ as they exhibit elements of the behaviour of both engineering plastics (apparent yield stresses) and of fluids (strain rate, time and shear history dependencies). These properties render rheological characterisation challenging to industrial and academic users alike. Food pastes present further challenges in that (i) the particulates are frequently deformable, giving rise to a range of (often small) yield stresses; (ii) the solid phase(s) may be partly soluble and/or interact strongly with the liquid phase; and (iii) material properties may vary widely with their botanical and geographical origins and time of harvest. A variety of approaches have been used to describe the rheology of soft solids, depending on the importance of yield and shear rate effects. Stiffer materials can be modelled as engineering plastics (Chakrabarty, 1987),
A. Cheyne et al. / Journal of Food Engineering 66 (2005) 1–12
while strongly shear rate dependent materials are often described using visco-plastic constitutive equations found in fluid mechanics (Steffe, 1996) such as the Herschel–Bulkley model. For intermediate behaviours, it is not always obvious which approach is most suitable for a given material in a particular situation on an a priori basis. This paper compares these two approaches for the moist starch solid dough mixtures under consideration. The Benbow–Bridgwater characterisation method (Benbow & Bridgwater, 1993) employs a plasticity approach to analyse capillary rheometry data: it has been successfully applied to many non-food paste formulations. Previous related work on potato pastes (Briscoe, Corfield, Lawrence, & Adams, 1998; Corfield, Adams, Briscoe, Fryer, & Lawrence, 1999; Halliday & Smith, 1995; Pruvost, Corfield, Kingman, & Lawrence, 1998) has favoured the use of viscous and visco-plastic constitutive equations to describe capillary rheometry data. 2.1. Benbow–Bridgwater characterisation Benbow and Bridgwater developed their characterisation approach to model the extrusion behaviour of dense suspensions of ceramics. It is an approximate analysis for interpreting the results from capillary flow experiments and allows the relative importance of different contributions to the work of extrusion to be quantified, compared, and extended to model other systems. It features some key assumptions whose validity varies with the material under study. Consider the element of paste undergoing extrusion in Fig. 1. The rate of work dissipation, expressed as an extrusion pressure, Pextrusion is described as originating from two components: a die entry term Pdie entry treated as being dominated by extensional deformation of material converging towards the die hole, and Pdie land describing the flow of paste under conditions of pure shear along the die itself. The extensional term is modelled using a simple lower bound result from plasticity theory, viz.
Pdie
entry
¼ ry ln
A0 A
ð1Þ
where ry describes an extensional shear yield property. Benbow and Bridgwater found that ry often exhibited a rate shear dependency and proposed a form: ry ¼ r0 þ aV m
ð2Þ
where r0 is a quasi-static yield stress; a, a velocity factor; V , the mean velocity of the paste in the die land and m, a velocity index. The aV m term represents a characteristic extensional shear rate in the die entry zone. The difficulty in defining a representative extensional shear rate has been discussed by Peck (2002). The accuracy of this lower bound form has been discussed in detail by Horrobin and Nedderman (1998). In the die land, a force balance gives: Pdie
land
¼ sw
CL A
ð3Þ
where sw is the wall shear stress. For solid–liquid pastes, shear flows are often found to be dominated by (apparent) slip at the wall so Benbow and Bridgwater assumed that this mechanism acted alone. Shear rate dependence was often observed, so they proposed a wall function of the form: sw ¼ s0 þ bV n
ð4Þ
where s0 is the shear stress extrapolated to zero velocity; b, a velocity factor and n, a velocity component. In pure slip flow, V is equivalent to the wall slip velocity, Vs , and Eq. (4) then describes a Herschel–Bulkley wall slip model. The total extrusion pressure is therefore given by the sum of Pdie entry and Pdie land , which for the coaxial cylindrical geometry used in capillary rheometry simplifies to: m
Pextrusion ¼ 2ðr0 þ aV Þ ln UN-EXTRUDED PASTE wall slip
EXTRUDED PASTE wall slip, mean velocity V
BARREL area A0, diameter D0
DIE ENTRY REGION static zone
DIE LAND length L, area A, diameter D
Fig. 1. Benbow–Bridgwater model of axi-symmetric ram extrusion of paste through capillary dies.
3
D0 D
L þ 4ðs0 þ bV Þ D n
ð5Þ A paste’s rheology may then be characterised in terms of six material parameters (r0 , s0 , a, b, m and n), which can be calculated from a simple set of capillary extrusion experiments. The advantage of this approach is that comparative values can be generated quickly, particularly for quantifying extensional effects. Its disadvantages include the uncertainty associated with those parameters, as the extensional term is rarely exact, and their application to flow geometries differing significantly from coaxial extrusion, e.g. Martin, Wilson, and Bonnett (submitted for publication).
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2.2. Fluid constitutive equations Pshear The use of fluid mechanical models to describe the rheology of materials such as polymer melts or food suspensions is well established (Heydon, Scott, & Tucker, 1996). Generally two sets of parameters are generated, one describing the bulk material rheology and other the behaviour at a solid interface. Previous work on dense starch suspensions has featured the power law and the more general Herschel–Bulkley models: Bulk
s ¼ sy þ k c_ p s > sy c_ ¼ 0 s 6 sy
Interface
sw ¼ swy þ KVsq Vs ¼ 0
sw 6 swy
ð6aÞ ð6bÞ sw > swy
ð7aÞ ð7bÞ
where c_ is the local shear rate, while sy (the bulk yield stress), swy (the interfacial yield stress), consistency factors k and K, and indices p and q are material parameters. As with the Benbow–Bridgwater approach, the model parameters are frequently calculated from a set of capillary flow experiments (Steffe, 1996). Data are first corrected for die entry effects using the Bagley end correction (which equates die entry pressure to an additional length of die land), before fitting to the Rabinowitsch–Mooney result: Z pR3 sw 2 Qtotal ¼ pR2 Vs þ 3 s f ðsÞ ds ð8Þ sw 0 where Qtotal is the total volumetric paste flow rate, and R is the die radius. The first term on the RHS describes slip flow, while the second term represents additional flow due to shear in the bulk. The above description refers to shear flow, but extensional shear is particularly important in forming processes. An analogous relationship between extensional shear stress, se , and extensional shear rate, c_ e , will also exist, for example: se ¼ Ec_ je
ð9Þ
Direct measures of extensional viscosity are particularly challenging in paste systems, as these materials, at high solids contents, exhibit different tensile and compressive behaviours. The advantage of the plasticity approach is that it assumes that extensional flow dominates in the forming region. An estimate of the contribution of extensional and shear flows is made here using the result of Gibson (see Steffe, 1996), which accounts for die entry pressures–– determined by techniques such as that of Bagley––in terms of both shear and extensional components, thus: Pdie
entry
¼ Pextensional þ Pshear
ð10Þ
Analytical solutions for simple power law fluid behaviour in concentric cylindrical dies exist, giving Pshear as
2kðsin3p hÞ ¼ 3ph1þ3p
1 þ 3p 4p
"
p
p
C 1
D D0
3p #
ð11Þ where k and p are those defined in Eq. (6), and are calculated from the Pdie land term: C, the apparent shear rate in the die land, and h is the angle of the paste flow entry to the die land. This angle may differ significantly from the die entry angle because of the existence of static zones in this region. Pextensional , calculated from the residual of Pdie entry , is given by: 2 sin hð1 þ cos hÞ p Pextensional ¼ ðEC Þ 3j 4 " # 3j D U 1 þ j ð12Þ D0 4 where U, the die exit effect integral, is given by: Z h j1 ðsinjþ1 hÞð1 þ cos hÞ dh U¼
ð13Þ
0
In practice, U is determined by numerical solution at various values of j and h. It is useful to compare the extensional and shear viscosities, expressed as the Trouton ratio, NTr which is the ratio of apparent extensional viscosity, ge and apparent shear viscosity, gs , given by: ge ¼ Ec_ j1 e
and
gs ¼ k c_ p1
ð14Þ
For uniaxial flow it is conventional to calculate the p apparent shear viscosity as 3 times the extensional shear viscosity, giving g c_ NTr ¼ pffiffieffi e 3gs c_
ð15Þ
2.3. Paste flow modelling caveats It should be noted that particular problems commonly arise in modelling pastes flows using fluid constitutive equations. Where solid and liquid components interact weakly, liquid phase redistribution (Rough, Bridgwater, & Wilson, 2000) through the solids matrix may invalidate the assumption of uniform material composition. Paste behaviour is then more like that of an undrained soil, or possibly a granular material (Nedderman, 1982). The continuity assumption may also be violated when paste is forced through narrow flow channels. Particle bridging is likely to occur when the duct size falls to 10 particle diameters or less. In such cases, the work done in deforming the paste involves a term describing particle deformation as well as rearrangement. Food pastes with complex formulations often contain solids with a range of particle sizes and deformation properties, so
A. Cheyne et al. / Journal of Food Engineering 66 (2005) 1–12
care must be taken when transferring rheological data to different sizes of equipment.
