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An Experimental and Theoretical Investigation of Bread Dough Sheeting
0960–3085/05/$30.00+0.00 # 2005 Institution of Chemical Engineers Trans IChemE, Part C, September 2005 Food and Bioproducts Processing, 83(C3): 175– 184
www.icheme.org/journals doi: 10.1205/fbp.04184
AN EXPERIMENTAL AND THEORETICAL INVESTIGATION OF BREAD DOUGH SHEETING J. ENGMANN1 , M. C. PECK2 and D. I. WILSON2 1 Nestle´ Product Technology Centre Kemptthal, Kemptthal, Switzerland Department of Chemical Engineering, University of Cambridge, Cambridge, UK
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he forming of wheat flour dough sheets passing through a pair of cylindrical rolls is studied experimentally and theoretically with regards to the stresses and strains experienced by the dough. Experimental information is obtained using an instrumented sheeting apparatus, which is similar in scale to small bakery equipment. The ratio of the feed sheet thickness to the roller gap width has a strong influence on strains and stresses, whereas the speed of the rollers is found to be of comparatively minor importance. An approximate model for the sheeting of dough is developed and compared to the experimental data. The model is able to predict the detachment thickness correctly, but not the final thickness of the sheet—most likely due to viscoelastic recoil after detachment—nor the experimentally observed forces, torques and surface normal stresses. Keywords: sheeting; bread dough; modelling; power law fluid.
INTRODUCTION
sheet and rolls, gap setting, speed of rolls and conveyor system, contact between rolls and dough). However, any mechanism postulated for the effects of sheeting on dough structure, dough rheology and on the baked product, should be related to the kinematics (strains) and/or dynamics (stresses, pressure, dissipated work) of the sheeting process. It is therefore desirable to understand how the process conditions in sheeting influence the strains and stresses imparted on the dough. It is not expected that such information alone will be sufficient to explain the effect of sheeting on dough structure, as this will also depend on other physico-chemical interactions (e.g., between gluten proteins and water), which may in turn depend strongly on the recipe, but it provides a necessary step towards an explanation. The flow of materials dragged between sheeting rolls has been described mathematically by a number of authors in the areas of metal forming (Hill, 1998; Chakrabarty, 1987; Wagoner and Chenot, 2001) and polymer processing (Kiparissides and Vlachopoulos, 1976; Middleman, 1977; Chung, 1983; Zahorski, 1986; Zheng and Tanner, 1988). The terminology and mathematical approaches used in the two fields are quite different, as are the rheological characteristics of the materials studied. Metal forming approaches are usually based on solid mechanics, use elastic – plastic constitutive equations with little or no rate dependence and consider different types of friction and slippage between the workpiece and sheeting rolls. Polymer processing approaches are based on fluid mechanics, use inelastic or viscoelastic rate-dependent constitutive equations and assume continuity of velocity between the worked material and the sheeting rolls. In metals processing one usually
Sheeting between counter-rotating rolls (as shown in Figure 1) is used by the baking industry as a dough forming process for a wide range of products, such as cookies, crackers, pizza, bread and pastry (Levine and Drew, 1990). Interest in a better understanding of the process arises from the fact that the sheeting process has been reported to have an impact on the dough’s behaviour in subsequent process steps, particularly proving and baking, and on the properties of the final products. Kilborn and Tipples (1974) as well as Morgenstern et al. (1999) found that the volume and crumb structure of bread could be modified by the number of sheetings that a dough was subjected to. Stenvert et al. (1979) reported the build-up and breakdown of a protein network structure with repeated sheeting and Moss (1980) found that the rheology of dough, characterized by extension testing, was influenced by the number of sheetings, with doughs becoming less resistant and more extensible during sheeting. Erlebach (1998) found that sheeting of bread dough increased the amount of elongated bubbles (‘streaking’) in bread produced from that dough and Morgenstern et al. (1999) reported the resistance and rupture stress of bread dough to reach a maximum after a small number of passes and to decrease thereafter. The above studies considered the number of sheetings rather than the sheeting process conditions (geometry of Correspondence to: Dr. J. Engmann, Nestle´ Research Center, Vers-chez-lesBlanc, P.O. Box 44, 1000 Lausanne 26, Switzerland. E-mail: [email protected]
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Figure 1. Schematic of rolling of a sheet through co-rotating rollers: A—attachment point; D—detachment point.
speaks of ‘rolling’ whereas ‘calendering’ is the term used in polymer processing. An intermediate class of materials are high solids fraction solid –liquid pastes, which exhibit a mixture of metal (large yield stress) and fluid (rate dependency) behaviours. Recent work by Peck (2002) has shown that the most appropriate technique to model pastes undergoing rolling depends strongly on the balance between these characteristics. Application of the models used in polymer processing to dough sheeting is most notably the work by Levine and co-workers (e.g., Levine, 1985; Levine and Drew, 1990) who have also explored modifications to the polymer calendering models such as differential roll speeds (Levine, 1996), dough compressibility (Levine, 1998) and lateral spreading of dough (Reid et al., 2001; Levine et al., 2002). Raghavan et al. (1995, 1996) assumed certain polynomial relations between the rheological material parameters and the fat, salt and water content of traditional Indian bread doughs and fitted power consumption data for dough sheeting to model predictions by optimization algorithms. Erlebach (1998) used one of Levine’s models to calculate approximate shear and extensional strains experienced by dough during sheeting and also explored numerical solutions for Newtonian and Bird –Carreau fluids in sheeting using the commercial finite-element software POLYFLOW (Fluent, Inc.). Whilst we also discuss a variation of polymer calendaring models in the second part of this paper, our main intention is to present some experimental data for both kinematic variables (bulk strains) and dynamic variables (roll closing force, energy input, surface normal stress) in a model sheeting process for a simple bread dough. This allows us to understand some of the main trends associated with different sheeting conditions and to assess the usefulness of different models to describe the sheeting process of bread doughs.
