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Melt growth and shrinkage at the exit of the die in the extrusion-cooking process
Journal of Food Engineering 60 (2003) 185–192 www.elsevier.com/locate/jfoodeng
Melt growth and shrinkage at the exit of the die in the extrusion-cooking process A. Arhaliass a
a,*
, J.M. Bouvier b, J. Legrand
a
GEPEA––UMR CNRS 6144, CRTT––Universit e de Nantes, IUT de Saint Nazaire, Boulevard de lÕUniversit e BP406, Saint Nazaire 44602, France b CLEXTRAL SA––B.P. 10, 42702 Firminy, France
Abstract Melt expansion by extrusion-cooking was investigated when processing corn grits in a twin-screw extruder. A growth phase followed by a shrinkage phase were experimentally observed through an image processing method, and analysed by use of classical expansion indices: sectional, longitudinal and volumetric expansion indices, for both growth and shrinkage phases. It was shown that the expansion phenomenon was strongly dependent on the geometrical characteristics of the die insert, and particularly on die insert diameter. Melt growth developed more in the radial direction which revealed an important structural anisotropy of the expanding melt, due probably to the elastic properties of the biopolymer-based melt. Melt shrinkage which occurred further, contributed to a significant decrease in the bulk density of the expanding melt, and could arise from either surface tension forces, or from the recovery of melt elasticity. 2003 Elsevier Ltd. All rights reserved.
1. Introduction The extrusion-cooking process is nowadays a wellknown processing unit operation, which gives a large variety of expanded food products (snacks, breakfast cereals, pet foods, pellet fish feeds, . . .). This unit operation consists of converting biopolymer-based raw materials into viscoelastic melts, which are further forced to flow through a narrow insert when it exits the die. In the extruder, the food mix is thermomechanically cooked thanks to high temperature, pressure and shear stress which are generated in the screw-barrel assembly. The cooked melt is then texturized and shaped in the die assembly. The extrusion-cooking of cereal-based products has been extensively studied during the last three decades. Several books provide relevant knowledge and information relative to extrusion technologies, as well as food science and engineering (Colonna & Della Valle, 1994; Guy, 2001; Harper, 1978; Kokini, Ho, & Karwe, 1992; Mercier, Linko, & Harper, 1989). Although the thermomechanical cooking of foodstuffs is quite well described and understood, it must be noted that product
*
Corresponding author. Tel./fax: +33-2-40-17-2631. E-mail address: [email protected] (A. Arhaliass).
0260-8774/03/$ - see front matter 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0260-8774(03)00039-6
texturization at the die is much less known. When extrusion-cooked melts exit the die, they suddenly goes from high pressure to atmospheric pressure. This pressure drop causes an extensive flash-off of internal moisture and the water vapour pressure, which is nucleated to form bubbles in the molten extrudate, allows the expansion of the melt. The expansion phenomenon was first investigated by Harper and Tribelhorn (1992) and by Alvarez-Martinez, Kondury, and Harper (1988). These authors suggested that melt expansion followed two different directions, that are sectional expansion and longitudinal expansion. The measurement of sectional and longitudinal expansion indices allowed a better description of the cell structure of expanded extrudates. Bouzaza, Arhaliass, and Bouvier (1996) and Desrumaux (1996) have shown that melt expansion is notably nonisotropic, depending upon melt composition, extent of melt cooking, and die design. Based on visual observations, Fan, Mitchell, and Blanshard (1994) and Mitchell, Fan, and Blanshard (1994), have suggested that melt expansion at the die consists of an expansion phase followed by a shrinkage phase. Both phases depend upon melt properties (temperature and rheological behaviour), melt flow rate and die design. Melt expansion in the extrusion-cooking process is not well understood. As a matter of fact, it is difficult to observe during the first seconds of the water flashing-off,
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and consequently the description of the structure development of extrudates stays unclear. Further investigation of the expansion mechanism is still needed to improve and better control extrudate structure and quality. In this work, a visualisation technique combined with an image processing method is presented and used to observe and quantify melt expansion and shrinkage at the extrusion die. This allowed measurement of expansion and shrinkage indices in both sectional and longitudinal directions, and determine characteristic times of expansion and shrinkage phases. The experimental results are then interpreted and discussed based on a theoretical development derived from the bubble growth modelling in high viscosity medium (Amon & Denson, 1984).
1990). According to the chosen steady-state extrusion cooking conditions, final feed rate and screw speed ranged from 25.4 to 43 kg/h and from 120 to 190 rpm, respectively, while the moisture content was kept constant at 18.4% (wet weight basis). On exiting the die, the cooked melt was directly visualised by a CCD camera and extrudate samples, 50 cm long, were cut once the melt shrinkage after the water vapour flashing was complete. Moisture content of stored extrudates was between 2% and 3% (wet weight basis). 2.2. Measurement of melt apparent viscosity Assuming that no slip occurred at the walls of the capillary viscometer, and the flow was fully developed in the axial direction, the wall shear stress, sw , could be calculated as follows:
2. Materials and methods sw ¼ 2.1. Extrusion-cooking experiments The extrusion-cooking experiments were carried out in a CLEXTRAL BC 45 corotating twin-screw extruder. The food mix consisted of corn grits (average particle size of 300 lm) with low moisture content in the extruder (18.4% wet weight basis). The screw-barrel assembly (L=D of 9) consisted of a 500 mm barrel in which the screw profile used had two 250 mm sections: with one 250 mm feeding section and one 250 mm compression and shearing section. The second section was heated by a 7 kW induction heater controlled at the desired wall temperature of 160 C. The mix was fed into the extruder at a constant mass flow rate, and water was added into the first section. The screw-barrel assembly terminated with a front die plate, where the pressure and the melt temperature were measured. The distance between the end points of the screws and the front die plate was adjusted to 1.5 mm. All the extruded mixture had to pass through a 5 mm diameter, 5 mm length orifice in the front die plate, and then into the viscometer. The extruder-viscometer assembly was characterised by a 9.24 mm hydraulic diameter (Dh ) and a 1.04 shape factor of the cross-section (k). An electrical resistance heater, combined with a temperature control system and a thermocouple, was used to maintain the melt temperature in the viscometer close to that in the front die plate. The extruded melt left the viscometer through a circular die in which length Ld and diameter Dd varied from 12 to 80 mm and from 5 to 8 mm respectively. Thus, the length to diameter ratio varied from 2 to 13.3. Experimental methodology of starting the extruder was described previously by Wang, Bouvier, and Gelus (1990), and the operating conditions (feed rate and screw speed) were changed simultaneously so as to apply a constant specific mechanical energy of 500 kJ/kg (Wang et al.,
Dh DPV LV
ð1Þ
where Dh is the hydraulic diameter of the channel of the viscometer, LV is the length across which a pressure drop, DPV , is measured. The wall shear rate, c_ w , could be calculated by c_ w ¼ k
ð3n þ 1Þ 32Q 4n pD3h
ð2Þ
Q is the feed rate (m3 /s) and n is the flow index of cornbased extrusion-cooked melt. Melt density within the capillary viscometer is assumed constant and equal to 1400 kg m3 . The melt apparent viscosity in the capillary viscometer, ðla ÞV , is calculated by sw ðla ÞV ¼ ð3Þ c_ w The melt apparent viscosity in the die insert, ðla Þd , was obtained by neglecting changes in the temperature between the capillary viscometer and the die insert, and by neglecting the entrance effects in the die. Then, the melt apparent viscosity in the die insert is calculated by !n1 ðc_ w Þd ðla Þd ¼ ðla ÞV ð4Þ ðc_ w ÞV ðc_ w Þd is the wall shear rate in the die. Fig. 1 shows the evolution of the melt apparent viscosity as a function of the wall shear rate in the die insert. For a constant temperature, of about 160 C, a constant specific mechanical energy of 500 kJ/kg and a constant moisture content (18.4%), the melt apparent viscosity decreases from 870 to 160 Pa s when the wall shear rate increases from 190 to 1300 s1 ; this illustrates clearly the shear-thinning behaviour of the corn-based extrusioncooked melt. The experimental values can be modelled by use of a power law equation, as follows:
A. Arhaliass et al. / Journal of Food Engineering 60 (2003) 185–192
ture content of the melt in the die and moisture content of the extrudate, respectively. As extrudates had a circular shape, the volume was estimated from the two characteristic dimensions of the final product at three different locations per extrudate. Volume and weight of extrudates were determined on eight samples in order to calculate the apparent density.