3. Experimental 3.1. Materials The starch paste used in this work contained three solid components, namely native potato starch and two forms of cooked potato flours. The formulation in Table 1 is typical of industrial pastes (or doughs) of this type. Water was added at 40 wt.% of the wet mix. Native starch (refined starch in the original state of its botanical origin), is a white powder with no taste and is commonly used as a filler. Individual granules are strong, glassy ellipsoids ranging between 10 and 100 lm in dimension. The cooked potato solids (Talburt and Smith, 1980), which are more expensive, give taste and colour to the product, but are also instrumental in determining handling and processing properties of the paste. These materials are generated by cooking, drying and milling fresh potato, so that the starch components have been completely gelatinised. Their properties differ only in the level of cellular rupture induced during the milling stage. Where this is low (potato granule) the gelatinised starch remains confined within the potato cell walls: this powder consists predominantly of individual potato cells. Where cell rupture is high (potato flake), the gelatinised starch is released and binds cells and cell fragments together: this powder consists of both small cell fragments and large agglomerates of cells and extra-cellular gelatinised starch. These microstructural differences are manifested in the mechanical behaviour of the materials. Hydrated flake and granule were readily deformed, so that particle size effects are not expected to be important. Characterisation of native starch particle micro-mechanical behaviour was performed at the University of Birmingham using the micro-manipulation technique developed by Zhang, Ferenczi, Lush, and Thomas (1991). Individual particles were compressed between parallel platens and the strain-deformation behaviour observed and recorded. Hydrated starch particles exhibited an initial elastic response followed by rupture at a linear strain of Table 1 Formulation of the paste used in this work Ingredient
Mass fraction (wt.%)
Modal particle size range (lm)
Native potato starch Potato granule Potato flake Salt Reverse osmosis water
28.3 23.9 6.6 1.2 40
40–57 75–150 250–425 – –
5
7–10% and bursting pressures (calculated as rupture force/cross-sectional area) of 0.1 MPa. Dry native starch particles behaved as elastic solids, with an elastic modulus over 100· that of the hydrated form. The level of extra-cellular gelatinised starch is therefore crucial to determining paste handling properties (e.g. cohesivity or compaction behaviour) and the texture, appearance and stability of green extrudates (i.e. the response of the paste to processing). 3.2. Paste mixing Mixing was performed in a Kenwood planetary mixer (Kenwood Ltd., Havant, UK) fitted with a ‘K’-beater, at the lowest set speed (approximately 40 rpm). The dry powders were mixed (under cover to avoid elutriation of fines) for 4 min so that segregation due to particle size did not affect paste properties. Reverse osmosis water was then added at 40 wt.% before mixing at the same speed for 4 min. The wet mixing time was determined in separate experiments by mixing for specific intervals and then measuring the moisture content of many (>10) samples taken from different locations throughout the paste mass. The coefficient of variation did not change appreciably after 4 min. The mixed paste had the appearance of a weakly cohesive damp powder. It should be noted that while water was evenly distributed at the macro-scale, at the micro-scale of individual particles there was a highly uneven distribution of water. This was due to uneven competitive absorption of water between the three powders, an effect which is highly significant for the extrudate microstructure and is reported in the parallel paper (Cheyne et al., 2004). 3.3. Extrusion Ram extrusion experiments were performed using a SA100 Loading Frame Twin Screw Machine manufactured by Dartec Ltd. of Stourbridge, England. The strain frame was operated in constant strain rate mode, the applied load being measured by a load cell on the cross-member, accurate to ±4 N. Piston velocity could be varied from 0.01 to 10 mm s1 , with an accuracy of 0.1% at the lowest velocity rising to 1% at the highest. The maximum ram displacement used for an experiment was limited to 100 mm by software. Time, extrusion force and ram displacement data were logged at a frequency of approximately 1000 Hz. Paste was loaded into a 25 mm diameter stainless steel barrel to a pre-determined height, compacted, then extruded using a stainless steel ram with a phosphor bronze seal at its head. A range of axi-symmetric, square entry capillary dies of varying length and diameter were used, the dies being made from stainless steel where possible, or of phosphor bronze where small diameters
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Table 2 Dies used in experiments to generate and test paste flow model parameters, and associated apparent shear rates, C Type
D (mm)
L=D
C (s1 )
Capillary
3 2 1.5 1
2, 4, 8, 12, 16 ’’ ’’ ’’
1.85–1850 6.25–6250 1.48–14,800 50–50,000
Orifice Conical Annular
1, 2, 3, 4.5, 6, 9 1, 2, 3, 4.5, 6, 9 o.d. 14, i.d. 12
– – L ¼ 30, 50, 80 mm
– – –
were required. Tests performed with different materials at the same die diameter did not indicate any significant effect of die wall material. The die specifications and equivalent Newtonian shear rates (apparent shear rate, C) associated with these experimental conditions are shown in Table 2. All experiments were performed under ambient conditions. As the paste properties changed noticeably on storage, each batch was discarded after 6 h. Frictional forces between the paste billet and the barrel walls were found to be negligible in separate uniaxial compaction tests (Cheyne, 2001).
4. Results and discussion
4.2. Benbow–Bridgwater characterisation Table 3 shows the parameters obtained from data obtained from 3 mm diameter dies, termed the standard parameters, over an apparent shear rate range of 1.85– 1850 s1 , along with a set for a model ceramic paste. The starch paste values were calculated from data sets from a series of five repeated tests. Comparison of the two parameter sets indicated that the potato paste is more strongly shear dependent than the ceramic, with a zero value of yield shear stress for slip at the wall. The two indices for the starch paste are similar and indicate that the material is strongly shear-thinning. A sensitivity analysis, based on the uncertainty in data discussed above, was performed on the paste results to estimate the uncertainty in the model parameters. Combinations of the lowest and highest values of parameters were then used to make new extrusion pressure predictions. These new predictions varied from the original by between 0.5% and 11% (standard deviation of all variations, 5.1%) depending on piston velocity and die land L=D ratio. This gives an indication of the error expected in model predictions. Fig. 2 shows a comparison of measured and predicted pressure data for the potato paste. The agreement between model and experimental data is excellent, being consistently close to the average measured value, with mean deviation 2.5%, which is comparable with the standard error in the experimental data and less than the expected model error from the above sensitivity analysis.
4.1. Data processing A common difficulty in characterising paste materials is variability in experimental data. It is not uncommon to observe pressure variations of 10% within a single experiment. This feature is usually due to inhomogeneities in the paste, such as air pockets or large agglomerates, or phase migration. It is also frequently observed that repeated, nominally identical experiments show noticeable variability due to other effects such as paste ageing, uneven paste packing, temperature sensitivity and drying. The consequence of these factors is that the variation in experimental data is large due to material variations in an otherwise well specified system. Starch pastes showed strong ageing affects, attributed to moisture redistribution. However, in other respects the material studied here gave very reproducible results compared to many ceramics studied in this laboratory. Experimental pressure profiles yielded a region of roughly constant extrusion pressure (i.e. featuring no effects of friction in the barrel) with a deviation of no more than 3% of the mean value. These mean values featured an average standard error of 2.3% from the mean values calculated from five repeated experiments. This compares with typical deviations of over 10% for ceramic pastes (Amarasinghe & Wilson, 1999).
4.3. Effect of die diameter The range of shear rates and die dimensions used in industry can feature processing conditions that pose challenges to continuum-based rheological models. For starchy food pastes, a flow channel of characteristic dimension 1 mm may represent less than 10 starch particle diameters. Particle bridging or arching might then be expected to occur, causing significant increases in deformation stresses. Interaction of individual partiTable 3 Benbow–Bridgwater characterisation parameters obtained for the potato paste and a typical ceramic Parameter
Potato paste ‘Standard’a
Ceramic pasteb
r0 (MPa) a (MPa sm mm ) m s0 (MPa) b (MPa sn mn ) n
0.11 1.3 0.33 0.00 0.30 0.36
0.30 0.04 0.51 0.07 0.27 0.72
a
Generated using 3 mm diameter dies. a-alumina (solids volume fraction 0.62) with aqueous liquid phase (Source: Cheyne, 2001). b
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7
4
25
3.5
L/D = 16 20
3 PExtrusion (MPa)
Pextrusion (MPa)
L/D = 12 15 L/D = 8 10
L/D = 4 L/D = 2
2.5 2 1.5 1
5 0.5 0
0 0
2
4
6 8 Ram Velocity (mms-1)
10
12
0
2
4
6
8
10
D (mm)
Fig. 2. Comparison of experimental data (points) and characterisation model (Eq. (5), lines) using standard parameters in Table 3 for axisymmetric capillary dies (D ¼ 3 mm).
cles is not considered in Eq. (5), which treats the material as a homogeneous continuum. In order to investigate the importance particle-process length scale effects, the paste was characterised using dies with D ¼ 1, 1.5 and 2 mm and the same L=D ratios as before. The results, summarised in Table 4, show distinct differences between the parameter sets. This variation, particularly in r, a and b, makes it clear that these parameters were not simply functions of material composition. As particle interaction effects were likely to manifest themselves most strongly in the die land, the validity of the parameters was tested using a set of orifice dies, with D0 ¼ 25 mm and D ranging from 1 to 9 mm. Fig. 3 shows average values of extrusion pressure for a piston velocity of 0.01 mm s1 without any precompaction, together with two sets of predictions using Eq. (5). The error bars represent the range of variation in experimental data. It can be seen that the predictions using the standard parameters fitted the data well except at the smallest and largest diameters (D ¼ 1 and 9 mm, respectively). In most cases the deviation from the average experimental value was within both the experimental variation and the 5.1% uncertainty in model predictions.
Fig. 3. Comparison of experimental extrusion pressures through axisymmetric orifice dies with predictions from Eq. (5): (points) experimental data; (black line) standard parameters; (grey line) 1 mm diameter parameters. The dashed line represents the joining pressure, (Pj ¼ 0:59 MPa), at which paste de-aeration is complete.
The deviation at the smallest die diameter could have been due to two effects: (i) that the paste exhibited internal shearing at the high apparent shear rates generated in smaller diameter dies, invalidating the assumption of simple plug flow, or (ii) that there was extensive particle interaction in the die land (i.e. the continuum assumption was no longer valid), as is found for granular materials and some highly packed suspensions. This would not be unexpected given the relatively large size of particles in the potato granule and flake. The deviation at larger D values when using the standard parameters is attributed to compaction in these previously uncompacted samples. Uniaxial compaction tests on paste samples using a blank die indicated that the paste with 40 wt.% water content exhibited a joining pressure, Pj , of 0.59 MPa (Cheyne et al., 2001). This level of stress was required to compact the paste into a cohesive mass before extrusion could take place, and thereby represents a threshold for extrusion of coherent product. Parallel studies (Cheyne, 2001) indicated that Pj was sensitive to water content: at 30 wt.% water, Pj was 0.61 MPa and compaction tests indicated frictional solid behaviour, characterised by a friction coefficient of 0.32.
Table 4 Benbow–Bridgwater parameters obtained for the potato paste for different die land diameters D (mm)
1
1.5
2
3 ‘Standard’
r0 (MPa) a (MPa sm mm ) m s0 (MPa) b (MPa sn mn ) n
0.18 1.1 0.35 0.00 0.37 0.24
0.06 0.77 0.38 0.00 0.33 0.32
0.08 0.90 0.34 0.00 0.26 0.28
0.11 1.3 0.33 0.00 0.30 0.36
A. Cheyne et al. / Journal of Food Engineering 66 (2005) 1–12
Fig. 3 shows that the parameters obtained from the 1 mm die tests consistently over-predicted the extrusion pressure for these orifice dies. Similar results were obtained with the 1.5 and 2 mm die parameter sets, albeit to a lesser extent as D increased. The failure to predict the 1 mm orifice die result, even though this size was employed in the characterisation, indicates that Eq. (5) does not describe the mechanics of the material deformation adequately at small D values, where particleprocess effects are expected to be significant. These result indicates that the parameters obtained for D < 3 mm were biased by factors not accounted for by the model and were therefore not true material constants. 4.4. Capillary flow analysis
12 Vs Vplug, 1 mm 10
Vplug, 3 mm Vplug, 1.5 mm Vplug, 2 mm
8 Velocity (ms-1)
8
6
4
2
0 0
A capillary flow analysis was performed in order to determine whether a fluid mechanical approach would be more appropriate, particularly in elucidating the die land flow behaviour. Bagley plots were used to estimate Pdie entry , and the corrected data were then used to construct a Mooney plot to determine the variation of Vs with sw . Excellent straight-line plots of C versus 1=R were obtained, but featured negative intercepts on the ordinate axis. This unphysical result suggests that Vs was greater than the average velocity, i.e. that paste underwent negative shear in the bulk. This problem has been reported previously by other workers, who have proposed various corrections and explanations. The most convincing explanations concern particle size effects (Cohen & Metzner, 1985) or sensitivity of the analysis to measurement errors (Corfield et al., 1999). The Pdie entry values were also compared with the die entry term estimated by Eq. (2): these gave good agreement for D ¼ 3 mm, and differed noticeably as D decreased. Fig. 4 shows the estimated paste slip velocity, Vs , as a function of wall shear stress. These data suggest a power law or Herschel–Bulkley relationship and the associated parameters are given in Table 5(a). Also shown in Fig. 4 are the velocities calculated for plug flow of the paste in the die land, Vplug , for D ¼ 1, 1.5, 2 and 3 mm, assuming an incompressible material. It can be seen that for the 3 mm diameter dies, Vplug was approximately equal to Vs (within the range of error), indicating that the slip assumption was valid. For smaller diameter dies, the average paste velocities were larger than the estimated slip velocity, indicating that the paste was being sheared in the bulk as well as exhibiting wall slip. The excess velocity (Vplug Vs ) was used to calculate bulk rheology parameters for a power law material and the values are given in Table 5(b). The parameters obtained for D < 3 mm show considerable variation, particularly in K (35%). This suggests that the flow pattern was not consistent between these three die sets, or that the power law model was not appropriate. This inconsistency is not surprising given the problems with the
0.1
0.2 τw (MPa)
0.3
0.4
Fig. 4. Wall slip velocity, Vs , as a function of wall shear stress. Also shown are the mean (i.e. plug flow) velocities, Vplug , calculated by continuity, for the paste with 1, 1.5, 2 and 3 mm diameter dies.