match any industrially used dough, this mixing procedure was developed with the help of an industrial baker to ensure that the dough was sufficiently ‘developed’ after mixing and thus comparable to a bread dough. For the preparation of the dough feed sheets, a piece of dough was cut from the mixed batch immediately after mixing and rolled out with a wooden cylinder on a kitchen board between two sheets of non-stick baking paper. Two brass rails were placed on either side of the dough piece to avoid reducing the dough to a lower thickness than desired. The sheet was then cut into 6 – 9 rectangular pieces with a pizza cutter (see Figure 2). The dimensions and thickness of the feed sheets were measured using a transparent ruler and calipers after the preparation and once again immediately before feeding them into the rotating rolls. For each batch of dough sheets a single setting of the roller gap, h0, was used. Since the thickness of the dough sheets varied considerably, this kept the variation of thickness reductions (¼hf/h0, frequently also referred to as ‘reduction ratio’ and abbreviated as RR in this paper) for each batch within reasonable limits. The speed of the rolls was usually kept constant throughout the experiment for each batch of dough sheets, but in some cases a different speed was chosen for each feed sheet. When this was done, the sequence was chosen such that the correlation between roll speed and dough age was minimal. Except for a few experiments where the sheets’ surfaces were deliberately sprinkled with flour prior to sheeting, the sheets always stuck to one of the rolls after leaving the gap. In nearly all cases the ‘sticky’ face was the face of the sheet which had been less exposed to air prior to sheeting and hence featured a higher moisture content. Rolled sheet width and thickness could therefore be conveniently measured on the rollers. A transparent ruler and calipers. Rolling tests were performed on an instrumented pilotscale unit previously developed and used in a study of ceramic pastes and biscuit doughs (Peck, 2002), shown schematically in Figure 3. The apparatus consisted of an electric motor driving two counter-rotating shafts connected by directly intermeshing cog wheels. Each shaft was fitted with a brass roller of diameter 100 mm and length 110 mm, connected via torque transducers so that the torque transmitted to each roller could be monitored individually. The roller separation could be varied between
EXPERIMENTAL The doughs, which were made from 2 kg Swiss wheat flour (Swissmill, ‘type 550’), 1.2 kg water, 60 g salt, 60 g fresh baker’s yeast and 60 g sunflower oil, were mixed in a Hobart A200 mixer fitted with a kneading hook (1 min at slow speed, followed by 5 min at medium speed). Although it was not the purpose of this study to precisely
Figure 2. Dough sheets after preparation for test in the sheeting apparatus.
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Figure 3. Sheeting apparatus.
0 and 40 mm, and this was monitored during sheeting by laser displacement sensors (Baumer Electric, resolution +60 mm). A load cell measured the roll separation force, while angular displacement was monitored to +18 via a light cell system. One roller surface contained a 100 kPa piezoelectric pressure sensor (Kulite Semiconductor Products, Basingstoke, UK) which indicated local normal stress. The circular flat surface of the transducer had a diameter of 3.75 mm, so that it was slightly recessed from the curved surface, by 0.1 mm. The transducer was connected to its instrumentation and a data-logging PC via slip rings. Although the instrumented sheeting apparatus differs significantly from industrial dough sheeting equipment, particularly with respect to the material and width of the rolls, the range of attainable thickness reductions and characteristic deformation rates included those of such equipment, thus giving useful experimental information, considering the effort that would be required to equip industrial dough sheeting equipment with equivalent instrumentation.
Figure 4 shows that after 40 min had elapsed, the feed thickness of the sheets increased markedly with time compared to the thickness immediately after preparation, as did the measured roll forces, F, torques, T (all expressed here per unit width) and surface normal stresses (represented by their maximum value, Pmax). We believe that the increase in the stresses with ageing (i.e., at preparation times larger than 40 min) is not primarily caused by rheological changes in the dough, but is mostly a consequence of the increase in sheet thickness. This is illustrated by plotting the forces, torques or maximum surface normal stresses for a given thickness reduction (RR) at different times. Figure 5 shows that once the variation of feed sheet thickness is eliminated, no significant ageing effect is evident, with the exception of the Pmax values at the highest thickness reduction. As a result of these trials, experiments were always carried out within a 40 minute ‘window’ following mixing to avoid changes in feed sheet thickness.
Dough Anisotropy EXPERIMENTAL RESULTS AND DISCUSSION Dough Ageing It has often been observed that the rheological properties of bread dough change with time (e.g., Dobraszczyk and Roberts, 1994). Potential mechanisms for such changes are stress relaxation within the microstructure, gas production by leaveners (e.g., yeast), enzymatic processes and drying of the sample surface. In our tests we observed that, for dough prepared in the above manner, there was little or no effect of ageing on feed sheet thickness and measured dynamic variables if the sheeting experiments were carried out less than 40 min after the end of mixing.
During the preparation of the doughs from an irregularlyshaped piece of mixed dough, the feed sheet was rolled out alternately in two directions perpendicular to each other, as it was speculated that an anisotropic texture may otherwise be produced. This hypothesis was also checked explicitly by rolling out some dough sheets in only one direction during sheet preparation. Some of these sheets were then fed into the rolling apparatus in this direction while others were turned by 908 before feeding. No significant effects were seen in the sheeted thickness, roll force, torque or normal stress, but the lateral spread (expressed as a percent increase in width) of the sheets was affected by the orientation in preparation. Whilst sheets fed to the rollers in the same direction as the preparative rolling
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Figure 4. Effect of dough ageing on dynamic variables and sheet height. Roll speed 2 rpm. Open symbols in (d)—sheet height after preparation; filled symbols—sheet height before rolling.
showed the same amount of spread observed in our usual experiments (around 10%), those sheets turned by 908 did not (on average) spread at all, and in some instances even exhibited lateral shrinkage (i.e., ‘negative spread’), as shown in Figure 6. The reason for this difference is presumably the tendency of the dough to minimize elongational stresses in the sheeting direction by extending laterally, constrained by the adherence to the rollers. For the sheets which were turned by 908, the dough had already been pre-stretched in this lateral direction and therefore lateral spreading was less favourable for minimizing elongational stresses. These experimental observations are in line with common practices in artisanal and industrial baking to reduce stress on the dough, such as folding dough back across the width of a sheet or using a ‘cross-roller’ between two thickness reduction steps. Apart from the effects on the shape of a dough product, gluten alignment induced by sheeting may also be a cause for elongated bubbles within the product, as was suggested in the case of bread doughs by Erlebach (1998). It would have also been interesting to investigate effects of repeated sheeting with the instrumented apparatus, but the configuration did not allow this to be pursued in a consistent manner. Variation Between Batches Initially, there was some concern about the reproducibility of mixing and thus the amount of variation to be expected for different batches of dough, so a relatively
large number of repetitions (eight) were performed for each combination of thickness reduction and roll speed. However, it was found that the variations between batches were not large compared to the variation of results within each batch, so the number of repetitions for each setting was reduced to 2 –3. Effect of Thickness Reduction Figure 7 shows that all dynamic parameters (roller force, roller torque, and maximum surface normal stress) increased more than proportionally with thickness reduction ratio hf/h0. Larger reduction ratios than those shown could not be achieved because the resulting normal stresses at the roller surface would have exceeded the range of the pressure transducer mounted in the roller. Furthermore, a flow instability was observed at the highest thickness reduction ratio (around 3.5), resulting in a rippled surface of the rolled sheets. This may be linked to recirculation near the contact point of the feed dough sheet with the roller (see Middleman, 1977; Pearson, 1985). From the width and thickness of the feed sheets and the rolled sheets, the ‘swell’ (percentage by which the sheeted dough exceeded the gap thickness) and ‘spread’ (percentage by which the sheets increased in width) could be calculated. Figure 8 shows that both values increased with increasing reduction ratio, and that the scatter of the data for swell and spread from different experimental series was larger than that of the dynamic variables, particularly at high thickness reductions.