1000
Apparent viscosity, Pa.s
187
500
3. Results and discussion 0
0
500
(γ w ) d , s −1
1000
1500
Fig. 1. Melt apparent viscosity versus wall shear rate in the die insert.
0:22
ðsw Þd ¼ 10:2ððc_ w Þd Þ
ð5Þ
The low value of the flow index of the cooked melt (n ¼ 0:22) is in good agreement with values obtained in previous studies (Singh & Smith, 1999). 2.3. Experimental observation of melt expansion An original visualisation technique was specifically developed to observe the dynamics of melt expansion at the die. This technique consisted of a lighting system together with a CCD camera (XC77RRCE Sony), equipped with an electronic shutter. The extruded melt was illuminated with a white light and the intensity of the light distribution over the product was visualised in real time (Pasquet, Arhaliass, Pain, & Bouvier, 1997; Pasquet & Arhaliass, 1997). The injection of a tracer allowed the visualisation of growth and shrinkage phenomena, and the image analysis of tracer trajectory lead to measure the characteristic times of growth and shrinkage phases. Images were recorded during 10 s with an acquisition period of 0.05 s under a high shutter speed (104 Hz), so that to examine the different brightness regions of the product spot image.
3.1. Melt expansion at the die insert Fig. 2 clearly shows the formation of the steam-induced bubbles at the exit of the die insert, and the evolution of the cell network of the extrudate matrix. As the melt flows into the die, its pressure and temperature are about 40–120 bars and 150–180 C, respectively. At such conditions, water is in liquid state and perfectly mixed with the starch melt. When it emerges from the die, the cooked melt suddenly goes from high pressure to atmospheric pressure. This pressure drop causes an extensive flash-off of internal moisture and the water vapour pressure, which is nucleated to form bubbles in the molten extrudate, allows the expansion of the melt. As shown in Fig. 2, two main phases may be distinguished in the expansion process: A growth phase which takes place quasi-adiabatically. It comprises the nucleation and growth of water vapour bubbles, up to a maximum expansion where steam is released to the environment. Let tg , be the duration time of melt growth from insert outlet to maximum expansion. Fig. 3 shows that the adiabatic step occurs very quickly, as melt growth time varies between 44 and 87 ms. At maximum expansion, rupture of steam bubbles is then caused by the loss of cell wall resistance which can no longer sustain the water vapour pressure inside the bubbles. Rupture of bubbles must occur
2.4. Expansion indices Expansion of dried extrudates was characterised by the classical expansion indices, such as the sectional expansion index (SEI), the longitudinal expansion index (LEI), and the volume expansion index (VEI), as described by Alvarez-Martinez et al. (1988): SEI ¼
Se ; Sd
LEI ¼
qd Sd ð1 Hd Þ ; qe Se ð1 He Þ
ð6Þ
VEI ¼ SEI LEI where qd is the melt density in the die; qe is the apparent density of the extrudate; Se and Sd are the cross-sections of extrudate and die, respectively; Hd and He are mois-
Fig. 2. Expansion and shrinkage of the melt at the die insert (insert diameter: 6 mm, insert length: 29 mm, throughput: Q ¼ 43 kg/h).
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120
Dd = 5 mm
tg, ms
80
40
Dd = 8 mm
0 0
40
ts, ms
80
120
Fig. 3. Melt growth time as a function of melt shrinkage time. (j) Dd ¼ 5 mm, Ld ¼ 29 mm; (N) Dd ¼ 6 mm, Ld ¼ 29 mm; (r) Dd ¼ 7 mm, Ld ¼ 29 mm; () Dd ¼ 8 mm, Ld ¼ 29 mm; (‘) Dd ¼ 6 mm, Ld ¼ 12–80 mm.