Mooney analysis described above. Table 5 also shows power law model parameters reported in the literature for several simple potato granule pastes. It is noteworthy that the parameters in the table lie mostly within an order of magnitude, despite marked differences in material composition and water contents. Halliday and Smith (1995) used simple power law (Navier) relationships to model both wall slip and bulk shear behaviour, whereas Corfield et al. (1999) and Pruvost et al. (1998) both used Herschel–Bulkley relationships. Uncertainty over the most suitable model is shown by the former’s consideration of a Herschel– Bulkley relationship for wall slip (interestingly with swy values of 50–100 kPa, cf. Table 5), and the comment by the latter two groups that the existence of a yield stress was uncertain. Pruvost et al. found that potato granules could completely absorb up to 53 wt.% water (cf. 40 wt.%, maximum, in this work): above this value water remained in interstices and increased the degree of slip exhibited by the paste. Below this limiting water content they found a Herschel–Bulkley relationship to be most appropriate for paste flow, and above it, a Navier condition. The models in Table 5 are compared in Fig. 5 and indicate that the Corfield et al. and Pruvost et al. material models predict lower slip velocities and more bulk deformation than expected for the paste material studied here. The Halliday and Smith predictions lie in between, most likely because the water content of their material was closer to that of the current paste. It can also be seen that the effect of choosing a Herschel– Bulkley type wall slip relationship for the current paste did not significantly affect the trends, except at very low slip velocities.
A. Cheyne et al. / Journal of Food Engineering 66 (2005) 1–12
9
Table 5 (a) Wall slip and (b) bulk shear parameters for the potato paste obtained using capillary flow analysis Material
Potato paste
(a) Bulk sy , kPa k, kPa sp p Wall swy , kPa K, kPa sq mq q
(b) K, kPa sp p
– 120 0.3
Potato granule, 40 wt.% (Halliday & Smith, 1995)
Potato granule, 48 wt.% (Pruvost et al., 1998)
Potato granule, 50 wt.% (Corfield et al., 1999)
– 230 0.14
30 18 0.30
11 8.2 0.36 50 110 0.38
– 42 0.31
50 17 0.42
– 80 0.41
40 170 0.33
D ¼ 1 mm
D ¼ 1:5 mm
D ¼ 2 mm
Average
93 0.30
120 0.32
150 0.28
120 0.30
Also shown are parameters for similar materials reported in the literature.
Table 6 shows the parameters for a power law extensional flow constitutive model obtained using the Gibson analysis using the bulk shear parameters given in Table 5. The associated Trouton ratios suggest that the extensional and shear contributions to the die entry work were comparable. The actual paste flow entry angle is difficult to determine because of the presence of static zones; however a value between 60 and 90 would be reasonable and consistent with the shape of plugs recovered after experiments, although these boundaries were often curved. These results suggest that the starch paste can be described using fluid constitutive models, but the parameters generated are subject to uncertainty owing to the systematic deviations from the models exhibited in the Mooney analysis. These problems indicate that the physics of these complex solid/fluid mixtures are not likely to be adequately described by simple lumped parameter models.
is not reported. Computational fluid mechanics modelling would also be subject to uncertainty in constitutive models and their parameters. 4.5.1. Conical dies The behaviour of the paste in dies with changing cross-section was investigated using a set of conical orifice dies, with die entry angle, w ¼ 45 and exit diameters between 1 and 9 mm, as detailed in Table 2. A typical set of extrusion pressure results (at a low piston velocity of 0.01 mm s1 , as found in small area reduction dies) is shown in Fig. 6. This figure also shows the extrusion pressures predicted by a modified form of Eq. (5), reported by Benbow and Bridgwater (1993): D0 Pextrusion ¼ 2ðr0 þ aV m þ s0 cot wÞ ln D n " 2n # bV cot w D 1 þ ð16Þ n D0
4.5. Modelling of complex dies Commercial product forms often require more complex die geometries than have been considered to this point. Annular dies are of considerable industrial importance, and often feature tapered and annular sections within a compound die. Here, the Benbow– Bridgwater approach is applied to model the flow through conical and then annular dies. This approach makes major assumptions about the flow fields, which allow rapid estimation of the extrusion pressure. Determining the flow field for even a power law fluid through these geometries is not straightforward, particularly as extensional contributions are significant, and
Here, V is the average (plug flow) velocity at the die exit. This analysis includes two approximations, which, though strictly invalid, are found adequate for many applications. These are: (i) transverse sections of paste deform without internal variation due to shear, and (ii) the shear stresses along the cone surface can be equated to axial stresses using the small angle theorem. The accuracy of the predictions was comparable to that for square entry orifice dies: in many cases the difference lay within the bounds of experimental and parameter uncertainty. As with the square entry orifice dies, the prediction was poor for large and small diameters, most likely for similar reasons.
10
A. Cheyne et al. / Journal of Food Engineering 66 (2005) 1–12 1600
2.5 Bulk behaviour
1400 2
1000
Pextrusion (MPa)
τ (kPa)
1200
800 600
1.5
1
400 0.5 200 0
0 0
500
1000
1500
(a)
2000
2500
3000
3500
4000
0
2
Γ (s-1)
4
6
8
10
D (mm)
Fig. 6. Axi-symmetric ram extrusion of paste through conical dies: (points) experimental data; (solid line) prediction from Eq. (16) using standard parameters. The dashed line represents the joining pressure, (Pj ¼ 0:59 MPa).
400 Wall slip behaviour 350
τω (kPa)
300
is proposed, which assumes equal wall shear stresses on the inner and outer surfaces of the annulus die land. The equation used was derived directly from Eq. (5) for a die land with two surfaces: A0 Aw Pextrusion ¼ ðr0 þ aV m Þ ln þ ðs0 þ bV n Þ Af Af
250 200 150 100
ð17Þ
50 0 0
1
2
3
4
5
6
Vs (ms-1)
(b)
Fig. 5. Comparison of flow curves from literature data for potato pastes: (a) bulk parameters, (b) wall slip parameters. Dashed line: Herschel–Bulkely model; solid line: power law model; circled line: Corfield et al. (1999); crossed line: Pruvost et al. (1998); grey line: Halliday and Smith (1995).
4.5.2. Annular dies Modelling of annular flows is often performed by numerical simulation because of the difficulties in determining stresses and flow patterns. An exception is the work of Fredrickson and Bird (1958), who reported analytical solutions for the flow of Bingham plastics and power law fluids in annuli, albeit without wall slip. Here, a new adaptation of the Benbow–Bridgwater approach
where Aw is the total die land wall area and Af is the die cross-sectional area for flow. Extrusion experiments were performed using the three annular dies described in Table 2, which feature an annular gap of 1 mm. Fig. 7 shows the experimental data and predicted extrusion pressure from Eq. (17) using the standard parameters. The experimental data were typically consistent (average variation ±9.4%), however the model gave very poor agreement (average deviation from average experimental values, 35.1%). The relatively low area reduction (7.7 compared to between 70 and 625 for the capillary dies) meant that the work in the die land was expected to be the dominant term: the standard parameters, obtained with D ¼ 3 mm, under-predicted the wall shear term. Although the flow channel was quite narrow, the confinement was effectively onedimensional (i.e. radial, but not azimuthal) in the annular slit as opposed to two-dimensional (radial) in
Table 6 Extensional shear parameters and Trouton ratios evaluated at different paste flow entry angles Paste flow entry angle, h j
E, kPa s Pj NTr
90
72
60
51
45
310 0.25 1.49
340 0.26 1.65
370 0.26 1.78
390 0.27 1.88
190 0.27 0.90
A. Cheyne et al. / Journal of Food Engineering 66 (2005) 1–12 20 18 16
Pextrusion (MPa)
14 12 10 8 6 4 2 0 0
2
4 6 Piston Velocity (mm s-1)
8
10
Fig. 7. Axi-symmetric ram extrusion of paste through annular dies: (points) experimental data, squares: L ¼ 30, diamonds: L ¼ 50 and circles: L ¼ 80 mm; (dashed lines) prediction from Eq. (17); (solid lines) prediction from Eq. (18).
the capillary, so it was expected that particle interaction effects would be reduced, but not eliminated. Reliable wall shear term parameters for smaller D values were not available, for the reasons outlined above. An alternative is to use the slip velocity model generated during the capillary analysis, giving A0 Aw Pextrusion ¼ ðr0 þ aV m Þ ln þ ðKVsp Þ ð18Þ Af Af where Vs (and V ) are assumed to be equal to Vplug , the average extrusion velocity in the annulus. Fig. 7 shows the prediction from this modified model using the parameters in Table 5. The average deviation between model and experimental values fell from 35.1% to 9.85%. In almost all cases (except the shortest die at low velocities) the predictions were still lower than the experimental data, although this could be attributed to shear in the bulk material. The agreement is certainly adequate for design and operability purposes. The importance of particle-process length scale interactions is again evident.