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Figure 6. Effect of anisotropy in dough preparation on lateral spreading. Roll speed 2.5 + 0.5 rpm. RR ¼ 2.4 + 0.2. Solid circles: rolling during sheet preparation and sheeting in same direction, solid line shows average value. Open circles: rolling during sheet preparation and sheeting at a 908 angle, dashed line shows averaged value.
stress growth in simple shear (data not reported). Transient shear stress data were measured since it seems not possible to obtain a (true) steady-shear viscosity for dough (PhanThien et al., 1997; Bagley et al., 1998) and the Cox – Merz rule, by which a steady-shear viscosity can sometimes be directly related to linear viscoelastic properties, cannot a priori be expected to be applicable to bread dough. Correlation Between Dynamic Variables Figure 10 shows that for the range of process parameters studied, the dynamic variables (roll force, torque,
Figure 5. Independence of dynamic variables from dough ageing. Symbols: circle—RR ¼ 3.0 + 0.1; triangles—RR ¼ 2.2 + 0.1; squares— RR ¼ 1.5 + 0.1. Rolling speed (mostly) at 2 rpm.
Effect of Roll Speed Figure 9 indicates that all dynamic rolling variables increased less than proportionally with roll speed, which suggests shear-rate-thinning behaviour of the dough. At an RR value of approximately 2.2, where we collected most data for different roll speeds, the rate dependence can be represented with a power-law index of approximately 0.25 –0.3. This was in good agreement with the values obtained from a double logarithmic plot of transient shear stress (at equivalent shear strain) versus shear rate from data obtained using a Rheometrics ARES device using a parallel-plate configuration to measure transient
Figure 7. Effect of thickness reduction ratio on rolling parameters. Roll speed: 2 rpm.
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Figure 8. Effect of reduction ratio RR on final strains.
maximum surface normal stress) were strongly correlated, as has previously been suggested and experimentally observed by Levine (1996) for a smaller set of experimental data. This result implies that accurate measurement of the time evolution of one of these values during the sheeting process may be sufficient to qualitatively predict the time evolution of the other variables. This may prove useful in developing online methods for quality control in dough processing lines, where one of the variables may be measured more readily than the others and may be used to indicate, for example, changes in mixer performance or effects of changing process line temperature on the dough properties. MATHEMATICAL MODEL OF THE SHEETING PROCESS A simple existing model for the sheeting process has been used here to generate testable predictions for the effects of feed thickness and roll speed on the stresses and strains imparted to the dough, for comparison with our experimental results. We apply the ‘lubrication approximation’ for the equations of motion in nearly parallel flow which has been used previously for the calendering of polymers (Middleman, 1977) and wheat flour doughs (Levine and Drew, 1990). In this approximation, the equations of motion reduce to @P @txy @x @y @P 0 @y
Figure 9. Effect of roll speed. Symbols: circles—RR ¼ 3.0 + 0.1; diamonds, RR ¼ 2.2 + 0.1; squares, RR ¼ 1.5 + 0.1.
Additionally, it is assumed that the pressure gradient @P/@x tends to zero at the detachment point, thereby allowing the detachment point to be located. An inelastic power-law model is used for the dough rheology
(1)
txy ¼ K
n @ux @y
(3)
(2)
and the pressure P is assumed to be atmospheric at the attachment and detachment sections of the sheet and the rolls (marked A and D on Figure 1, respectively).
where K is the consistency and n the flow index of the material. The compressibility of the dough can also be considered, as described previously by Levine (1998), by requiring the mass flow rate, rather than the volumetric flow rate, to be
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AN EXPERIMENTAL AND THEORETICAL INVESTIGATION OF BREAD DOUGH SHEETING us (assuming no slip), were used: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi h(x) ¼ h0 þ R 1 1 (x=R)2 h(x) h0 us,x (x) ¼ vR 1 R
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(6) (7)
The equations were solved using an explicit numerical integration approach on a Microsoft ExcelTM spreadsheet. Since the ‘lubrication approximation’ contained in equations (1) and (2) is only strictly accurate in the limit h0 R, no major accuracy improvement is actually gained by using equations (6) and (7), but using these in the numerical scheme, which was primarily employed in order to allow introduction of compressibility in the model, does not introduce additional complexity.
Basic Trend Predictions
Figure 10. Correlation between torque, roll separating force and maximum surface normal stress. Reduction ratio RR ¼ 2–4.5, roll speed: 2 rpm.
constant and by assuming gas compressibility to be governed by the ideal gas law (at constant temperature), viz. P Pf ¼ r rf
(4)
which gives the following expression for the dough density dependence on pressure
r ¼ rf
fþ1 (Pf =P)f þ 1
(5)
where f is the initial relative volume, or void fraction, of gas in the dough (Vgas,f/Vtotal,f) and the subscript f denotes the feed condition. This expression predicts that the dough density converges to the ‘liquid dough’ density rf as the pressure approaches infinity and gives a pressure-independent density for vanishing gas content f. This simple model does not consider mass transfer between bubbles and ‘liquid dough’ (which would affect the void fraction), nor bubble deformation, orientation or break-up (which would not affect the void fraction, but the rheology of the dough). To describe the circular roller surface and the velocity along the roller surface, approximations are often used to obtain analytical solutions for the pressure P(x) and velocity ux(x, y). Here we have used a numerical (finite difference) approach here to solve the stress equation, so the exact expressions for roller surface and surface velocity,
A dimensional analysis of the model equations yields a set of dimensionless relationships for the dependence of final sheet half-thickness (h ), flow rate (Q), roll separating force per unit width (F), roll torque per unit width (T) and maximum surface normal stress (Pmax) on the feed sheet half-thickness (hf), gap half-width (h0), roll radius (R), dough rheological properties (K, n), relative gas volume (f) and rolling speed (v): h hf R ¼ f1 , , n, f (8) h0 h0 h0 Q=W hf R ¼ f2 , , n, f (9) vRh0 h0 h0 F=R hf R ; F ¼ f3 , , n, f (10) K(vR=h0 )n h0 h 0 T=(Rh0 ) hf R ; T ¼ f4 , , n, f (11) K(vR=h0 )n h0 h0 Pmax hf R ; Pmax ¼ f5 , , n, f (12) K(vR=h0 )n h 0 h0 This analysis shows that a change in power-law consistency K has no effect on the flow kinematics [equations (8) and (9)] whereas the dynamic properties (F, T, Pmax) are proportional to the consistency [equations (10) –(12)]. The roll speed has no effect on the sheet thickness, while the flow rate scales proportionally with the roll speed v and the dynamic properties increase with the roll speed raised to the power of n. Exact or approximate solutions of the model equations therefore provide only additional information concerning the effect of the four dimensionless variables: reduction ratio, radius-to-gap-ratio, flow index and gas content. Model solutions were generated for parameters lying within the parameter range relevant to our experimental data, and the results are now presented and discussed. Figures 11 and 12 show that the sheeted thickness (relative to gap width) is not very sensitive to gap width/roller ratio R/h0 or flow index n, but depends more strongly on the reduction ratio, RR. The dependence on R/h0 arises from the use of equation (6), whereas the commonly used
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Figure 11. Dependence of sheeted thickness on ratio of roller radius to gap width. Circles, RR ¼ 2; triangles, RR ¼ 4.