because the water balance calculated before and after expansion, reveals larger amount of water loss than the air volume of final extrudate. This results in water vapour loss and an open foam structure in the extrudate. During the steam release, the heat necessary to vaporise liquid water causes a fast cooling of the melt, down to approximately 100 C. A shrinkage phase when the steam release is completed. Let ts , be the duration time of melt shrinkage from maximum expansion to the equilibrium of shrinkage. Fig. 3 shows that shrinkage phase occurs also quickly, as melt shrinkage time varies between 24 and 115 ms. During shrinkage, the structure of the expanded melt changes from an open to a closed foam structure. Fig. 4a and b show the effect of feed rate on growth and shrinkage phenomena, at constant die insert diameter (Dd ¼ 6 mm) and insert land length (Ld ¼ 40 mm). It occurs that both Dg and Ds of growth and shrinkage phases increase very slightly when feed rate increases from 25.4 kg/h (Fig. 4a) to 32.3 kg/h (Fig. 4b). The influence of die insert diameter is presented in Fig. 4c and d, at constant feed rate (32.3 kg/h) and die land length (29 mm). The data show that melt diameter at maximum expansion (Dg ) and melt diameter at the equilibrium of shrinkage (Ds ) increase very importantly when die insert diameter decreases. It must be noted that the extent of shrinkage increases notably as die insert diameter increases. Fig. 4e and f show the effect of die land length, at constant feed rate (32.3 kg/h) and die insert diameter (6 mm). Die land length has very little effect on growth and shrinkage phases: both Dg and Ds increase very slightly when insert land length increases; the extent of shrinkage increases as insert land length decreases. In conclusion, it appears that melt expansion at the die insert is very much affected by the insert diameter: the lower the die insert diameter, the larger the melt
growth, and the larger the extent of melt shrinkage. But, both feed rate and insert land length do not influence significantly melt growth and shrinkage. After shrinkage, the melt cools due to convective heat exchange between ambient air and texturizing extrudate. As its temperature decreases, the melt reaches a temperature at which bubble wall movement ceases because its viscosity becomes extremely high as it approaches the glass transition temperature, Tg . Mitchell et al. (1994), stipulated that bubble wall movement would stop around (Tg þ 40 C), where the extrudate starts to fix its internal structure. 3.2. Physical analysis of growth and shrinkage phases The dynamics of melt expansion can be investigated by analysing the images of melt expansion at the die insert. This allows to determine physical parameters of both growth and shrinkage phases that are • Extrudate diameter at the maximum of the expansion: Dg • Distance from insert outlet to maximum expansion: Zg • Extrudate diameter at the equilibrium of shrinkage: Ds • Distance from maximum expansion to the equilibrium of shrinkage: Zs : The distance Zg and Zs together with the duration times tg and ts , allow to calculate the average growth velocity, Vg , and the average shrinkage velocity, Vs . Then, specific expansion indices of both growth and shrinkage phases can be deduced as follows: 2 Dg ðseiÞg ¼ ; Dd 1 Zg ; ðleiÞg ¼ Vd t g ðveiÞg ¼ ðseiÞg ðleiÞg 2 Ds ; ðseiÞs ¼ Dd 1 Zs ; ðleiÞg ¼ Vd t s ðveiÞs ¼ ðseiÞs ðleiÞs
ð7Þ
ð8Þ
where ðseiÞg , ðveiÞg and ðveiÞg are the sectional expansion index, the longitudinal expansion and the volumetric expansion index of the growth phase, respectively; ðseiÞs , ðleiÞs and ðveiÞs are the sectional expansion index, the longitudinal expansion index and the volumetric expansion index of the shrinkage phase respectively; Dd and Vd are the insert diameter and melt velocity in the die insert, respectively. It is worth noting that expansion indices SEI and LEI measured on final extrudates, and
A. Arhaliass et al. / Journal of Food Engineering 60 (2003) 185–192
189
Fig. 4. (a) and (b) Effect of feed rate on melt growth and melt shrinkage at the die insert: (a) Q ¼ 25:4 kg/h, Dd ¼ 6 mm, Ld ¼ 40 mm, Dg ¼ 24:1 mm, Ds ¼ 19:6 mm; (b) Q ¼ 32:3 kg/h, Dd ¼ 6 mm, Ld ¼ 40 mm, Dg ¼ 24:5 mm, Ds ¼ 20:3 mm. (c) and (d) Effect of insert diameter on melt growth and melt shrinkage at the die insert: (c) Dd ¼ 5 mm, Ld ¼ 29 mm, Q ¼ 32:3 kg/h, Dg ¼ 21:6 mm, Ds ¼ 17:3 mm; (d) Dd ¼ 8 mm, Ld ¼ 29 mm, Q ¼ 32:3 kg/h, Dg ¼ 28:9 mm, Ds ¼ 21:7 mm. (e) and (f) Effect of insert land length on melt growth and melt shrinkage at the die insert: (e) Ld ¼ 80 mm, Dd ¼ 6 mm, Q ¼ 25:4 kg/h, Dg ¼ 24:5 mm, Ds ¼ 20:5 mm (f): Ld ¼ 40 mm, Dd ¼ 6 mm, Q ¼ 25:4 kg/h, Dg ¼ 24:1 mm, Ds ¼ 19:6 mm.
expansion indices ðseiÞs and ðleiÞs determined by image analysis of melt expansion at the die insert, are well correlated. In fact, Fig. 5a and b show that the visualisation technique developed in this study gives expansion data which are in good agreement with those determined by the classical method introduced by Alvarez-Martinez et al. (1988). Fig. 6 shows ðleiÞg –ðseiÞg chart, that is the melt growth chart, with iso-ðveiÞg curves going from 5 to 15, and the isotropic expansion curve given by the equation 0:5 ðleiÞg ¼ ½ðseiÞg . This chart allows discussion of the characteristics of growth phase. It is shown that the radial expansion predominates importantly, as all samples reveal high ðseiÞg and low ðleiÞg values. Also, radial expansion tends to decrease, and consequently longitudinal expansion tends to increase when die insert diameter increases: the lower the die insert diameter, the higher the anisotropy of expansion. Such observation can be compared to die swell when extruding viscoelastic
polymer melts. It is known that starch-based biopolymer melts are viscoelastic, and radial expansion at the die insert would arise from the normal stresses generated by the shear flow within the die insert. It is worth noting that growth and shrinkage phases are dependent, as expansion indices of both phases are correlated. In fact, Fig. 7a shows a unique linear relationship between ðseiÞg and ðseiÞs : ðseiÞg ¼ 11 when ðseiÞs ¼ 0; the slope is around 0.5. However, the relation between ðleiÞg and ðleiÞs is influenced bye the geometrical characteristics of the die insert and by the feed rate (Fig. 7b). Although the mechanism of melt shrinkage is not well understood, three physical explanations may then be suggested. The first one could be due to vacuum shrinkage of closed steam bubbles. In fact, the expanded melt starts to shrink when the pressure inside the bubbles equals to atmospheric pressure. At that condition, the liquid water of the melt is in equilibrium with its
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A. Arhaliass et al. / Journal of Food Engineering 60 (2003) 185–192
20
25
20
(sei)s
(sei)g
15
10
(sei)g = 0.48(sei)s + 11
15
10
5
5
0
0 0
5
10
(a)
15
20
SEI
0
5
10
15
20
25
(sei)s
(a) 2.5
1.5
Dd = 8 mm
Q = 25.4 kg/h
2 Q = 32.3 kg/h
(lei)g
1
Q = 37.6 kg/h
(lei)s
1.5
Q = 43 kg/h
1
0.5 0.5 Dd = 5 mm
0
0 0
0.5
1
(b)
1.5
LEI
Fig. 5. (a) ðseiÞs as a function of SEI, (b) ðleiÞs as a function of LEI.
0
0.4
(b)
0.8
1.2
(lei)s
Fig. 7. (a) Correlation between ðseiÞg and ðseiÞs . (b) Correlation between ðleiÞg and ðleiÞs (Ld ¼ 29 mm; feed rate ¼ 25:4–43 kg/h). (j) Dd ¼ 5 mm, (N) Dd ¼ 6 mm, (r) Dd ¼ 7 mm, () Dd ¼ 8 mm.