11
and (ii) a fluid constitutive approach, using a power law model for bulk deformation and both power law and Herschel–Bulkley models for wall slip. The Benbow–Bridgwater approach yielded a set of standard parameters, based on 3 mm diameter dies, which have been used with some success for modelling purposes. Flow through small diameter dies yielded inconsistent results, which were attributed to internal shearing of the paste, and significant particle–particle and particle–duct interaction. Under these conditions the material did not move in slip flow and could not be treated as a true continuum, and so the plasticity model was insufficient. The importance of consolidation of the material into a cohesive mass was also evident. A Mooney wall slip analysis gave good linear results, but suffered from an oft-reported non-physicality. Accepting the uncertainty in this analysis, constitutive parameters for power and Herschel–Bulkley models were comparable to those reported in the literature for similar materials, but there was further indication of non-consistent flow patterns for the data set. An estimate of extensional viscosity indicated that this was comparable with shear viscosity. Three likely flow regimes were identified: (i) plug flow at low shear rates in flow channels of size greater than 3 mm, (ii) slip flow of paste plus some internal shearing where shear rates are higher, (iii) flow dominated by particle interactions in flow channels smaller than about 1.5 mm. With due modifications for geometry, Eq. (5) was shown to describe conical die entries adequately. Application of the Benbow–Bridgwater approach to annular dies in an a priori fashion was less successful, owing to the challenge in describing flow in the narrow annular duct. The wall slip model obtained from the more laborious capillary flow analysis gave better agreement, as it featured contributions from small D experiments. The Benbow–Bridgwater approach has thus been shown to give reasonable predictions of extrusion pressure for even annular dies, but it should be noted that the validity of this continuum approach is compromised when particle–process interactions are significant.
5. Conclusions Acknowledgements The potato starch paste studied here exhibited complex flow behaviour. It can be considered as a dense suspension with a very viscous deformable phase, consisting of a hydrated starch gel, and its classification lies on the boundary between frictional solids and viscoplastics. Two methods were applied to quantify its extrusion behaviour: (i) a modified plasticity approach,
Funding for AC from the Biotechnology and Biological Sciences Research Council is gratefully acknowledged, as is support for the project from United Biscuits. Assistance with the micro-manipulation facilities at the University of Birmingham from Dr. Z. Zhang and co-workers is also gratefully acknowledged.
12
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References Aguilera, J. M., & Stanley, D. W. (1990). Microstructural principles of food processing and engineering. Barking, UK: Elsevier Science Publishers Ltd. Amarasinghe, A. D. U. S., & Wilson, D. I. (1999). On-line monitoring of ceramic extrusion. Journal of the American Ceramic Society, 82, 2305–2312. Benbow, J. J., & Bridgwater, J. (1993). Paste flow and extrusion. Oxford, UK: Clarendon Press. Briscoe, B. J., Corfield, G. M, Lawrence, C. J., & Adams, M. J. (1998). ‘Low-order’ optimisation of soft solids processing. Transactions of IChemE: Chemical Engineering Research and Design, 76A, 16– 21. Chakrabarty, J. (1987). The theory of plasticity. New York, USA: McGraw-Hill Company. Cheyne, A. (2001). Extrusion behaviour of starch-based food pastes. Ph.D. Thesis, Department of Chemical Engineering, University of Cambridge, UK. Cheyne, A., Barnes, J., Gedney, S., & Wilson, D. I. (2004). Extrusion behaviour of cohesive potato starch pastes. II. Microstructureprocess interactions, Journal of Food Engineering. doi:10.1016/ j.jfoodeng.2004.02.036. Cheyne, A., Wilson, D. I., Barnes, J., & Sala€ un, Y. (2001). Modelling of starch extrusion and damage in industrial forming processes. In T. L. Barsby, A. M. Donald, & P. J. Frazier (Eds.), Starch structure and functionality (pp. 8–26). Cambridge, UK: Royal Society of Chemistry. Cohen, Y., & Metzner, A. B. (1985). Apparent slip flow of polymer solutions. Journal of Rheology, 29, 67–102. Corfield, G. M., Adams, M. J., Briscoe, B. J., Fryer, P. J., & Lawrence, C. J. (1999). A critical examination of capillary rheometry for foods (exhibiting wall slip). Transactions of IChemE: Food and Bioproducts Processing, 77, 3–10. FAO (1999). Production Yearbook Volume 1998, FAO Statistics Series No. 148 (Vol. 53). Food and Agriculture Organisation of the United Nations, Rome, Italy. Fredrickson, A. G., & Bird, R. B. (1958). Non-Newtonian flow in annuli. Industrial Engineering Chemical Research, 50, 347–352. Halliday, P. J., & Smith, A. C. (1995). Estimation of the wall slip velocity in the capillary flow of potato granule pastes. Journal of Rheology, 39, 139–149. Hermansson, A.-M., & Svegmark, K. (1996). Developments in the understanding of starch functionality. Trends in Food Science and Technology, 7, 345–353. Heydon, C. J., Scott, G. M., & Tucker, G. S. (1996). Applications of tube viscometry for the characterisation of flow of gelatinised food starches under UHT conditions. Transactions of IChemE: Food and Bioproducts Processing, 74C, 81–91.
Horrobin, D. M., & Nedderman, R. M. (1998). Die entry pressure drops in paste extrusion. Chemical Engineering Science, 53(18), 3215. Hulleman, S. D. H., Janssen, F. H. P., & Feil, H. (1998). The role of water during the plasticization of native starches. Polymer, 39, 2043–2048. Martin, P. J., Wilson, D. I., & Bonnett, P. E. (submitted for publication). Extrusion of pastes through non-axisymmetric geometries. Transactions of IChemE: Chemical Engineering Research and Design. Matz, S. A. (1991). The chemistry and technology of cereals as food and feed. New York, USA: Van Nostrand Reinhold. Meuser, F., Manners, D. J., & Seibel, W. (1995). Progress in plant polymeric carbohydrate research. Berlin, Germany: Simon Druck. Mitchell, J. R., Hill, S. E., Paterson, L., Valles, B., Barclay, F., & Blanshard, J. M. (1997). The role of molecular weight in the conversion of starch. In P. J. Frazier, A. M. Donald, & P. Richmond (Eds.), Starch structure and functionality. Cambridge: Royal Society of Chemistry. Nedderman, R. M. (1982). The theoretical prediction of stress distributions in hoppers. Transactions of IChemE: Chemical Engineering Research and Design, 60A, 259–275. Noel, T. R., Ring, S. G., & Whittam, M. A. (1990). Physical properties of starch products: structure and function. Norwich, UK: AFRC Institute of Food Research. Peck, M. C. (2002). Roller extrusion Pastes. Ph.D. Thesis, Department of Chemical Engineering, University of Cambridge, UK. Pruvost, K., Corfield, G. M., Kingman, S., & Lawrence, C. J. (1998). Effect of moisture content on the bulk and wall constitutive behaviour of starch pastes. Transactions of IChemE: Food and Bioproducts Processing, 76C, 188–192. Rough, S. L., Bridgwater, J., & Wilson, D. I. (2000). Effects of liquid phase migration on extrusion of microcrystalline cellulose pastes. International Journal of Pharmaceutics, 204, 117–126. Senouci, A., & Smith, A. C. (1986). The extrusion cooking of potato starch material. Starch/St€arke, 38, 78–82. Steffe, J. F. (1996). Rheological methods in food process engineering. East Lancing, USA: Freeman Press. Svegmark, K., & Hermansson, A.-M. (1991). Distribution of amylose and amylopectin in potato starch pastes: Effects of heating and shearing. Food Structure, 10, 117–129. Talburt, W. F., & Smith, O. (1980). Potato processing. New York, USA: Van Nostrand Reinhold Company. van Soest, J. J. G. (1996). Starch plastics: Structure––property relationships. Netherlands: Universiteit Utrecht. Zhang, Z., Ferenczi, M. A., Lush, A. C., & Thomas, C. R. (1991). A novel micromanipulation technique for measuring the bursting strength of single mammalian cells. Applied Microbiology and Applied Biotechnology, 36, 208–210.
Extrusion behaviour of cohesive potato starch pastes: I. Rheological characterisation A. Cheyne a, J. Barnes b, D.I. Wilson a
a,*
Department of Chemical Engineering, University of Cambridge, Pembroke Street, Cambridge CB2 3RA, UK b United Biscuits Research and Development, Lane End Road, High Wycombe, UK Received 12 September 2003; accepted 21 February 2004
Abstract The extrusion behaviour of a cohesive mixture of hydrated potato starch solids was characterised using capillary rheometry. Data were collected from isothermal ram extrusion tests and were modelled using (i) the modified plasticity approach described by Benbow and Bridgwater, and (ii) standard fluid mechanics approaches for power law and Herschel–Bulkley fluids. Neither approach proved to be entirely satisfactory, with particle size effects strongly manifested in the Benbow–Bridgwater parameters, and problems with the Mooney analysis for describing the materials as a fluid. Shear-thinning behaviour, as reported elsewhere other starch doughs/mixtures, was evident, while both wall slip and extensional shear contributions were important. The utility of the Benbow– Bridgwater approach was demonstrated by its application to modelling of annular dies, where it provided reasonably accurate predictions once particle size effects were accounted for. 2004 Elsevier Ltd. All rights reserved. Keywords: Starch; Potato; Extrusion; Rheology; Annulus; Plastic
1. Introduction Extrusion is widely used in the food industry to generate solid or semi-solid products with particular product shapes and textures. Indeed, certain shapes and microstructures are only achievable via extrusion routes. The effect of shear, temperature, and local temperature changes induced by shear during extrusion, are frequently critical parameters in modifying the microstructure of the food materials being processed (Matz, 1991). Understanding the interactions between ingredients, process parameters and equipment design and operation is therefore essential in order to achieve product quality targets and develop new products. Key mechanical parameters required for equipment design and operation principally involve the response of the material to deformation via extensional and simple shear, while key product quality parameters are related to the microstructure of the final form. Linking these two groups of data is not straightforward, owing to difficulties in quantifying the rheology and in measuring appropriate *
Corresponding author. Tel.: +44-1223-334-791; fax: +44-1223-331796. E-mail address: [email protected] (D.I. Wilson). 0260-8774/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2004.02.028
microstructural features. These links have been studied for many applications (Aguilera & Stanley, 1990; Noel, Ring, & Whittam, 1990); however the physical and chemical complexity of many biomaterials, such as the starches used in foods, means that such relationships can rarely be predicted in advance (Meuser, Manners, & Seibel, 1995). Today, starchy foods comprise 58% of total world food production and represent the major source of carbohydrate in the human diet (estimated to comprise 80% of the global average calorie intake (FAO, 1999)). Starch must be processed to promote conversion (i.e. structural disordering) before it has nutritive value. Conversion processes such as gelatinisation, involving the application of heat, moisture and possibly mechanical disruption, feature microstructural changes over length scales between 109 and 104 m. The microstructural changes occurring during conversion vary with the processing route, and have been studied extensively for certain applications (Hulleman, Janssen, & Feil, 1998; Mitchell et al., 1997; Senouci & Smith, 1986; Svegmark & Hermansson, 1991; van Soest, 1996). Extrusion of starch–water pastes enables products to be formed with controlled conversion at a large scale. There is a significant body of work in the literature on
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A. Cheyne et al. / Journal of Food Engineering 66 (2005) 1–12
Nomenclature die land flow cross-sectional area (capillary die) Af die land flow cross-sectional area (annular die) A0 barrel flow cross-sectional area Aw total die wall area (annular die) C circumference of die cross-section D die land diameter D0 barrel diameter E extensional shear consistency factor in Eq. (9) k bulk shear consistency factor in Eq. (6a) K wall slip consistency factor in Eq. (7a) L die land length j extensional shear index in Eq. (9) m bulk yield stress index in Eq. (2) n wall shear stress index in Eq. (4) NTr Trouton ratio Pdie entry extrusion pressure across die entry Pdie land extrusion pressure through die land Pextrusion total extrusion pressure Pj joining pressure Pextensional the pressure drop associated with extensional flow at die entry Pshear the pressure drop associated with shear flow at die entry p bulk shear strain rate index in Eq. (6a) A
relationships between process parameters and non-food starch characteristics, e.g. shear and temperature on starch microstructures during extrusion cooking (Senouci & Smith, 1986). Similarly, the rheology and microstructural development during shear of dilute starch suspensions at lower temperatures has been studied extensively (Hermansson & Svegmark, 1996). There is little reported work, however, on extrusion of starch pastes with intermediate water contents below the gelatinisation temperature range, or mixtures of native and pre-processed starches, despite their common use in the food industry. This work is concerned with the extrusion behaviour of a mixture of potato solids, containing native and gelatinised starches, used in the manufacture of snack food products. The key processing stage is ram extrusion at ambient temperatures, such that extrusion cooking does not occur (Cheyne, Wilson, Barnes, & Sala€ un, 2001).. The products are cooked following the extrusion forming step. The use of potato solids means that visco-elastic effects associated with gluten hydration and network development are minimal. This paper describes mechanical (rheological) characterisation and extrusion modelling of a model industrial starch paste.