parabolic approximation to (6) would yield a sheeted thickness independent of R/h0. However, it must again be pointed out that the accuracy of the lubrication approximation contained in (1) and (2) deteriorates rapidly for small values of R/h0. The dependency of the flow rate on n and RR is essentially the same as for the sheeted thickness since they are related via the exit velocity, which depends only very weakly on the location of the detachment point. The very large values of RR in Figure 12 are unlikely to be achievable in practice, so the plot indicates that the strong dependence of h /h0 on RR is likely to be observed over all practical reductions. Figure 13(a) shows that the (dimensionless) maximum depends strongly on the surface normal stress Pmax reduction ratio and weakly on the flow index, while the curves flatten out at higher reduction ratios. Similar behaviour was predicted for the roll separating force, plotted in Figure 13(b). Compressibility can be included in this approximation without much additional effort: the local flow rate from which the pressure gradient is calculated simply needs to be corrected with the local dough density, which depends on the local pressure. The initial gas content of the dough is unknown, but a value of 20% can be expected to represent a realistic upper limit (Campbell et al., 1998; Campbell, 2003). For this value of initial gas content, Figure 12 shows that the sheeted thickness and ‘swell’
Figure 12. Effect of flow index and reduction ratio on sheeted thickness, including compressibility. Solid circles, n ¼ 0.2; triangles, n ¼ 0.3. Open circles, n ¼ 0.2 with compressibility effect (for f ¼ 0.2).
Figure 13. Effect of reduction ratio on (a) maximum surface normal stress [non-dimensionalized as in equation (12)] and (b) roll separating force [non-dimensionalized as in equation (10)]. Solid lines, n ¼ 0.2; dashed line, n ¼ 0.3.
increase slightly. Calculations also showed that there was only a marginal effect on roll separating force and on Pmax.
COMPARISON OF MODEL AND EXPERIMENTS Figure 14 shows that the degree of swelling in the experiments increased with reduction ratio, as predicted by the model. At a fixed roll speed, the incompressible model underpredicted the degree of swelling by approximately a factor of two, and the compressible model improved the prediction only slightly. There are several possible explanations for this discrepancy. Adherence of the dough to the rolls (as mentioned above, the sheets always stuck to one of the rolls after passing through the apparatus) or non-Newtonian flow effects between the rolls could lead to later detachment and hence a greater sheet thickness. This should be indicated by the surface pressure transducer data. However, when determining the point where the surface normal stress recorded by the pressure transducer reaches zero, as illustrated in Figure 15, and calculating the gap between the rolls at this point, the detachment gap width agreed quite well with the predicted sheeted thickness, shown in Figure 14. It seems therefore likely that the observed greater final sheet thicknesses arise from the viscoelasticity of the dough (as previously observed by Morgenstern et al. 2000), causing residual
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Moreover, the experimental roll torque data were an order of magnitude smaller than the model estimates, if the power-law consistency was chosen such that the roll separating forces were best fitted. The simple lubrication model is therefore unable to quantify the gross behaviour of the system (reflected in torque and separating forces) accurately.
CONCLUSIONS
Figure 14. Effect of thickness reduction ratio (RR) on sheet thickness. Solid circles, calculated from detachment via surface normal stress profile; open circles, measured from sheet on roll; solid line, model prediction; dashed line, compressible dough model with f ¼ 0.20.
stresses in the sheet along the direction of sheeting and delayed recoil after detachment from one of the rolls. The experimental data also showed a weak dependence of sheet thickness on roll speed (not explicitly shown) whereas the model predicted no roll speed dependence because it has no time dependence. This indicates that there must be another time-dependent physical mechanism occurring in the sheeting process. When comparing the trends in roll separating force and surface normal stress in Figures 7(a) and (c) and 13(a) and (b), respectively, it is apparent that the model cannot correctly describe the dependence of the roll separating force and maximum surface normal stress on the reduction ratio, particularly for reduction ratios larger than three. While the model suggests convergence towards a finite value, the experimental data show a strong increase of the maximum stress with RR. This conclusion holds independently of the value of the power-law consistency K, which changes only the absolute values, but not the shape of the curves, as follows from equation (12). The strong increase of the normal stresses observed experimentally at high reduction ratios may be due to elastic stresses arising from the stretching of polymeric molecules (gluten proteins) in the dough, which is not accounted for by the simple inelastic model.
Comparison of experimental data from the model sheeting system with predictions from an inelastic lubrication model, similar to the one described previously by Levine, showed that this model can correctly predict the detachment point for (at least some) viscoelastic bread doughs, but fails to predict the final sheeted thickness accurately. The thicknesses of the final sheets are significantly larger, therefore the disagreement between model and experiment is most likely due to substantial viscoelastic recoil after detachment, as was for the first time experimentally supported in this study via measurements of normal stresses directly at the roll surface. The agreement between experiment and model for the dynamic variables (surface normal stress, roll separating force and roll torque) is poor and may be attributed to the use of too simple a rheological model to describe a complex material such as bread dough. It is therefore of major interest to explore the consequences of more complex rheological models, even although this requires a much larger mathematical effort.