5 0.5
(lei)g = (sei)g
(lei)g
4
3
2
1 (vei)g=15 (vei)g=10
(vei)g=5
0 0
5
10
15
20
25
(sei)g Fig. 6. Melt growth chart: ðleiÞg versus ðseiÞg (Ld ¼ 29 mm; feed rate ¼ 25:4–43 kg/h). (j) Dd ¼ 5 mm, (N) Dd ¼ 6 mm, (r) Dd ¼ 7 mm, () Dd ¼ 8 mm.
vapour phase, and then the partial pressure of water vapour depends on the temperature and entire composition of the melt. As the melt temperature decreases due to convective heat exchange between the hot melt and the surrounding air (ambient temperature), small amount of water vapour should condense which should tend to decrease the pressure inside the bubbles, and consequently create a light vacuum in bubbles and the shrinkage of the whole melt. But, such phenomenon
should follow the kinetics of heat exchange between the expanded melt and the surrounding air, and should occur over several seconds, much more than the shrinkage times observed in this study (25–115 ms). The second explanation might relate to surface tension forces which should contract each bubble and should occur quasi-instantaneously. Finally, the third explanation might be based on the elastic recovery of the melt after maximum expansion; elastic recovery should also occur instantaneously. For pseudo-elastic product, such as maize product, shrinkage phenomena is the result of instantaneous elastic recovery. 3.3. Melt growth modelling Expanding melt at the die insert can be considered as a network of steam bubbles surrounded by a viscous melt. Assuming that the melt is homogeneous and isothermal, each steam bubble follows the same expansion mechanism, and consequently behaves similarly to the expansion of the whole melt. Thus, the experimental data obtained from the expanding melt can be used to figure out the behaviour of steam bubbles. Consider a symmetrical spherical vapour bubble surrounded concentrically by a viscous medium. The
A. Arhaliass et al. / Journal of Food Engineering 60 (2003) 185–192
dR DP ¼ dt R 4ðla Þd
ð9Þ
where DP ¼ Pv Pa is assumed to be a function of temperature only; Pv and Pa are vapour pressure at melt temperature in the die and atmospheric pressure, respectively; R is the radius of a vapour bubble; ðla Þd is the melt apparent viscosity in the die insert. The bubble growth dynamics depends on thermorheological properties of the melt. Eq. (9) shows a quantity t0 ¼ ðla Þd =DP , which is the characteristic time of bubble formation (Mitchell et al., 1994). t0 can be considered as the characteristic time of melt growth at the die insert. Fig. 8 presents the relationship between tg and t0 . It occurs that tg decreases when t0 increases, that is when the melt temperature at the die insert decreases; in such condition, a temperature decrease would tend to reinforce the melt elasticity, and so to decrease the growth time of steam bubbles, tg . Based on the experimental data obtained with corn grits in this study, the evolution of tg as a function of t0 follows a power law equation, as follows: tg ¼ bðt0 Þa ;
b ¼ 3 103 ; a ¼ 1:4
ð10Þ
where the parameters a and b are only function of the type of the starch melt. Eq. (9) can be integrated for one steam bubble, when assuming an isothermal flow (Pv R3 ¼ cte), and neglecting the effects of elasticity and surface tension of the
tg, s
0.1
0.05
25
Growth expansion index
bubble growth is controlled by the pressure difference (DP ) between the vapour pressure of water at the melt temperature and the atmospheric pressure, and by the apparent viscosity of the melt as well as the surface tension (Amon & Denson, 1984). Taking into account the boundary conditions of the melt/vapour interface and neglecting the inertial effects (the melt is highly viscous) and the surface tension, the dynamics of bubble growth in a viscous melt is given by
191
20
15
10
5
0 0
100
200
tg/t0
300
Fig. 9. Radial and volumetric expansion indices as a function of tg =t0 , in growth phase (d: ðveiÞg and j: ðseiÞg ).
melt. This leads to describe the dynamics of the bubble growth: 3 Rg tg ¼aþb ð11Þ Ri t0 where a and b are function of the initial radius of the bubble, Ri , at the exit of the die insert. Ri is assumed to be only function of the die radius (Ri ¼ eRd ), and Rg is the bubble radius at the maximum expansion. Eq. (11) predicts that the bubble growth, and consequently the melt growth, is linearly correlated with the ratio tg =t0 . The experimental results are in good agreement with that prediction (Fig. 9) as the volumetric expansion index is proportional to tg =t0 . The sectional expansion index, ðseiÞg , is not linearly correlated with tg =t0 ; but it shows a slight decrease of the slope when tg =t0 increases, which should be due to the reinforcement of the elastic properties of the melt as tg =t0 increases. 4. Conclusion This experimental investigation has proven that melt expansion at the exit of the die insert showed two distinct phases: a growth phase followed by a shrinkage phase. The melt growth is apparently governed by the viscous characteristic time of the melt; whereas the bubble structure of the melt would be controlled by the elastic properties of the melt. This tends to favour importantly the radial expansion, which generates some anisotropy in the internal structure of the expanding melt. This result is important as it determines the ultimate texture, and so the textural quality of expanded extrudates. References
0 0
0.0005
0.001
0.0015
t0, s Fig. 8. Evolution of tg as a function of t0 .
0.002
Alvarez-Martinez, L., Kondury, K. P., & Harper, J. M. (1988). A general model for expansion of extruded products. Journal of Food Science, 53(2), 609–615.