Qtotal q R V Vplug Vs
total volumetric paste flow rate wall slip velocity index in Eq. (6b) die radius (capillary die) extrudate velocity velocity for pure slip (plug flow) wall slip velocity
Greek symbols a shear rate dependency factor in Eq. (2) b wall shear rate dependency factor in Eq. (4) C apparent shear rate c_ shear rate extensional shear rate c_ e e strain ge apparent extensional viscosity gs apparent shear viscosity h paste flow entry angle in Eq. (11) r0 bulk yield stress at zero flow rate in Eq. (2) ry yield stress s shear stress se extensional shear stress s0 wall yield stress at zero flow rate in Eq. (4) sw , swy wall shear stress, wall yield shear stress sy bulk yield shear stress U die exit effect integral from Eq. (12) w die entry angle (conical dies)
An accompanying paper (Cheyne, Barnes, Gedney, & Wilson, 2004) reports associated studies of microstructure development during extrusion.
2. Modelling pastes undergoing extrusion Pastes, along with concentrated suspensions, are often termed ‘soft solids’ as they exhibit elements of the behaviour of both engineering plastics (apparent yield stresses) and of fluids (strain rate, time and shear history dependencies). These properties render rheological characterisation challenging to industrial and academic users alike. Food pastes present further challenges in that (i) the particulates are frequently deformable, giving rise to a range of (often small) yield stresses; (ii) the solid phase(s) may be partly soluble and/or interact strongly with the liquid phase; and (iii) material properties may vary widely with their botanical and geographical origins and time of harvest. A variety of approaches have been used to describe the rheology of soft solids, depending on the importance of yield and shear rate effects. Stiffer materials can be modelled as engineering plastics (Chakrabarty, 1987),
A. Cheyne et al. / Journal of Food Engineering 66 (2005) 1–12
while strongly shear rate dependent materials are often described using visco-plastic constitutive equations found in fluid mechanics (Steffe, 1996) such as the Herschel–Bulkley model. For intermediate behaviours, it is not always obvious which approach is most suitable for a given material in a particular situation on an a priori basis. This paper compares these two approaches for the moist starch solid dough mixtures under consideration. The Benbow–Bridgwater characterisation method (Benbow & Bridgwater, 1993) employs a plasticity approach to analyse capillary rheometry data: it has been successfully applied to many non-food paste formulations. Previous related work on potato pastes (Briscoe, Corfield, Lawrence, & Adams, 1998; Corfield, Adams, Briscoe, Fryer, & Lawrence, 1999; Halliday & Smith, 1995; Pruvost, Corfield, Kingman, & Lawrence, 1998) has favoured the use of viscous and visco-plastic constitutive equations to describe capillary rheometry data. 2.1. Benbow–Bridgwater characterisation Benbow and Bridgwater developed their characterisation approach to model the extrusion behaviour of dense suspensions of ceramics. It is an approximate analysis for interpreting the results from capillary flow experiments and allows the relative importance of different contributions to the work of extrusion to be quantified, compared, and extended to model other systems. It features some key assumptions whose validity varies with the material under study. Consider the element of paste undergoing extrusion in Fig. 1. The rate of work dissipation, expressed as an extrusion pressure, Pextrusion is described as originating from two components: a die entry term Pdie entry treated as being dominated by extensional deformation of material converging towards the die hole, and Pdie land describing the flow of paste under conditions of pure shear along the die itself. The extensional term is modelled using a simple lower bound result from plasticity theory, viz.
Pdie
entry
¼ ry ln
A0 A
ð1Þ
where ry describes an extensional shear yield property. Benbow and Bridgwater found that ry often exhibited a rate shear dependency and proposed a form: ry ¼ r0 þ aV m
ð2Þ
where r0 is a quasi-static yield stress; a, a velocity factor; V , the mean velocity of the paste in the die land and m, a velocity index. The aV m term represents a characteristic extensional shear rate in the die entry zone. The difficulty in defining a representative extensional shear rate has been discussed by Peck (2002). The accuracy of this lower bound form has been discussed in detail by Horrobin and Nedderman (1998). In the die land, a force balance gives: Pdie
land
¼ sw
CL A
ð3Þ
where sw is the wall shear stress. For solid–liquid pastes, shear flows are often found to be dominated by (apparent) slip at the wall so Benbow and Bridgwater assumed that this mechanism acted alone. Shear rate dependence was often observed, so they proposed a wall function of the form: sw ¼ s0 þ bV n
ð4Þ
where s0 is the shear stress extrapolated to zero velocity; b, a velocity factor and n, a velocity component. In pure slip flow, V is equivalent to the wall slip velocity, Vs , and Eq. (4) then describes a Herschel–Bulkley wall slip model. The total extrusion pressure is therefore given by the sum of Pdie entry and Pdie land , which for the coaxial cylindrical geometry used in capillary rheometry simplifies to: m
Pextrusion ¼ 2ðr0 þ aV Þ ln UN-EXTRUDED PASTE wall slip
EXTRUDED PASTE wall slip, mean velocity V
BARREL area A0, diameter D0
DIE ENTRY REGION static zone
DIE LAND length L, area A, diameter D
Fig. 1. Benbow–Bridgwater model of axi-symmetric ram extrusion of paste through capillary dies.
3
D0 D
L þ 4ðs0 þ bV Þ D n
ð5Þ A paste’s rheology may then be characterised in terms of six material parameters (r0 , s0 , a, b, m and n), which can be calculated from a simple set of capillary extrusion experiments. The advantage of this approach is that comparative values can be generated quickly, particularly for quantifying extensional effects. Its disadvantages include the uncertainty associated with those parameters, as the extensional term is rarely exact, and their application to flow geometries differing significantly from coaxial extrusion, e.g. Martin, Wilson, and Bonnett (submitted for publication).
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2.2. Fluid constitutive equations Pshear The use of fluid mechanical models to describe the rheology of materials such as polymer melts or food suspensions is well established (Heydon, Scott, & Tucker, 1996). Generally two sets of parameters are generated, one describing the bulk material rheology and other the behaviour at a solid interface. Previous work on dense starch suspensions has featured the power law and the more general Herschel–Bulkley models: Bulk
s ¼ sy þ k c_ p s > sy c_ ¼ 0 s 6 sy
Interface
sw ¼ swy þ KVsq Vs ¼ 0
sw 6 swy
ð6aÞ ð6bÞ sw > swy
ð7aÞ ð7bÞ
where c_ is the local shear rate, while sy (the bulk yield stress), swy (the interfacial yield stress), consistency factors k and K, and indices p and q are material parameters. As with the Benbow–Bridgwater approach, the model parameters are frequently calculated from a set of capillary flow experiments (Steffe, 1996). Data are first corrected for die entry effects using the Bagley end correction (which equates die entry pressure to an additional length of die land), before fitting to the Rabinowitsch–Mooney result: Z pR3 sw 2 Qtotal ¼ pR2 Vs þ 3 s f ðsÞ ds ð8Þ sw 0 where Qtotal is the total volumetric paste flow rate, and R is the die radius. The first term on the RHS describes slip flow, while the second term represents additional flow due to shear in the bulk. The above description refers to shear flow, but extensional shear is particularly important in forming processes. An analogous relationship between extensional shear stress, se , and extensional shear rate, c_ e , will also exist, for example: se ¼ Ec_ je
ð9Þ
Direct measures of extensional viscosity are particularly challenging in paste systems, as these materials, at high solids contents, exhibit different tensile and compressive behaviours. The advantage of the plasticity approach is that it assumes that extensional flow dominates in the forming region. An estimate of the contribution of extensional and shear flows is made here using the result of Gibson (see Steffe, 1996), which accounts for die entry pressures–– determined by techniques such as that of Bagley––in terms of both shear and extensional components, thus: Pdie
entry
¼ Pextensional þ Pshear
ð10Þ
Analytical solutions for simple power law fluid behaviour in concentric cylindrical dies exist, giving Pshear as
2kðsin3p hÞ ¼ 3ph1þ3p
1 þ 3p 4p
"
p
p
C 1
D D0
3p #
ð11Þ where k and p are those defined in Eq. (6), and are calculated from the Pdie land term: C, the apparent shear rate in the die land, and h is the angle of the paste flow entry to the die land. This angle may differ significantly from the die entry angle because of the existence of static zones in this region. Pextensional , calculated from the residual of Pdie entry , is given by: 2 sin hð1 þ cos hÞ p Pextensional ¼ ðEC Þ 3j 4 " # 3j D U 1 þ j ð12Þ D0 4 where U, the die exit effect integral, is given by: Z h j1 ðsinjþ1 hÞð1 þ cos hÞ dh U¼
ð13Þ
0
In practice, U is determined by numerical solution at various values of j and h. It is useful to compare the extensional and shear viscosities, expressed as the Trouton ratio, NTr which is the ratio of apparent extensional viscosity, ge and apparent shear viscosity, gs , given by: ge ¼ Ec_ j1 e
and
gs ¼ k c_ p1
ð14Þ
For uniaxial flow it is conventional to calculate the p apparent shear viscosity as 3 times the extensional shear viscosity, giving g c_ NTr ¼ pffiffieffi e 3gs c_
ð15Þ
2.3. Paste flow modelling caveats It should be noted that particular problems commonly arise in modelling pastes flows using fluid constitutive equations. Where solid and liquid components interact weakly, liquid phase redistribution (Rough, Bridgwater, & Wilson, 2000) through the solids matrix may invalidate the assumption of uniform material composition. Paste behaviour is then more like that of an undrained soil, or possibly a granular material (Nedderman, 1982). The continuity assumption may also be violated when paste is forced through narrow flow channels. Particle bridging is likely to occur when the duct size falls to 10 particle diameters or less. In such cases, the work done in deforming the paste involves a term describing particle deformation as well as rearrangement. Food pastes with complex formulations often contain solids with a range of particle sizes and deformation properties, so
A. Cheyne et al. / Journal of Food Engineering 66 (2005) 1–12
care must be taken when transferring rheological data to different sizes of equipment.