NOMENCLATURE hf h0 he h F F K n P Pmax Pmax Q R RR T u us,x V W x y
initial sheet half-thickness, m roller gap half-thickness, m rolled sheet final half-thickness, m final sheet half-thickness at detachment point, m roll separating force (per unit width), N m21 dimensionless roll separating force dough (shear) consistency, Pa sn dough shear index pressure, Pa maximum surface normal stress, Pa dimensionless maximum surface normal stress flow rate, m3 s21 roller radius, m reduction ratio normalized torque (per unit width), N m21 velocity, m s21 velocity in x direction at roller surface, m s21 volume, m3 sheet width, m cartesian co-ordinate, m cartesian co-ordinate, m
Greek symbols f initial relative volume of gas in dough r dough density, kg m23 t shear stress, Pa v roller rotational speed, rad s21
Figure 15. Surface normal stress profile during dough rolling. Roller position of zero corresponds to roll nip; negative values to feed side. Dashed line indicates detachment point (D in Figure 1).
Subscripts f feed condition 0 roll gap location
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Bagley, E.B., Dintzis, F.R. and Chakrabarti, S., 1998, Experimental and conceptual problems in the rheological characterization of wheat flour doughs, Rheologica Acta, 37: 556– 565. Campbell, G.M., Rielly, C.D., Fryer, P.J. and Sadd, P.A., 1998, Measurement and interpretation of dough densities, Food Bioprod Proc, 70(5): 517– 521. Campbell, G.M., 2003, Bread aeration, in Bread Making: Improving Quality, Cauvain, S.P. (ed.). 360 (Woodhead Publishing Ltd, Cambridge, UK). Chakrabarty, J., 1987, The Theory of Plasticity (McGraw-Hill, NY, USA). Chung, T., 1983, Analysis of the calendering of compressible fluids, J Appl Polym Sci, 28: 2119–2124. Dobraszczyk, B.J. and Roberts, C.A., 1994, Strain hardening and dough gas cell-wall failure in biaxial extension, J Cereal Sci, 20: 265–274. Erlebach, C.B., 1998, Bubble heterogeneities in bread caused by sheeting, PhD dissertation, University of Cambridge, Cambridge, UK. Hill, R., 1998, The Mathematical Theory of Plasticity (Clarendon Press, Oxford, UK). Kilborn, R.H. and Tipples, K.H. 1974, Implications of the mechanical development of bread dough by means of sheeting rolls, Cereal Chem, 51: 648. Kiparissides, C. and Vlachopoulos, J., 1976, The study of viscous dissipation in the calendering of power law fluids, Polym Eng Sci, 18: 210– 214. Levine, L., 1985, Throughput and power of dough sheeting rolls, J Food Proc Eng, 7: 223–228. Levine, L., 1996, Model for the sheeting of dough between rolls operating at different speeds, Cereal Foods World, 41(8): 690 –697. Levine, L., 1998, Models for dough compressibility in sheeting, Cereal Foods World, 43(8): 629–634. Levine, L. and Drew, B.A., 1990, Rheological and engineering aspects of the sheeting and laminating of doughs, in Dough Rheology and Baked Product Texture, Faridi, H.M. and Faubion, J.M. (eds). (van Nostrand Reinhold, NY, USA). Levine, L., Corvalan, C.M., Campanella, O.H. and Okos, M.R., 2002, A model describing the two-dimensional calendering of finite width sheets, Chem Eng Sci, 57: 643–650. Middleman, S., 1977, Fundamentals of Polymer Processing (McGrawHill, NY, USA). Morgenstern, M.P., Zheng, H., Ross, H. and Campanella, O.H., 1999, Rheological properties of sheeted wheat flour dough measured with large deformations, Intl J Food Prop, 2(3): 265– 275. Morgenstern, M.P., Wilson, A.J., Ross, M. and Al-Hakkak, F., 2000, The importance of visco-elasticity in sheeting of wheat flour dough, Proc 8th
Intl Congress on Engineering and Food (ICEF 8), Welti-Chanes, J., Barbosa-Ca´novas, G.V. and Aguilera, J.M. (eds). 519–523 (Technomic Publishing, Lancaster, UK). Moss, H.J., 1980, Strength requirements of doughs destined for repeated sheeting compared with those of normal doughs, Cereal Chem, 57: 195. Pearson, J.R.A., 1985, Mechanics of Polymer Processing, 362–392, (Elsevier, London, UK). Peck, M.C., 2002, Roller extrusion of pastes, PhD dissertation, University of Cambridge, Cambridge, UK. Phan-Thien, N., Safari-Ardi, M. and Morales-Patin˜o, A., 1997, Oscillatory and simple shear flows of a flour-water dough, Rheologica Acta, 36: 38–48. Raghavan, C.V., Chand, N., Srichandan Babu, R. and Srinivasa Rao, P.N., 1995, Modeling the power consumption during sheeting of doughs for traditional Indian foods, J Food Proc Eng, 18: 397–415. Raghavan, C.V., Srichandan Babu, R., Chand, N. and Srinivasa Rao, P.N., 1996, Response surface analysis of power consumption of dough sheeting as a function of gap reduction ratio, water, salt and fat, J Food Sci Tech, 33(4): 313–321. Reid, J.D., Corvalan, C.M., Levine, L., Campanella, O.H. and Okos, M.R., 2001, Estimation of final sheet width and the forces and power exerted by sheeting rolls, Cereal Food World, 46(2): 63– 69. Stenvert, N.L., Moss, R., Pointing, G., Worthington, G. and Bond, E.E., 1979, Bread production by dough rollers: influence of flour type formulation and process, Baker’s Digest, 53(2): 22– 27. Wagoner, R.H. and Chenot, J.-L., 2001, Metal Forming Analysis (Cambridge University Press, Cambridge, UK). Zahorski, S., 1986, Viscoelastic flow between two rotating cylinders— application to rolling or calendering processes, Archives of Mechanics, 38(4): 473–491. Zheng, R. and Tanner, R.I., 1988, A numerical analysis of calendering, J Non-Newtonian Fluid Mechanics, 28(2): 149–170.
ACKNOWLEDGEMENTS We are grateful to Nestec S.A., Switzerland, for permission to publish this work and to the reviewers of the manuscript for their insightful comments and suggestions. The support of Dr Simon Butler and Prof. Malcolm Mackley in generating rheological data is also gratefully acknowledged. The manuscript was received 7 July 2004 and accepted for publication after revision 15 April 2005.