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Amon, M., & Denson, C. D. (1984). A study of the dynamics of foam growth: analysis of the growth of closely spaced spherical bubbles. Polymer Engineering Science, 24(13), 1026–1034. Bouzaza, D., Arhaliass, A., & Bouvier, J. M. (1996). Die design and dough expansion in low moisture extrusion-cooking process. Journal of Food Engineering, 29, 139–152. Desrumaux, A. (1996). Comportement technologique des semoules de ma€ıs en cuisson-extrusion. Doctoral Thesis. Universite de Technologie, Compiegne, France. Colonna, P., & Della Valle, G. (1994). La cuisson-extrusion. Technique and documentation. Paris: Lavoisier. Fan, J., Mitchell, J. R., & Blanshard, J. M. V. (1994). A computer simulation of the dynamics of bubble growth and shrinkage during extrudate expansion. Journal of Food Engineering, 23, 337– 356. Guy, R. (2001). Extrusion cooking. Technologies and applications. Cambridge, England: Woodhead Publishing Limited. Harper, J. M. (1978). Extrusion of foods (Vols. I and II). Boca Raton, FL, USA: CRC Press Inc. Harper, J. M., & Tribelhorn, R. E. (1992). Expansion of native cereal starch extrudates. In J. L. Kokini et al. (Eds.), Food extrusion
science and technology (pp. 653–667). New York: Marcel Dekker Inc. Kokini, J. L., Ho, C. T., & Karwe, M. V. (1992). Food extrusion science and technology. New York, USA: Marcel Dekker, Inc. Mercier, C., Linko, P., & Harper, J. M. (1989). Extrusion cooking. St. Paul, MA, USA: AACC Inc. Mitchell, J. R., Fan, J., & Blanshard, J. M. V. (1994). The shrinkage domain. Extrusion Communique (March), 10–12. Pasquet, S., & Arhaliass, A. (1997). Etude en ligne des proprietes rheologiques de lÕexpansion et de la contraction des extrudes lors de la cuisson-extrusion. Les Cahiers de Rheologie, 15(4), 168–177. Pasquet, S., Arhaliass, A., Pain, J. P., & Bouvier, J. M. (1997). Modelisation de la dynamique de lÕexpansion et de la retraction des produits alimentaires en sortie de filiere dÕextrudeurs. Recents Progres en Genie des Procedes, Lavoisier, Paris, 11(56), 193–199. Singh, N., & Smith, A. C. (1999). Rheological behaviour of different cereals using capillary rheometry. Journal of Food Engineering, 39, 203–209. Wang, S. M., Bouvier, J. M., & Gelus, M. (1990). Rheological behaviour of wheat flour dough in twin-screw extrusion cooking. International Journal of Food Science and Technology, 25, 129–139.
Melt growth and shrinkage at the exit of the die in the extrusion-cooking process A. Arhaliass a
a,*
, J.M. Bouvier b, J. Legrand
a
GEPEA––UMR CNRS 6144, CRTT––Universit e de Nantes, IUT de Saint Nazaire, Boulevard de lÕUniversit e BP406, Saint Nazaire 44602, France b CLEXTRAL SA––B.P. 10, 42702 Firminy, France
Abstract Melt expansion by extrusion-cooking was investigated when processing corn grits in a twin-screw extruder. A growth phase followed by a shrinkage phase were experimentally observed through an image processing method, and analysed by use of classical expansion indices: sectional, longitudinal and volumetric expansion indices, for both growth and shrinkage phases. It was shown that the expansion phenomenon was strongly dependent on the geometrical characteristics of the die insert, and particularly on die insert diameter. Melt growth developed more in the radial direction which revealed an important structural anisotropy of the expanding melt, due probably to the elastic properties of the biopolymer-based melt. Melt shrinkage which occurred further, contributed to a significant decrease in the bulk density of the expanding melt, and could arise from either surface tension forces, or from the recovery of melt elasticity. 2003 Elsevier Ltd. All rights reserved.
1. Introduction The extrusion-cooking process is nowadays a wellknown processing unit operation, which gives a large variety of expanded food products (snacks, breakfast cereals, pet foods, pellet fish feeds, . . .). This unit operation consists of converting biopolymer-based raw materials into viscoelastic melts, which are further forced to flow through a narrow insert when it exits the die. In the extruder, the food mix is thermomechanically cooked thanks to high temperature, pressure and shear stress which are generated in the screw-barrel assembly. The cooked melt is then texturized and shaped in the die assembly. The extrusion-cooking of cereal-based products has been extensively studied during the last three decades. Several books provide relevant knowledge and information relative to extrusion technologies, as well as food science and engineering (Colonna & Della Valle, 1994; Guy, 2001; Harper, 1978; Kokini, Ho, & Karwe, 1992; Mercier, Linko, & Harper, 1989). Although the thermomechanical cooking of foodstuffs is quite well described and understood, it must be noted that product
*
Corresponding author. Tel./fax: +33-2-40-17-2631. E-mail address: [email protected] (A. Arhaliass).
0260-8774/03/$ - see front matter 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0260-8774(03)00039-6
texturization at the die is much less known. When extrusion-cooked melts exit the die, they suddenly goes from high pressure to atmospheric pressure. This pressure drop causes an extensive flash-off of internal moisture and the water vapour pressure, which is nucleated to form bubbles in the molten extrudate, allows the expansion of the melt. The expansion phenomenon was first investigated by Harper and Tribelhorn (1992) and by Alvarez-Martinez, Kondury, and Harper (1988). These authors suggested that melt expansion followed two different directions, that are sectional expansion and longitudinal expansion. The measurement of sectional and longitudinal expansion indices allowed a better description of the cell structure of expanded extrudates. Bouzaza, Arhaliass, and Bouvier (1996) and Desrumaux (1996) have shown that melt expansion is notably nonisotropic, depending upon melt composition, extent of melt cooking, and die design. Based on visual observations, Fan, Mitchell, and Blanshard (1994) and Mitchell, Fan, and Blanshard (1994), have suggested that melt expansion at the die consists of an expansion phase followed by a shrinkage phase. Both phases depend upon melt properties (temperature and rheological behaviour), melt flow rate and die design. Melt expansion in the extrusion-cooking process is not well understood. As a matter of fact, it is difficult to observe during the first seconds of the water flashing-off,
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and consequently the description of the structure development of extrudates stays unclear. Further investigation of the expansion mechanism is still needed to improve and better control extrudate structure and quality. In this work, a visualisation technique combined with an image processing method is presented and used to observe and quantify melt expansion and shrinkage at the extrusion die. This allowed measurement of expansion and shrinkage indices in both sectional and longitudinal directions, and determine characteristic times of expansion and shrinkage phases. The experimental results are then interpreted and discussed based on a theoretical development derived from the bubble growth modelling in high viscosity medium (Amon & Denson, 1984).