3. Experimental 3.1. Materials The starch paste used in this work contained three solid components, namely native potato starch and two forms of cooked potato flours. The formulation in Table 1 is typical of industrial pastes (or doughs) of this type. Water was added at 40 wt.% of the wet mix. Native starch (refined starch in the original state of its botanical origin), is a white powder with no taste and is commonly used as a filler. Individual granules are strong, glassy ellipsoids ranging between 10 and 100 lm in dimension. The cooked potato solids (Talburt and Smith, 1980), which are more expensive, give taste and colour to the product, but are also instrumental in determining handling and processing properties of the paste. These materials are generated by cooking, drying and milling fresh potato, so that the starch components have been completely gelatinised. Their properties differ only in the level of cellular rupture induced during the milling stage. Where this is low (potato granule) the gelatinised starch remains confined within the potato cell walls: this powder consists predominantly of individual potato cells. Where cell rupture is high (potato flake), the gelatinised starch is released and binds cells and cell fragments together: this powder consists of both small cell fragments and large agglomerates of cells and extra-cellular gelatinised starch. These microstructural differences are manifested in the mechanical behaviour of the materials. Hydrated flake and granule were readily deformed, so that particle size effects are not expected to be important. Characterisation of native starch particle micro-mechanical behaviour was performed at the University of Birmingham using the micro-manipulation technique developed by Zhang, Ferenczi, Lush, and Thomas (1991). Individual particles were compressed between parallel platens and the strain-deformation behaviour observed and recorded. Hydrated starch particles exhibited an initial elastic response followed by rupture at a linear strain of Table 1 Formulation of the paste used in this work Ingredient
Mass fraction (wt.%)
Modal particle size range (lm)
Native potato starch Potato granule Potato flake Salt Reverse osmosis water
28.3 23.9 6.6 1.2 40
40–57 75–150 250–425 – –
5
7–10% and bursting pressures (calculated as rupture force/cross-sectional area) of 0.1 MPa. Dry native starch particles behaved as elastic solids, with an elastic modulus over 100· that of the hydrated form. The level of extra-cellular gelatinised starch is therefore crucial to determining paste handling properties (e.g. cohesivity or compaction behaviour) and the texture, appearance and stability of green extrudates (i.e. the response of the paste to processing). 3.2. Paste mixing Mixing was performed in a Kenwood planetary mixer (Kenwood Ltd., Havant, UK) fitted with a ‘K’-beater, at the lowest set speed (approximately 40 rpm). The dry powders were mixed (under cover to avoid elutriation of fines) for 4 min so that segregation due to particle size did not affect paste properties. Reverse osmosis water was then added at 40 wt.% before mixing at the same speed for 4 min. The wet mixing time was determined in separate experiments by mixing for specific intervals and then measuring the moisture content of many (>10) samples taken from different locations throughout the paste mass. The coefficient of variation did not change appreciably after 4 min. The mixed paste had the appearance of a weakly cohesive damp powder. It should be noted that while water was evenly distributed at the macro-scale, at the micro-scale of individual particles there was a highly uneven distribution of water. This was due to uneven competitive absorption of water between the three powders, an effect which is highly significant for the extrudate microstructure and is reported in the parallel paper (Cheyne et al., 2004). 3.3. Extrusion Ram extrusion experiments were performed using a SA100 Loading Frame Twin Screw Machine manufactured by Dartec Ltd. of Stourbridge, England. The strain frame was operated in constant strain rate mode, the applied load being measured by a load cell on the cross-member, accurate to ±4 N. Piston velocity could be varied from 0.01 to 10 mm s1 , with an accuracy of 0.1% at the lowest velocity rising to 1% at the highest. The maximum ram displacement used for an experiment was limited to 100 mm by software. Time, extrusion force and ram displacement data were logged at a frequency of approximately 1000 Hz. Paste was loaded into a 25 mm diameter stainless steel barrel to a pre-determined height, compacted, then extruded using a stainless steel ram with a phosphor bronze seal at its head. A range of axi-symmetric, square entry capillary dies of varying length and diameter were used, the dies being made from stainless steel where possible, or of phosphor bronze where small diameters
6
A. Cheyne et al. / Journal of Food Engineering 66 (2005) 1–12
Table 2 Dies used in experiments to generate and test paste flow model parameters, and associated apparent shear rates, C Type
D (mm)
L=D
C (s1 )
Capillary
3 2 1.5 1
2, 4, 8, 12, 16 ’’ ’’ ’’
1.85–1850 6.25–6250 1.48–14,800 50–50,000
Orifice Conical Annular
1, 2, 3, 4.5, 6, 9 1, 2, 3, 4.5, 6, 9 o.d. 14, i.d. 12
– – L ¼ 30, 50, 80 mm
– – –
were required. Tests performed with different materials at the same die diameter did not indicate any significant effect of die wall material. The die specifications and equivalent Newtonian shear rates (apparent shear rate, C) associated with these experimental conditions are shown in Table 2. All experiments were performed under ambient conditions. As the paste properties changed noticeably on storage, each batch was discarded after 6 h. Frictional forces between the paste billet and the barrel walls were found to be negligible in separate uniaxial compaction tests (Cheyne, 2001).
4. Results and discussion
4.2. Benbow–Bridgwater characterisation Table 3 shows the parameters obtained from data obtained from 3 mm diameter dies, termed the standard parameters, over an apparent shear rate range of 1.85– 1850 s1 , along with a set for a model ceramic paste. The starch paste values were calculated from data sets from a series of five repeated tests. Comparison of the two parameter sets indicated that the potato paste is more strongly shear dependent than the ceramic, with a zero value of yield shear stress for slip at the wall. The two indices for the starch paste are similar and indicate that the material is strongly shear-thinning. A sensitivity analysis, based on the uncertainty in data discussed above, was performed on the paste results to estimate the uncertainty in the model parameters. Combinations of the lowest and highest values of parameters were then used to make new extrusion pressure predictions. These new predictions varied from the original by between 0.5% and 11% (standard deviation of all variations, 5.1%) depending on piston velocity and die land L=D ratio. This gives an indication of the error expected in model predictions. Fig. 2 shows a comparison of measured and predicted pressure data for the potato paste. The agreement between model and experimental data is excellent, being consistently close to the average measured value, with mean deviation 2.5%, which is comparable with the standard error in the experimental data and less than the expected model error from the above sensitivity analysis.
4.1. Data processing A common difficulty in characterising paste materials is variability in experimental data. It is not uncommon to observe pressure variations of 10% within a single experiment. This feature is usually due to inhomogeneities in the paste, such as air pockets or large agglomerates, or phase migration. It is also frequently observed that repeated, nominally identical experiments show noticeable variability due to other effects such as paste ageing, uneven paste packing, temperature sensitivity and drying. The consequence of these factors is that the variation in experimental data is large due to material variations in an otherwise well specified system. Starch pastes showed strong ageing affects, attributed to moisture redistribution. However, in other respects the material studied here gave very reproducible results compared to many ceramics studied in this laboratory. Experimental pressure profiles yielded a region of roughly constant extrusion pressure (i.e. featuring no effects of friction in the barrel) with a deviation of no more than 3% of the mean value. These mean values featured an average standard error of 2.3% from the mean values calculated from five repeated experiments. This compares with typical deviations of over 10% for ceramic pastes (Amarasinghe & Wilson, 1999).
4.3. Effect of die diameter The range of shear rates and die dimensions used in industry can feature processing conditions that pose challenges to continuum-based rheological models. For starchy food pastes, a flow channel of characteristic dimension 1 mm may represent less than 10 starch particle diameters. Particle bridging or arching might then be expected to occur, causing significant increases in deformation stresses. Interaction of individual partiTable 3 Benbow–Bridgwater characterisation parameters obtained for the potato paste and a typical ceramic Parameter
Potato paste ‘Standard’a
Ceramic pasteb
r0 (MPa) a (MPa sm mm ) m s0 (MPa) b (MPa sn mn ) n
0.11 1.3 0.33 0.00 0.30 0.36
0.30 0.04 0.51 0.07 0.27 0.72
a
Generated using 3 mm diameter dies. a-alumina (solids volume fraction 0.62) with aqueous liquid phase (Source: Cheyne, 2001). b
A. Cheyne et al. / Journal of Food Engineering 66 (2005) 1–12
7
4
25
3.5
L/D = 16 20
3 PExtrusion (MPa)
Pextrusion (MPa)
L/D = 12 15 L/D = 8 10
L/D = 4 L/D = 2
2.5 2 1.5 1
5 0.5 0
0 0
2
4
6 8 Ram Velocity (mms-1)
10
12
0
2
4
6
8
10
D (mm)
Fig. 2. Comparison of experimental data (points) and characterisation model (Eq. (5), lines) using standard parameters in Table 3 for axisymmetric capillary dies (D ¼ 3 mm).
cles is not considered in Eq. (5), which treats the material as a homogeneous continuum. In order to investigate the importance particle-process length scale effects, the paste was characterised using dies with D ¼ 1, 1.5 and 2 mm and the same L=D ratios as before. The results, summarised in Table 4, show distinct differences between the parameter sets. This variation, particularly in r, a and b, makes it clear that these parameters were not simply functions of material composition. As particle interaction effects were likely to manifest themselves most strongly in the die land, the validity of the parameters was tested using a set of orifice dies, with D0 ¼ 25 mm and D ranging from 1 to 9 mm. Fig. 3 shows average values of extrusion pressure for a piston velocity of 0.01 mm s1 without any precompaction, together with two sets of predictions using Eq. (5). The error bars represent the range of variation in experimental data. It can be seen that the predictions using the standard parameters fitted the data well except at the smallest and largest diameters (D ¼ 1 and 9 mm, respectively). In most cases the deviation from the average experimental value was within both the experimental variation and the 5.1% uncertainty in model predictions.