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www.icheme.org/journals doi: 10.1205/fbp.04184
AN EXPERIMENTAL AND THEORETICAL INVESTIGATION OF BREAD DOUGH SHEETING J. ENGMANN1 , M. C. PECK2 and D. I. WILSON2 1 Nestle´ Product Technology Centre Kemptthal, Kemptthal, Switzerland Department of Chemical Engineering, University of Cambridge, Cambridge, UK
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he forming of wheat flour dough sheets passing through a pair of cylindrical rolls is studied experimentally and theoretically with regards to the stresses and strains experienced by the dough. Experimental information is obtained using an instrumented sheeting apparatus, which is similar in scale to small bakery equipment. The ratio of the feed sheet thickness to the roller gap width has a strong influence on strains and stresses, whereas the speed of the rollers is found to be of comparatively minor importance. An approximate model for the sheeting of dough is developed and compared to the experimental data. The model is able to predict the detachment thickness correctly, but not the final thickness of the sheet—most likely due to viscoelastic recoil after detachment—nor the experimentally observed forces, torques and surface normal stresses. Keywords: sheeting; bread dough; modelling; power law fluid.
INTRODUCTION
sheet and rolls, gap setting, speed of rolls and conveyor system, contact between rolls and dough). However, any mechanism postulated for the effects of sheeting on dough structure, dough rheology and on the baked product, should be related to the kinematics (strains) and/or dynamics (stresses, pressure, dissipated work) of the sheeting process. It is therefore desirable to understand how the process conditions in sheeting influence the strains and stresses imparted on the dough. It is not expected that such information alone will be sufficient to explain the effect of sheeting on dough structure, as this will also depend on other physico-chemical interactions (e.g., between gluten proteins and water), which may in turn depend strongly on the recipe, but it provides a necessary step towards an explanation. The flow of materials dragged between sheeting rolls has been described mathematically by a number of authors in the areas of metal forming (Hill, 1998; Chakrabarty, 1987; Wagoner and Chenot, 2001) and polymer processing (Kiparissides and Vlachopoulos, 1976; Middleman, 1977; Chung, 1983; Zahorski, 1986; Zheng and Tanner, 1988). The terminology and mathematical approaches used in the two fields are quite different, as are the rheological characteristics of the materials studied. Metal forming approaches are usually based on solid mechanics, use elastic – plastic constitutive equations with little or no rate dependence and consider different types of friction and slippage between the workpiece and sheeting rolls. Polymer processing approaches are based on fluid mechanics, use inelastic or viscoelastic rate-dependent constitutive equations and assume continuity of velocity between the worked material and the sheeting rolls. In metals processing one usually
Sheeting between counter-rotating rolls (as shown in Figure 1) is used by the baking industry as a dough forming process for a wide range of products, such as cookies, crackers, pizza, bread and pastry (Levine and Drew, 1990). Interest in a better understanding of the process arises from the fact that the sheeting process has been reported to have an impact on the dough’s behaviour in subsequent process steps, particularly proving and baking, and on the properties of the final products. Kilborn and Tipples (1974) as well as Morgenstern et al. (1999) found that the volume and crumb structure of bread could be modified by the number of sheetings that a dough was subjected to. Stenvert et al. (1979) reported the build-up and breakdown of a protein network structure with repeated sheeting and Moss (1980) found that the rheology of dough, characterized by extension testing, was influenced by the number of sheetings, with doughs becoming less resistant and more extensible during sheeting. Erlebach (1998) found that sheeting of bread dough increased the amount of elongated bubbles (‘streaking’) in bread produced from that dough and Morgenstern et al. (1999) reported the resistance and rupture stress of bread dough to reach a maximum after a small number of passes and to decrease thereafter. The above studies considered the number of sheetings rather than the sheeting process conditions (geometry of Correspondence to: Dr. J. Engmann, Nestle´ Research Center, Vers-chez-lesBlanc, P.O. Box 44, 1000 Lausanne 26, Switzerland. E-mail: [email protected]
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Figure 1. Schematic of rolling of a sheet through co-rotating rollers: A—attachment point; D—detachment point.
speaks of ‘rolling’ whereas ‘calendering’ is the term used in polymer processing. An intermediate class of materials are high solids fraction solid –liquid pastes, which exhibit a mixture of metal (large yield stress) and fluid (rate dependency) behaviours. Recent work by Peck (2002) has shown that the most appropriate technique to model pastes undergoing rolling depends strongly on the balance between these characteristics. Application of the models used in polymer processing to dough sheeting is most notably the work by Levine and co-workers (e.g., Levine, 1985; Levine and Drew, 1990) who have also explored modifications to the polymer calendering models such as differential roll speeds (Levine, 1996), dough compressibility (Levine, 1998) and lateral spreading of dough (Reid et al., 2001; Levine et al., 2002). Raghavan et al. (1995, 1996) assumed certain polynomial relations between the rheological material parameters and the fat, salt and water content of traditional Indian bread doughs and fitted power consumption data for dough sheeting to model predictions by optimization algorithms. Erlebach (1998) used one of Levine’s models to calculate approximate shear and extensional strains experienced by dough during sheeting and also explored numerical solutions for Newtonian and Bird –Carreau fluids in sheeting using the commercial finite-element software POLYFLOW (Fluent, Inc.). Whilst we also discuss a variation of polymer calendaring models in the second part of this paper, our main intention is to present some experimental data for both kinematic variables (bulk strains) and dynamic variables (roll closing force, energy input, surface normal stress) in a model sheeting process for a simple bread dough. This allows us to understand some of the main trends associated with different sheeting conditions and to assess the usefulness of different models to describe the sheeting process of bread doughs.