1990). According to the chosen steady-state extrusion cooking conditions, final feed rate and screw speed ranged from 25.4 to 43 kg/h and from 120 to 190 rpm, respectively, while the moisture content was kept constant at 18.4% (wet weight basis). On exiting the die, the cooked melt was directly visualised by a CCD camera and extrudate samples, 50 cm long, were cut once the melt shrinkage after the water vapour flashing was complete. Moisture content of stored extrudates was between 2% and 3% (wet weight basis). 2.2. Measurement of melt apparent viscosity Assuming that no slip occurred at the walls of the capillary viscometer, and the flow was fully developed in the axial direction, the wall shear stress, sw , could be calculated as follows:
2. Materials and methods sw ¼ 2.1. Extrusion-cooking experiments The extrusion-cooking experiments were carried out in a CLEXTRAL BC 45 corotating twin-screw extruder. The food mix consisted of corn grits (average particle size of 300 lm) with low moisture content in the extruder (18.4% wet weight basis). The screw-barrel assembly (L=D of 9) consisted of a 500 mm barrel in which the screw profile used had two 250 mm sections: with one 250 mm feeding section and one 250 mm compression and shearing section. The second section was heated by a 7 kW induction heater controlled at the desired wall temperature of 160 C. The mix was fed into the extruder at a constant mass flow rate, and water was added into the first section. The screw-barrel assembly terminated with a front die plate, where the pressure and the melt temperature were measured. The distance between the end points of the screws and the front die plate was adjusted to 1.5 mm. All the extruded mixture had to pass through a 5 mm diameter, 5 mm length orifice in the front die plate, and then into the viscometer. The extruder-viscometer assembly was characterised by a 9.24 mm hydraulic diameter (Dh ) and a 1.04 shape factor of the cross-section (k). An electrical resistance heater, combined with a temperature control system and a thermocouple, was used to maintain the melt temperature in the viscometer close to that in the front die plate. The extruded melt left the viscometer through a circular die in which length Ld and diameter Dd varied from 12 to 80 mm and from 5 to 8 mm respectively. Thus, the length to diameter ratio varied from 2 to 13.3. Experimental methodology of starting the extruder was described previously by Wang, Bouvier, and Gelus (1990), and the operating conditions (feed rate and screw speed) were changed simultaneously so as to apply a constant specific mechanical energy of 500 kJ/kg (Wang et al.,
Dh DPV LV
ð1Þ
where Dh is the hydraulic diameter of the channel of the viscometer, LV is the length across which a pressure drop, DPV , is measured. The wall shear rate, c_ w , could be calculated by c_ w ¼ k
ð3n þ 1Þ 32Q 4n pD3h
ð2Þ
Q is the feed rate (m3 /s) and n is the flow index of cornbased extrusion-cooked melt. Melt density within the capillary viscometer is assumed constant and equal to 1400 kg m3 . The melt apparent viscosity in the capillary viscometer, ðla ÞV , is calculated by sw ðla ÞV ¼ ð3Þ c_ w The melt apparent viscosity in the die insert, ðla Þd , was obtained by neglecting changes in the temperature between the capillary viscometer and the die insert, and by neglecting the entrance effects in the die. Then, the melt apparent viscosity in the die insert is calculated by !n1 ðc_ w Þd ðla Þd ¼ ðla ÞV ð4Þ ðc_ w ÞV ðc_ w Þd is the wall shear rate in the die. Fig. 1 shows the evolution of the melt apparent viscosity as a function of the wall shear rate in the die insert. For a constant temperature, of about 160 C, a constant specific mechanical energy of 500 kJ/kg and a constant moisture content (18.4%), the melt apparent viscosity decreases from 870 to 160 Pa s when the wall shear rate increases from 190 to 1300 s1 ; this illustrates clearly the shear-thinning behaviour of the corn-based extrusioncooked melt. The experimental values can be modelled by use of a power law equation, as follows:
A. Arhaliass et al. / Journal of Food Engineering 60 (2003) 185–192
ture content of the melt in the die and moisture content of the extrudate, respectively. As extrudates had a circular shape, the volume was estimated from the two characteristic dimensions of the final product at three different locations per extrudate. Volume and weight of extrudates were determined on eight samples in order to calculate the apparent density.
1000
Apparent viscosity, Pa.s
187
500
3. Results and discussion 0
0
500
(γ w ) d , s −1
1000
1500
Fig. 1. Melt apparent viscosity versus wall shear rate in the die insert.
0:22
ðsw Þd ¼ 10:2ððc_ w Þd Þ
ð5Þ
The low value of the flow index of the cooked melt (n ¼ 0:22) is in good agreement with values obtained in previous studies (Singh & Smith, 1999). 2.3. Experimental observation of melt expansion An original visualisation technique was specifically developed to observe the dynamics of melt expansion at the die. This technique consisted of a lighting system together with a CCD camera (XC77RRCE Sony), equipped with an electronic shutter. The extruded melt was illuminated with a white light and the intensity of the light distribution over the product was visualised in real time (Pasquet, Arhaliass, Pain, & Bouvier, 1997; Pasquet & Arhaliass, 1997). The injection of a tracer allowed the visualisation of growth and shrinkage phenomena, and the image analysis of tracer trajectory lead to measure the characteristic times of growth and shrinkage phases. Images were recorded during 10 s with an acquisition period of 0.05 s under a high shutter speed (104 Hz), so that to examine the different brightness regions of the product spot image.
3.1. Melt expansion at the die insert Fig. 2 clearly shows the formation of the steam-induced bubbles at the exit of the die insert, and the evolution of the cell network of the extrudate matrix. As the melt flows into the die, its pressure and temperature are about 40–120 bars and 150–180 C, respectively. At such conditions, water is in liquid state and perfectly mixed with the starch melt. When it emerges from the die, the cooked melt suddenly goes from high pressure to atmospheric pressure. This pressure drop causes an extensive flash-off of internal moisture and the water vapour pressure, which is nucleated to form bubbles in the molten extrudate, allows the expansion of the melt. As shown in Fig. 2, two main phases may be distinguished in the expansion process: A growth phase which takes place quasi-adiabatically. It comprises the nucleation and growth of water vapour bubbles, up to a maximum expansion where steam is released to the environment. Let tg , be the duration time of melt growth from insert outlet to maximum expansion. Fig. 3 shows that the adiabatic step occurs very quickly, as melt growth time varies between 44 and 87 ms. At maximum expansion, rupture of steam bubbles is then caused by the loss of cell wall resistance which can no longer sustain the water vapour pressure inside the bubbles. Rupture of bubbles must occur
2.4. Expansion indices Expansion of dried extrudates was characterised by the classical expansion indices, such as the sectional expansion index (SEI), the longitudinal expansion index (LEI), and the volume expansion index (VEI), as described by Alvarez-Martinez et al. (1988): SEI ¼
Se ; Sd
LEI ¼
qd Sd ð1 Hd Þ ; qe Se ð1 He Þ
ð6Þ
VEI ¼ SEI LEI where qd is the melt density in the die; qe is the apparent density of the extrudate; Se and Sd are the cross-sections of extrudate and die, respectively; Hd and He are mois-
Fig. 2. Expansion and shrinkage of the melt at the die insert (insert diameter: 6 mm, insert length: 29 mm, throughput: Q ¼ 43 kg/h).