Fig. 3. Comparison of experimental extrusion pressures through axisymmetric orifice dies with predictions from Eq. (5): (points) experimental data; (black line) standard parameters; (grey line) 1 mm diameter parameters. The dashed line represents the joining pressure, (Pj ¼ 0:59 MPa), at which paste de-aeration is complete.
The deviation at the smallest die diameter could have been due to two effects: (i) that the paste exhibited internal shearing at the high apparent shear rates generated in smaller diameter dies, invalidating the assumption of simple plug flow, or (ii) that there was extensive particle interaction in the die land (i.e. the continuum assumption was no longer valid), as is found for granular materials and some highly packed suspensions. This would not be unexpected given the relatively large size of particles in the potato granule and flake. The deviation at larger D values when using the standard parameters is attributed to compaction in these previously uncompacted samples. Uniaxial compaction tests on paste samples using a blank die indicated that the paste with 40 wt.% water content exhibited a joining pressure, Pj , of 0.59 MPa (Cheyne et al., 2001). This level of stress was required to compact the paste into a cohesive mass before extrusion could take place, and thereby represents a threshold for extrusion of coherent product. Parallel studies (Cheyne, 2001) indicated that Pj was sensitive to water content: at 30 wt.% water, Pj was 0.61 MPa and compaction tests indicated frictional solid behaviour, characterised by a friction coefficient of 0.32.
Table 4 Benbow–Bridgwater parameters obtained for the potato paste for different die land diameters D (mm)
1
1.5
2
3 ‘Standard’
r0 (MPa) a (MPa sm mm ) m s0 (MPa) b (MPa sn mn ) n
0.18 1.1 0.35 0.00 0.37 0.24
0.06 0.77 0.38 0.00 0.33 0.32
0.08 0.90 0.34 0.00 0.26 0.28
0.11 1.3 0.33 0.00 0.30 0.36
A. Cheyne et al. / Journal of Food Engineering 66 (2005) 1–12
Fig. 3 shows that the parameters obtained from the 1 mm die tests consistently over-predicted the extrusion pressure for these orifice dies. Similar results were obtained with the 1.5 and 2 mm die parameter sets, albeit to a lesser extent as D increased. The failure to predict the 1 mm orifice die result, even though this size was employed in the characterisation, indicates that Eq. (5) does not describe the mechanics of the material deformation adequately at small D values, where particleprocess effects are expected to be significant. These result indicates that the parameters obtained for D < 3 mm were biased by factors not accounted for by the model and were therefore not true material constants. 4.4. Capillary flow analysis
12 Vs Vplug, 1 mm 10
Vplug, 3 mm Vplug, 1.5 mm Vplug, 2 mm
8 Velocity (ms-1)
8
6
4
2
0 0
A capillary flow analysis was performed in order to determine whether a fluid mechanical approach would be more appropriate, particularly in elucidating the die land flow behaviour. Bagley plots were used to estimate Pdie entry , and the corrected data were then used to construct a Mooney plot to determine the variation of Vs with sw . Excellent straight-line plots of C versus 1=R were obtained, but featured negative intercepts on the ordinate axis. This unphysical result suggests that Vs was greater than the average velocity, i.e. that paste underwent negative shear in the bulk. This problem has been reported previously by other workers, who have proposed various corrections and explanations. The most convincing explanations concern particle size effects (Cohen & Metzner, 1985) or sensitivity of the analysis to measurement errors (Corfield et al., 1999). The Pdie entry values were also compared with the die entry term estimated by Eq. (2): these gave good agreement for D ¼ 3 mm, and differed noticeably as D decreased. Fig. 4 shows the estimated paste slip velocity, Vs , as a function of wall shear stress. These data suggest a power law or Herschel–Bulkley relationship and the associated parameters are given in Table 5(a). Also shown in Fig. 4 are the velocities calculated for plug flow of the paste in the die land, Vplug , for D ¼ 1, 1.5, 2 and 3 mm, assuming an incompressible material. It can be seen that for the 3 mm diameter dies, Vplug was approximately equal to Vs (within the range of error), indicating that the slip assumption was valid. For smaller diameter dies, the average paste velocities were larger than the estimated slip velocity, indicating that the paste was being sheared in the bulk as well as exhibiting wall slip. The excess velocity (Vplug Vs ) was used to calculate bulk rheology parameters for a power law material and the values are given in Table 5(b). The parameters obtained for D < 3 mm show considerable variation, particularly in K (35%). This suggests that the flow pattern was not consistent between these three die sets, or that the power law model was not appropriate. This inconsistency is not surprising given the problems with the
0.1
0.2 τw (MPa)
0.3
0.4
Fig. 4. Wall slip velocity, Vs , as a function of wall shear stress. Also shown are the mean (i.e. plug flow) velocities, Vplug , calculated by continuity, for the paste with 1, 1.5, 2 and 3 mm diameter dies.
Mooney analysis described above. Table 5 also shows power law model parameters reported in the literature for several simple potato granule pastes. It is noteworthy that the parameters in the table lie mostly within an order of magnitude, despite marked differences in material composition and water contents. Halliday and Smith (1995) used simple power law (Navier) relationships to model both wall slip and bulk shear behaviour, whereas Corfield et al. (1999) and Pruvost et al. (1998) both used Herschel–Bulkley relationships. Uncertainty over the most suitable model is shown by the former’s consideration of a Herschel– Bulkley relationship for wall slip (interestingly with swy values of 50–100 kPa, cf. Table 5), and the comment by the latter two groups that the existence of a yield stress was uncertain. Pruvost et al. found that potato granules could completely absorb up to 53 wt.% water (cf. 40 wt.%, maximum, in this work): above this value water remained in interstices and increased the degree of slip exhibited by the paste. Below this limiting water content they found a Herschel–Bulkley relationship to be most appropriate for paste flow, and above it, a Navier condition. The models in Table 5 are compared in Fig. 5 and indicate that the Corfield et al. and Pruvost et al. material models predict lower slip velocities and more bulk deformation than expected for the paste material studied here. The Halliday and Smith predictions lie in between, most likely because the water content of their material was closer to that of the current paste. It can also be seen that the effect of choosing a Herschel– Bulkley type wall slip relationship for the current paste did not significantly affect the trends, except at very low slip velocities.
A. Cheyne et al. / Journal of Food Engineering 66 (2005) 1–12
9
Table 5 (a) Wall slip and (b) bulk shear parameters for the potato paste obtained using capillary flow analysis Material
Potato paste
(a) Bulk sy , kPa k, kPa sp p Wall swy , kPa K, kPa sq mq q
(b) K, kPa sp p
– 120 0.3
Potato granule, 40 wt.% (Halliday & Smith, 1995)
Potato granule, 48 wt.% (Pruvost et al., 1998)
Potato granule, 50 wt.% (Corfield et al., 1999)
– 230 0.14
30 18 0.30
11 8.2 0.36 50 110 0.38
– 42 0.31
50 17 0.42
– 80 0.41
40 170 0.33
D ¼ 1 mm
D ¼ 1:5 mm
D ¼ 2 mm
Average
93 0.30
120 0.32
150 0.28
120 0.30
Also shown are parameters for similar materials reported in the literature.
Table 6 shows the parameters for a power law extensional flow constitutive model obtained using the Gibson analysis using the bulk shear parameters given in Table 5. The associated Trouton ratios suggest that the extensional and shear contributions to the die entry work were comparable. The actual paste flow entry angle is difficult to determine because of the presence of static zones; however a value between 60 and 90 would be reasonable and consistent with the shape of plugs recovered after experiments, although these boundaries were often curved. These results suggest that the starch paste can be described using fluid constitutive models, but the parameters generated are subject to uncertainty owing to the systematic deviations from the models exhibited in the Mooney analysis. These problems indicate that the physics of these complex solid/fluid mixtures are not likely to be adequately described by simple lumped parameter models.
is not reported. Computational fluid mechanics modelling would also be subject to uncertainty in constitutive models and their parameters. 4.5.1. Conical dies The behaviour of the paste in dies with changing cross-section was investigated using a set of conical orifice dies, with die entry angle, w ¼ 45 and exit diameters between 1 and 9 mm, as detailed in Table 2. A typical set of extrusion pressure results (at a low piston velocity of 0.01 mm s1 , as found in small area reduction dies) is shown in Fig. 6. This figure also shows the extrusion pressures predicted by a modified form of Eq. (5), reported by Benbow and Bridgwater (1993): D0 Pextrusion ¼ 2ðr0 þ aV m þ s0 cot wÞ ln D n " 2n # bV cot w D 1 þ ð16Þ n D0
4.5. Modelling of complex dies Commercial product forms often require more complex die geometries than have been considered to this point. Annular dies are of considerable industrial importance, and often feature tapered and annular sections within a compound die. Here, the Benbow– Bridgwater approach is applied to model the flow through conical and then annular dies. This approach makes major assumptions about the flow fields, which allow rapid estimation of the extrusion pressure. Determining the flow field for even a power law fluid through these geometries is not straightforward, particularly as extensional contributions are significant, and
Here, V is the average (plug flow) velocity at the die exit. This analysis includes two approximations, which, though strictly invalid, are found adequate for many applications. These are: (i) transverse sections of paste deform without internal variation due to shear, and (ii) the shear stresses along the cone surface can be equated to axial stresses using the small angle theorem. The accuracy of the predictions was comparable to that for square entry orifice dies: in many cases the difference lay within the bounds of experimental and parameter uncertainty. As with the square entry orifice dies, the prediction was poor for large and small diameters, most likely for similar reasons.
10
A. Cheyne et al. / Journal of Food Engineering 66 (2005) 1–12 1600
2.5 Bulk behaviour
1400 2
1000
Pextrusion (MPa)
τ (kPa)
1200
800 600
1.5
1
400 0.5 200 0
0 0
500
1000
1500
(a)
2000
2500
3000
3500
4000
0
2
Γ (s-1)
4
6
8
10
D (mm)
Fig. 6. Axi-symmetric ram extrusion of paste through conical dies: (points) experimental data; (solid line) prediction from Eq. (16) using standard parameters. The dashed line represents the joining pressure, (Pj ¼ 0:59 MPa).
400 Wall slip behaviour 350
τω (kPa)
300
is proposed, which assumes equal wall shear stresses on the inner and outer surfaces of the annulus die land. The equation used was derived directly from Eq. (5) for a die land with two surfaces: A0 Aw Pextrusion ¼ ðr0 þ aV m Þ ln þ ðs0 þ bV n Þ Af Af
250 200 150 100
ð17Þ
50 0 0
1
2
3
4
5
6
Vs (ms-1)
(b)
Fig. 5. Comparison of flow curves from literature data for potato pastes: (a) bulk parameters, (b) wall slip parameters. Dashed line: Herschel–Bulkely model; solid line: power law model; circled line: Corfield et al. (1999); crossed line: Pruvost et al. (1998); grey line: Halliday and Smith (1995).