match any industrially used dough, this mixing procedure was developed with the help of an industrial baker to ensure that the dough was sufficiently ‘developed’ after mixing and thus comparable to a bread dough. For the preparation of the dough feed sheets, a piece of dough was cut from the mixed batch immediately after mixing and rolled out with a wooden cylinder on a kitchen board between two sheets of non-stick baking paper. Two brass rails were placed on either side of the dough piece to avoid reducing the dough to a lower thickness than desired. The sheet was then cut into 6 – 9 rectangular pieces with a pizza cutter (see Figure 2). The dimensions and thickness of the feed sheets were measured using a transparent ruler and calipers after the preparation and once again immediately before feeding them into the rotating rolls. For each batch of dough sheets a single setting of the roller gap, h0, was used. Since the thickness of the dough sheets varied considerably, this kept the variation of thickness reductions (¼hf/h0, frequently also referred to as ‘reduction ratio’ and abbreviated as RR in this paper) for each batch within reasonable limits. The speed of the rolls was usually kept constant throughout the experiment for each batch of dough sheets, but in some cases a different speed was chosen for each feed sheet. When this was done, the sequence was chosen such that the correlation between roll speed and dough age was minimal. Except for a few experiments where the sheets’ surfaces were deliberately sprinkled with flour prior to sheeting, the sheets always stuck to one of the rolls after leaving the gap. In nearly all cases the ‘sticky’ face was the face of the sheet which had been less exposed to air prior to sheeting and hence featured a higher moisture content. Rolled sheet width and thickness could therefore be conveniently measured on the rollers. A transparent ruler and calipers. Rolling tests were performed on an instrumented pilotscale unit previously developed and used in a study of ceramic pastes and biscuit doughs (Peck, 2002), shown schematically in Figure 3. The apparatus consisted of an electric motor driving two counter-rotating shafts connected by directly intermeshing cog wheels. Each shaft was fitted with a brass roller of diameter 100 mm and length 110 mm, connected via torque transducers so that the torque transmitted to each roller could be monitored individually. The roller separation could be varied between
EXPERIMENTAL The doughs, which were made from 2 kg Swiss wheat flour (Swissmill, ‘type 550’), 1.2 kg water, 60 g salt, 60 g fresh baker’s yeast and 60 g sunflower oil, were mixed in a Hobart A200 mixer fitted with a kneading hook (1 min at slow speed, followed by 5 min at medium speed). Although it was not the purpose of this study to precisely
Figure 2. Dough sheets after preparation for test in the sheeting apparatus.
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Figure 3. Sheeting apparatus.
0 and 40 mm, and this was monitored during sheeting by laser displacement sensors (Baumer Electric, resolution +60 mm). A load cell measured the roll separation force, while angular displacement was monitored to +18 via a light cell system. One roller surface contained a 100 kPa piezoelectric pressure sensor (Kulite Semiconductor Products, Basingstoke, UK) which indicated local normal stress. The circular flat surface of the transducer had a diameter of 3.75 mm, so that it was slightly recessed from the curved surface, by 0.1 mm. The transducer was connected to its instrumentation and a data-logging PC via slip rings. Although the instrumented sheeting apparatus differs significantly from industrial dough sheeting equipment, particularly with respect to the material and width of the rolls, the range of attainable thickness reductions and characteristic deformation rates included those of such equipment, thus giving useful experimental information, considering the effort that would be required to equip industrial dough sheeting equipment with equivalent instrumentation.
Figure 4 shows that after 40 min had elapsed, the feed thickness of the sheets increased markedly with time compared to the thickness immediately after preparation, as did the measured roll forces, F, torques, T (all expressed here per unit width) and surface normal stresses (represented by their maximum value, Pmax). We believe that the increase in the stresses with ageing (i.e., at preparation times larger than 40 min) is not primarily caused by rheological changes in the dough, but is mostly a consequence of the increase in sheet thickness. This is illustrated by plotting the forces, torques or maximum surface normal stresses for a given thickness reduction (RR) at different times. Figure 5 shows that once the variation of feed sheet thickness is eliminated, no significant ageing effect is evident, with the exception of the Pmax values at the highest thickness reduction. As a result of these trials, experiments were always carried out within a 40 minute ‘window’ following mixing to avoid changes in feed sheet thickness.
Dough Anisotropy EXPERIMENTAL RESULTS AND DISCUSSION Dough Ageing It has often been observed that the rheological properties of bread dough change with time (e.g., Dobraszczyk and Roberts, 1994). Potential mechanisms for such changes are stress relaxation within the microstructure, gas production by leaveners (e.g., yeast), enzymatic processes and drying of the sample surface. In our tests we observed that, for dough prepared in the above manner, there was little or no effect of ageing on feed sheet thickness and measured dynamic variables if the sheeting experiments were carried out less than 40 min after the end of mixing.
During the preparation of the doughs from an irregularlyshaped piece of mixed dough, the feed sheet was rolled out alternately in two directions perpendicular to each other, as it was speculated that an anisotropic texture may otherwise be produced. This hypothesis was also checked explicitly by rolling out some dough sheets in only one direction during sheet preparation. Some of these sheets were then fed into the rolling apparatus in this direction while others were turned by 908 before feeding. No significant effects were seen in the sheeted thickness, roll force, torque or normal stress, but the lateral spread (expressed as a percent increase in width) of the sheets was affected by the orientation in preparation. Whilst sheets fed to the rollers in the same direction as the preparative rolling
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Figure 4. Effect of dough ageing on dynamic variables and sheet height. Roll speed 2 rpm. Open symbols in (d)—sheet height after preparation; filled symbols—sheet height before rolling.
showed the same amount of spread observed in our usual experiments (around 10%), those sheets turned by 908 did not (on average) spread at all, and in some instances even exhibited lateral shrinkage (i.e., ‘negative spread’), as shown in Figure 6. The reason for this difference is presumably the tendency of the dough to minimize elongational stresses in the sheeting direction by extending laterally, constrained by the adherence to the rollers. For the sheets which were turned by 908, the dough had already been pre-stretched in this lateral direction and therefore lateral spreading was less favourable for minimizing elongational stresses. These experimental observations are in line with common practices in artisanal and industrial baking to reduce stress on the dough, such as folding dough back across the width of a sheet or using a ‘cross-roller’ between two thickness reduction steps. Apart from the effects on the shape of a dough product, gluten alignment induced by sheeting may also be a cause for elongated bubbles within the product, as was suggested in the case of bread doughs by Erlebach (1998). It would have also been interesting to investigate effects of repeated sheeting with the instrumented apparatus, but the configuration did not allow this to be pursued in a consistent manner. Variation Between Batches Initially, there was some concern about the reproducibility of mixing and thus the amount of variation to be expected for different batches of dough, so a relatively
large number of repetitions (eight) were performed for each combination of thickness reduction and roll speed. However, it was found that the variations between batches were not large compared to the variation of results within each batch, so the number of repetitions for each setting was reduced to 2 –3. Effect of Thickness Reduction Figure 7 shows that all dynamic parameters (roller force, roller torque, and maximum surface normal stress) increased more than proportionally with thickness reduction ratio hf/h0. Larger reduction ratios than those shown could not be achieved because the resulting normal stresses at the roller surface would have exceeded the range of the pressure transducer mounted in the roller. Furthermore, a flow instability was observed at the highest thickness reduction ratio (around 3.5), resulting in a rippled surface of the rolled sheets. This may be linked to recirculation near the contact point of the feed dough sheet with the roller (see Middleman, 1977; Pearson, 1985). From the width and thickness of the feed sheets and the rolled sheets, the ‘swell’ (percentage by which the sheeted dough exceeded the gap thickness) and ‘spread’ (percentage by which the sheets increased in width) could be calculated. Figure 8 shows that both values increased with increasing reduction ratio, and that the scatter of the data for swell and spread from different experimental series was larger than that of the dynamic variables, particularly at high thickness reductions.