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120
Dd = 5 mm
tg, ms
80
40
Dd = 8 mm
0 0
40
ts, ms
80
120
Fig. 3. Melt growth time as a function of melt shrinkage time. (j) Dd ¼ 5 mm, Ld ¼ 29 mm; (N) Dd ¼ 6 mm, Ld ¼ 29 mm; (r) Dd ¼ 7 mm, Ld ¼ 29 mm; () Dd ¼ 8 mm, Ld ¼ 29 mm; (‘) Dd ¼ 6 mm, Ld ¼ 12–80 mm.
because the water balance calculated before and after expansion, reveals larger amount of water loss than the air volume of final extrudate. This results in water vapour loss and an open foam structure in the extrudate. During the steam release, the heat necessary to vaporise liquid water causes a fast cooling of the melt, down to approximately 100 C. A shrinkage phase when the steam release is completed. Let ts , be the duration time of melt shrinkage from maximum expansion to the equilibrium of shrinkage. Fig. 3 shows that shrinkage phase occurs also quickly, as melt shrinkage time varies between 24 and 115 ms. During shrinkage, the structure of the expanded melt changes from an open to a closed foam structure. Fig. 4a and b show the effect of feed rate on growth and shrinkage phenomena, at constant die insert diameter (Dd ¼ 6 mm) and insert land length (Ld ¼ 40 mm). It occurs that both Dg and Ds of growth and shrinkage phases increase very slightly when feed rate increases from 25.4 kg/h (Fig. 4a) to 32.3 kg/h (Fig. 4b). The influence of die insert diameter is presented in Fig. 4c and d, at constant feed rate (32.3 kg/h) and die land length (29 mm). The data show that melt diameter at maximum expansion (Dg ) and melt diameter at the equilibrium of shrinkage (Ds ) increase very importantly when die insert diameter decreases. It must be noted that the extent of shrinkage increases notably as die insert diameter increases. Fig. 4e and f show the effect of die land length, at constant feed rate (32.3 kg/h) and die insert diameter (6 mm). Die land length has very little effect on growth and shrinkage phases: both Dg and Ds increase very slightly when insert land length increases; the extent of shrinkage increases as insert land length decreases. In conclusion, it appears that melt expansion at the die insert is very much affected by the insert diameter: the lower the die insert diameter, the larger the melt
growth, and the larger the extent of melt shrinkage. But, both feed rate and insert land length do not influence significantly melt growth and shrinkage. After shrinkage, the melt cools due to convective heat exchange between ambient air and texturizing extrudate. As its temperature decreases, the melt reaches a temperature at which bubble wall movement ceases because its viscosity becomes extremely high as it approaches the glass transition temperature, Tg . Mitchell et al. (1994), stipulated that bubble wall movement would stop around (Tg þ 40 C), where the extrudate starts to fix its internal structure. 3.2. Physical analysis of growth and shrinkage phases The dynamics of melt expansion can be investigated by analysing the images of melt expansion at the die insert. This allows to determine physical parameters of both growth and shrinkage phases that are • Extrudate diameter at the maximum of the expansion: Dg • Distance from insert outlet to maximum expansion: Zg • Extrudate diameter at the equilibrium of shrinkage: Ds • Distance from maximum expansion to the equilibrium of shrinkage: Zs : The distance Zg and Zs together with the duration times tg and ts , allow to calculate the average growth velocity, Vg , and the average shrinkage velocity, Vs . Then, specific expansion indices of both growth and shrinkage phases can be deduced as follows: 2 Dg ðseiÞg ¼ ; Dd 1 Zg ; ðleiÞg ¼ Vd t g ðveiÞg ¼ ðseiÞg ðleiÞg 2 Ds ; ðseiÞs ¼ Dd 1 Zs ; ðleiÞg ¼ Vd t s ðveiÞs ¼ ðseiÞs ðleiÞs
ð7Þ
ð8Þ
where ðseiÞg , ðveiÞg and ðveiÞg are the sectional expansion index, the longitudinal expansion and the volumetric expansion index of the growth phase, respectively; ðseiÞs , ðleiÞs and ðveiÞs are the sectional expansion index, the longitudinal expansion index and the volumetric expansion index of the shrinkage phase respectively; Dd and Vd are the insert diameter and melt velocity in the die insert, respectively. It is worth noting that expansion indices SEI and LEI measured on final extrudates, and
A. Arhaliass et al. / Journal of Food Engineering 60 (2003) 185–192
189
Fig. 4. (a) and (b) Effect of feed rate on melt growth and melt shrinkage at the die insert: (a) Q ¼ 25:4 kg/h, Dd ¼ 6 mm, Ld ¼ 40 mm, Dg ¼ 24:1 mm, Ds ¼ 19:6 mm; (b) Q ¼ 32:3 kg/h, Dd ¼ 6 mm, Ld ¼ 40 mm, Dg ¼ 24:5 mm, Ds ¼ 20:3 mm. (c) and (d) Effect of insert diameter on melt growth and melt shrinkage at the die insert: (c) Dd ¼ 5 mm, Ld ¼ 29 mm, Q ¼ 32:3 kg/h, Dg ¼ 21:6 mm, Ds ¼ 17:3 mm; (d) Dd ¼ 8 mm, Ld ¼ 29 mm, Q ¼ 32:3 kg/h, Dg ¼ 28:9 mm, Ds ¼ 21:7 mm. (e) and (f) Effect of insert land length on melt growth and melt shrinkage at the die insert: (e) Ld ¼ 80 mm, Dd ¼ 6 mm, Q ¼ 25:4 kg/h, Dg ¼ 24:5 mm, Ds ¼ 20:5 mm (f): Ld ¼ 40 mm, Dd ¼ 6 mm, Q ¼ 25:4 kg/h, Dg ¼ 24:1 mm, Ds ¼ 19:6 mm.
expansion indices ðseiÞs and ðleiÞs determined by image analysis of melt expansion at the die insert, are well correlated. In fact, Fig. 5a and b show that the visualisation technique developed in this study gives expansion data which are in good agreement with those determined by the classical method introduced by Alvarez-Martinez et al. (1988). Fig. 6 shows ðleiÞg –ðseiÞg chart, that is the melt growth chart, with iso-ðveiÞg curves going from 5 to 15, and the isotropic expansion curve given by the equation 0:5 ðleiÞg ¼ ½ðseiÞg . This chart allows discussion of the characteristics of growth phase. It is shown that the radial expansion predominates importantly, as all samples reveal high ðseiÞg and low ðleiÞg values. Also, radial expansion tends to decrease, and consequently longitudinal expansion tends to increase when die insert diameter increases: the lower the die insert diameter, the higher the anisotropy of expansion. Such observation can be compared to die swell when extruding viscoelastic
polymer melts. It is known that starch-based biopolymer melts are viscoelastic, and radial expansion at the die insert would arise from the normal stresses generated by the shear flow within the die insert. It is worth noting that growth and shrinkage phases are dependent, as expansion indices of both phases are correlated. In fact, Fig. 7a shows a unique linear relationship between ðseiÞg and ðseiÞs : ðseiÞg ¼ 11 when ðseiÞs ¼ 0; the slope is around 0.5. However, the relation between ðleiÞg and ðleiÞs is influenced bye the geometrical characteristics of the die insert and by the feed rate (Fig. 7b). Although the mechanism of melt shrinkage is not well understood, three physical explanations may then be suggested. The first one could be due to vacuum shrinkage of closed steam bubbles. In fact, the expanded melt starts to shrink when the pressure inside the bubbles equals to atmospheric pressure. At that condition, the liquid water of the melt is in equilibrium with its
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20
25
20
(sei)s
(sei)g
15
10
(sei)g = 0.48(sei)s + 11
15
10
5
5
0
0 0
5
10
(a)
15
20
SEI
0
5
10
15
20
25
(sei)s
(a) 2.5
1.5
Dd = 8 mm
Q = 25.4 kg/h
2 Q = 32.3 kg/h
(lei)g
1
Q = 37.6 kg/h
(lei)s
1.5
Q = 43 kg/h
1
0.5 0.5 Dd = 5 mm
0
0 0
0.5
1
(b)
1.5
LEI
Fig. 5. (a) ðseiÞs as a function of SEI, (b) ðleiÞs as a function of LEI.