4.5.2. Annular dies Modelling of annular flows is often performed by numerical simulation because of the difficulties in determining stresses and flow patterns. An exception is the work of Fredrickson and Bird (1958), who reported analytical solutions for the flow of Bingham plastics and power law fluids in annuli, albeit without wall slip. Here, a new adaptation of the Benbow–Bridgwater approach
where Aw is the total die land wall area and Af is the die cross-sectional area for flow. Extrusion experiments were performed using the three annular dies described in Table 2, which feature an annular gap of 1 mm. Fig. 7 shows the experimental data and predicted extrusion pressure from Eq. (17) using the standard parameters. The experimental data were typically consistent (average variation ±9.4%), however the model gave very poor agreement (average deviation from average experimental values, 35.1%). The relatively low area reduction (7.7 compared to between 70 and 625 for the capillary dies) meant that the work in the die land was expected to be the dominant term: the standard parameters, obtained with D ¼ 3 mm, under-predicted the wall shear term. Although the flow channel was quite narrow, the confinement was effectively onedimensional (i.e. radial, but not azimuthal) in the annular slit as opposed to two-dimensional (radial) in
Table 6 Extensional shear parameters and Trouton ratios evaluated at different paste flow entry angles Paste flow entry angle, h j
E, kPa s Pj NTr
90
72
60
51
45
310 0.25 1.49
340 0.26 1.65
370 0.26 1.78
390 0.27 1.88
190 0.27 0.90
A. Cheyne et al. / Journal of Food Engineering 66 (2005) 1–12 20 18 16
Pextrusion (MPa)
14 12 10 8 6 4 2 0 0
2
4 6 Piston Velocity (mm s-1)
8
10
Fig. 7. Axi-symmetric ram extrusion of paste through annular dies: (points) experimental data, squares: L ¼ 30, diamonds: L ¼ 50 and circles: L ¼ 80 mm; (dashed lines) prediction from Eq. (17); (solid lines) prediction from Eq. (18).
the capillary, so it was expected that particle interaction effects would be reduced, but not eliminated. Reliable wall shear term parameters for smaller D values were not available, for the reasons outlined above. An alternative is to use the slip velocity model generated during the capillary analysis, giving A0 Aw Pextrusion ¼ ðr0 þ aV m Þ ln þ ðKVsp Þ ð18Þ Af Af where Vs (and V ) are assumed to be equal to Vplug , the average extrusion velocity in the annulus. Fig. 7 shows the prediction from this modified model using the parameters in Table 5. The average deviation between model and experimental values fell from 35.1% to 9.85%. In almost all cases (except the shortest die at low velocities) the predictions were still lower than the experimental data, although this could be attributed to shear in the bulk material. The agreement is certainly adequate for design and operability purposes. The importance of particle-process length scale interactions is again evident.
11
and (ii) a fluid constitutive approach, using a power law model for bulk deformation and both power law and Herschel–Bulkley models for wall slip. The Benbow–Bridgwater approach yielded a set of standard parameters, based on 3 mm diameter dies, which have been used with some success for modelling purposes. Flow through small diameter dies yielded inconsistent results, which were attributed to internal shearing of the paste, and significant particle–particle and particle–duct interaction. Under these conditions the material did not move in slip flow and could not be treated as a true continuum, and so the plasticity model was insufficient. The importance of consolidation of the material into a cohesive mass was also evident. A Mooney wall slip analysis gave good linear results, but suffered from an oft-reported non-physicality. Accepting the uncertainty in this analysis, constitutive parameters for power and Herschel–Bulkley models were comparable to those reported in the literature for similar materials, but there was further indication of non-consistent flow patterns for the data set. An estimate of extensional viscosity indicated that this was comparable with shear viscosity. Three likely flow regimes were identified: (i) plug flow at low shear rates in flow channels of size greater than 3 mm, (ii) slip flow of paste plus some internal shearing where shear rates are higher, (iii) flow dominated by particle interactions in flow channels smaller than about 1.5 mm. With due modifications for geometry, Eq. (5) was shown to describe conical die entries adequately. Application of the Benbow–Bridgwater approach to annular dies in an a priori fashion was less successful, owing to the challenge in describing flow in the narrow annular duct. The wall slip model obtained from the more laborious capillary flow analysis gave better agreement, as it featured contributions from small D experiments. The Benbow–Bridgwater approach has thus been shown to give reasonable predictions of extrusion pressure for even annular dies, but it should be noted that the validity of this continuum approach is compromised when particle–process interactions are significant.
5. Conclusions Acknowledgements The potato starch paste studied here exhibited complex flow behaviour. It can be considered as a dense suspension with a very viscous deformable phase, consisting of a hydrated starch gel, and its classification lies on the boundary between frictional solids and viscoplastics. Two methods were applied to quantify its extrusion behaviour: (i) a modified plasticity approach,
Funding for AC from the Biotechnology and Biological Sciences Research Council is gratefully acknowledged, as is support for the project from United Biscuits. Assistance with the micro-manipulation facilities at the University of Birmingham from Dr. Z. Zhang and co-workers is also gratefully acknowledged.
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References Aguilera, J. M., & Stanley, D. W. (1990). Microstructural principles of food processing and engineering. Barking, UK: Elsevier Science Publishers Ltd. Amarasinghe, A. D. U. S., & Wilson, D. I. (1999). On-line monitoring of ceramic extrusion. Journal of the American Ceramic Society, 82, 2305–2312. Benbow, J. J., & Bridgwater, J. (1993). Paste flow and extrusion. Oxford, UK: Clarendon Press. Briscoe, B. J., Corfield, G. M, Lawrence, C. J., & Adams, M. J. (1998). ‘Low-order’ optimisation of soft solids processing. Transactions of IChemE: Chemical Engineering Research and Design, 76A, 16– 21. Chakrabarty, J. (1987). The theory of plasticity. New York, USA: McGraw-Hill Company. Cheyne, A. (2001). Extrusion behaviour of starch-based food pastes. Ph.D. Thesis, Department of Chemical Engineering, University of Cambridge, UK. Cheyne, A., Barnes, J., Gedney, S., & Wilson, D. I. (2004). Extrusion behaviour of cohesive potato starch pastes. II. Microstructureprocess interactions, Journal of Food Engineering. doi:10.1016/ j.jfoodeng.2004.02.036. Cheyne, A., Wilson, D. I., Barnes, J., & Sala€ un, Y. (2001). Modelling of starch extrusion and damage in industrial forming processes. In T. L. Barsby, A. M. Donald, & P. J. Frazier (Eds.), Starch structure and functionality (pp. 8–26). Cambridge, UK: Royal Society of Chemistry. Cohen, Y., & Metzner, A. B. (1985). Apparent slip flow of polymer solutions. Journal of Rheology, 29, 67–102. Corfield, G. M., Adams, M. J., Briscoe, B. J., Fryer, P. J., & Lawrence, C. J. (1999). A critical examination of capillary rheometry for foods (exhibiting wall slip). Transactions of IChemE: Food and Bioproducts Processing, 77, 3–10. FAO (1999). Production Yearbook Volume 1998, FAO Statistics Series No. 148 (Vol. 53). Food and Agriculture Organisation of the United Nations, Rome, Italy. Fredrickson, A. G., & Bird, R. B. (1958). Non-Newtonian flow in annuli. Industrial Engineering Chemical Research, 50, 347–352. Halliday, P. J., & Smith, A. C. (1995). Estimation of the wall slip velocity in the capillary flow of potato granule pastes. Journal of Rheology, 39, 139–149. Hermansson, A.-M., & Svegmark, K. (1996). Developments in the understanding of starch functionality. Trends in Food Science and Technology, 7, 345–353. Heydon, C. J., Scott, G. M., & Tucker, G. S. (1996). Applications of tube viscometry for the characterisation of flow of gelatinised food starches under UHT conditions. Transactions of IChemE: Food and Bioproducts Processing, 74C, 81–91.
Horrobin, D. M., & Nedderman, R. M. (1998). Die entry pressure drops in paste extrusion. Chemical Engineering Science, 53(18), 3215. Hulleman, S. D. H., Janssen, F. H. P., & Feil, H. (1998). The role of water during the plasticization of native starches. Polymer, 39, 2043–2048. Martin, P. J., Wilson, D. I., & Bonnett, P. E. (submitted for publication). Extrusion of pastes through non-axisymmetric geometries. Transactions of IChemE: Chemical Engineering Research and Design. Matz, S. A. (1991). The chemistry and technology of cereals as food and feed. New York, USA: Van Nostrand Reinhold. Meuser, F., Manners, D. J., & Seibel, W. (1995). Progress in plant polymeric carbohydrate research. Berlin, Germany: Simon Druck. Mitchell, J. R., Hill, S. E., Paterson, L., Valles, B., Barclay, F., & Blanshard, J. M. (1997). The role of molecular weight in the conversion of starch. In P. J. Frazier, A. M. Donald, & P. Richmond (Eds.), Starch structure and functionality. Cambridge: Royal Society of Chemistry. Nedderman, R. M. (1982). The theoretical prediction of stress distributions in hoppers. Transactions of IChemE: Chemical Engineering Research and Design, 60A, 259–275. Noel, T. R., Ring, S. G., & Whittam, M. A. (1990). Physical properties of starch products: structure and function. Norwich, UK: AFRC Institute of Food Research. Peck, M. C. (2002). Roller extrusion Pastes. Ph.D. Thesis, Department of Chemical Engineering, University of Cambridge, UK. Pruvost, K., Corfield, G. M., Kingman, S., & Lawrence, C. J. (1998). Effect of moisture content on the bulk and wall constitutive behaviour of starch pastes. Transactions of IChemE: Food and Bioproducts Processing, 76C, 188–192. Rough, S. L., Bridgwater, J., & Wilson, D. I. (2000). Effects of liquid phase migration on extrusion of microcrystalline cellulose pastes. International Journal of Pharmaceutics, 204, 117–126. Senouci, A., & Smith, A. C. (1986). The extrusion cooking of potato starch material. Starch/St€arke, 38, 78–82. Steffe, J. F. (1996). Rheological methods in food process engineering. East Lancing, USA: Freeman Press. Svegmark, K., & Hermansson, A.-M. (1991). Distribution of amylose and amylopectin in potato starch pastes: Effects of heating and shearing. Food Structure, 10, 117–129. Talburt, W. F., & Smith, O. (1980). Potato processing. New York, USA: Van Nostrand Reinhold Company. van Soest, J. J. G. (1996). Starch plastics: Structure––property relationships. Netherlands: Universiteit Utrecht. Zhang, Z., Ferenczi, M. A., Lush, A. C., & Thomas, C. R. (1991). A novel micromanipulation technique for measuring the bursting strength of single mammalian cells. Applied Microbiology and Applied Biotechnology, 36, 208–210.