0
0.4
(b)
0.8
1.2
(lei)s
Fig. 7. (a) Correlation between ðseiÞg and ðseiÞs . (b) Correlation between ðleiÞg and ðleiÞs (Ld ¼ 29 mm; feed rate ¼ 25:4–43 kg/h). (j) Dd ¼ 5 mm, (N) Dd ¼ 6 mm, (r) Dd ¼ 7 mm, () Dd ¼ 8 mm.
5 0.5
(lei)g = (sei)g
(lei)g
4
3
2
1 (vei)g=15 (vei)g=10
(vei)g=5
0 0
5
10
15
20
25
(sei)g Fig. 6. Melt growth chart: ðleiÞg versus ðseiÞg (Ld ¼ 29 mm; feed rate ¼ 25:4–43 kg/h). (j) Dd ¼ 5 mm, (N) Dd ¼ 6 mm, (r) Dd ¼ 7 mm, () Dd ¼ 8 mm.
vapour phase, and then the partial pressure of water vapour depends on the temperature and entire composition of the melt. As the melt temperature decreases due to convective heat exchange between the hot melt and the surrounding air (ambient temperature), small amount of water vapour should condense which should tend to decrease the pressure inside the bubbles, and consequently create a light vacuum in bubbles and the shrinkage of the whole melt. But, such phenomenon
should follow the kinetics of heat exchange between the expanded melt and the surrounding air, and should occur over several seconds, much more than the shrinkage times observed in this study (25–115 ms). The second explanation might relate to surface tension forces which should contract each bubble and should occur quasi-instantaneously. Finally, the third explanation might be based on the elastic recovery of the melt after maximum expansion; elastic recovery should also occur instantaneously. For pseudo-elastic product, such as maize product, shrinkage phenomena is the result of instantaneous elastic recovery. 3.3. Melt growth modelling Expanding melt at the die insert can be considered as a network of steam bubbles surrounded by a viscous melt. Assuming that the melt is homogeneous and isothermal, each steam bubble follows the same expansion mechanism, and consequently behaves similarly to the expansion of the whole melt. Thus, the experimental data obtained from the expanding melt can be used to figure out the behaviour of steam bubbles. Consider a symmetrical spherical vapour bubble surrounded concentrically by a viscous medium. The
A. Arhaliass et al. / Journal of Food Engineering 60 (2003) 185–192
dR DP ¼ dt R 4ðla Þd
ð9Þ
where DP ¼ Pv Pa is assumed to be a function of temperature only; Pv and Pa are vapour pressure at melt temperature in the die and atmospheric pressure, respectively; R is the radius of a vapour bubble; ðla Þd is the melt apparent viscosity in the die insert. The bubble growth dynamics depends on thermorheological properties of the melt. Eq. (9) shows a quantity t0 ¼ ðla Þd =DP , which is the characteristic time of bubble formation (Mitchell et al., 1994). t0 can be considered as the characteristic time of melt growth at the die insert. Fig. 8 presents the relationship between tg and t0 . It occurs that tg decreases when t0 increases, that is when the melt temperature at the die insert decreases; in such condition, a temperature decrease would tend to reinforce the melt elasticity, and so to decrease the growth time of steam bubbles, tg . Based on the experimental data obtained with corn grits in this study, the evolution of tg as a function of t0 follows a power law equation, as follows: tg ¼ bðt0 Þa ;
b ¼ 3 103 ; a ¼ 1:4
ð10Þ
where the parameters a and b are only function of the type of the starch melt. Eq. (9) can be integrated for one steam bubble, when assuming an isothermal flow (Pv R3 ¼ cte), and neglecting the effects of elasticity and surface tension of the
tg, s
0.1
0.05
25
Growth expansion index
bubble growth is controlled by the pressure difference (DP ) between the vapour pressure of water at the melt temperature and the atmospheric pressure, and by the apparent viscosity of the melt as well as the surface tension (Amon & Denson, 1984). Taking into account the boundary conditions of the melt/vapour interface and neglecting the inertial effects (the melt is highly viscous) and the surface tension, the dynamics of bubble growth in a viscous melt is given by
191
20
15
10
5
0 0
100
200
tg/t0
300
Fig. 9. Radial and volumetric expansion indices as a function of tg =t0 , in growth phase (d: ðveiÞg and j: ðseiÞg ).
melt. This leads to describe the dynamics of the bubble growth: 3 Rg tg ¼aþb ð11Þ Ri t0 where a and b are function of the initial radius of the bubble, Ri , at the exit of the die insert. Ri is assumed to be only function of the die radius (Ri ¼ eRd ), and Rg is the bubble radius at the maximum expansion. Eq. (11) predicts that the bubble growth, and consequently the melt growth, is linearly correlated with the ratio tg =t0 . The experimental results are in good agreement with that prediction (Fig. 9) as the volumetric expansion index is proportional to tg =t0 . The sectional expansion index, ðseiÞg , is not linearly correlated with tg =t0 ; but it shows a slight decrease of the slope when tg =t0 increases, which should be due to the reinforcement of the elastic properties of the melt as tg =t0 increases. 4. Conclusion This experimental investigation has proven that melt expansion at the exit of the die insert showed two distinct phases: a growth phase followed by a shrinkage phase. The melt growth is apparently governed by the viscous characteristic time of the melt; whereas the bubble structure of the melt would be controlled by the elastic properties of the melt. This tends to favour importantly the radial expansion, which generates some anisotropy in the internal structure of the expanding melt. This result is important as it determines the ultimate texture, and so the textural quality of expanded extrudates. References
0 0
0.0005
0.001
0.0015
t0, s Fig. 8. Evolution of tg as a function of t0 .
0.002
Alvarez-Martinez, L., Kondury, K. P., & Harper, J. M. (1988). A general model for expansion of extruded products. Journal of Food Science, 53(2), 609–615.
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