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Figure 6. Effect of anisotropy in dough preparation on lateral spreading. Roll speed 2.5 + 0.5 rpm. RR ¼ 2.4 + 0.2. Solid circles: rolling during sheet preparation and sheeting in same direction, solid line shows average value. Open circles: rolling during sheet preparation and sheeting at a 908 angle, dashed line shows averaged value.
stress growth in simple shear (data not reported). Transient shear stress data were measured since it seems not possible to obtain a (true) steady-shear viscosity for dough (PhanThien et al., 1997; Bagley et al., 1998) and the Cox – Merz rule, by which a steady-shear viscosity can sometimes be directly related to linear viscoelastic properties, cannot a priori be expected to be applicable to bread dough. Correlation Between Dynamic Variables Figure 10 shows that for the range of process parameters studied, the dynamic variables (roll force, torque,
Figure 5. Independence of dynamic variables from dough ageing. Symbols: circle—RR ¼ 3.0 + 0.1; triangles—RR ¼ 2.2 + 0.1; squares— RR ¼ 1.5 + 0.1. Rolling speed (mostly) at 2 rpm.
Effect of Roll Speed Figure 9 indicates that all dynamic rolling variables increased less than proportionally with roll speed, which suggests shear-rate-thinning behaviour of the dough. At an RR value of approximately 2.2, where we collected most data for different roll speeds, the rate dependence can be represented with a power-law index of approximately 0.25 –0.3. This was in good agreement with the values obtained from a double logarithmic plot of transient shear stress (at equivalent shear strain) versus shear rate from data obtained using a Rheometrics ARES device using a parallel-plate configuration to measure transient
Figure 7. Effect of thickness reduction ratio on rolling parameters. Roll speed: 2 rpm.
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Figure 8. Effect of reduction ratio RR on final strains.
maximum surface normal stress) were strongly correlated, as has previously been suggested and experimentally observed by Levine (1996) for a smaller set of experimental data. This result implies that accurate measurement of the time evolution of one of these values during the sheeting process may be sufficient to qualitatively predict the time evolution of the other variables. This may prove useful in developing online methods for quality control in dough processing lines, where one of the variables may be measured more readily than the others and may be used to indicate, for example, changes in mixer performance or effects of changing process line temperature on the dough properties. MATHEMATICAL MODEL OF THE SHEETING PROCESS A simple existing model for the sheeting process has been used here to generate testable predictions for the effects of feed thickness and roll speed on the stresses and strains imparted to the dough, for comparison with our experimental results. We apply the ‘lubrication approximation’ for the equations of motion in nearly parallel flow which has been used previously for the calendering of polymers (Middleman, 1977) and wheat flour doughs (Levine and Drew, 1990). In this approximation, the equations of motion reduce to @P @txy @x @y @P 0 @y
Figure 9. Effect of roll speed. Symbols: circles—RR ¼ 3.0 + 0.1; diamonds, RR ¼ 2.2 + 0.1; squares, RR ¼ 1.5 + 0.1.
Additionally, it is assumed that the pressure gradient @P/@x tends to zero at the detachment point, thereby allowing the detachment point to be located. An inelastic power-law model is used for the dough rheology
(1)
txy ¼ K
n @ux @y
(3)
(2)
and the pressure P is assumed to be atmospheric at the attachment and detachment sections of the sheet and the rolls (marked A and D on Figure 1, respectively).
where K is the consistency and n the flow index of the material. The compressibility of the dough can also be considered, as described previously by Levine (1998), by requiring the mass flow rate, rather than the volumetric flow rate, to be
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AN EXPERIMENTAL AND THEORETICAL INVESTIGATION OF BREAD DOUGH SHEETING us (assuming no slip), were used: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi h(x) ¼ h0 þ R 1 1 (x=R)2 h(x) h0 us,x (x) ¼ vR 1 R
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(6) (7)
The equations were solved using an explicit numerical integration approach on a Microsoft ExcelTM spreadsheet. Since the ‘lubrication approximation’ contained in equations (1) and (2) is only strictly accurate in the limit h0 R, no major accuracy improvement is actually gained by using equations (6) and (7), but using these in the numerical scheme, which was primarily employed in order to allow introduction of compressibility in the model, does not introduce additional complexity.
Basic Trend Predictions
Figure 10. Correlation between torque, roll separating force and maximum surface normal stress. Reduction ratio RR ¼ 2–4.5, roll speed: 2 rpm.
constant and by assuming gas compressibility to be governed by the ideal gas law (at constant temperature), viz. P Pf ¼ r rf
(4)
which gives the following expression for the dough density dependence on pressure
r ¼ rf
fþ1 (Pf =P)f þ 1
(5)
where f is the initial relative volume, or void fraction, of gas in the dough (Vgas,f/Vtotal,f) and the subscript f denotes the feed condition. This expression predicts that the dough density converges to the ‘liquid dough’ density rf as the pressure approaches infinity and gives a pressure-independent density for vanishing gas content f. This simple model does not consider mass transfer between bubbles and ‘liquid dough’ (which would affect the void fraction), nor bubble deformation, orientation or break-up (which would not affect the void fraction, but the rheology of the dough). To describe the circular roller surface and the velocity along the roller surface, approximations are often used to obtain analytical solutions for the pressure P(x) and velocity ux(x, y). Here we have used a numerical (finite difference) approach here to solve the stress equation, so the exact expressions for roller surface and surface velocity,
A dimensional analysis of the model equations yields a set of dimensionless relationships for the dependence of final sheet half-thickness (h ), flow rate (Q), roll separating force per unit width (F), roll torque per unit width (T) and maximum surface normal stress (Pmax) on the feed sheet half-thickness (hf), gap half-width (h0), roll radius (R), dough rheological properties (K, n), relative gas volume (f) and rolling speed (v): h hf R ¼ f1 , , n, f (8) h0 h0 h0 Q=W hf R ¼ f2 , , n, f (9) vRh0 h0 h0 F=R hf R ; F ¼ f3 , , n, f (10) K(vR=h0 )n h0 h 0 T=(Rh0 ) hf R ; T ¼ f4 , , n, f (11) K(vR=h0 )n h0 h0 Pmax hf R ; Pmax ¼ f5 , , n, f (12) K(vR=h0 )n h 0 h0 This analysis shows that a change in power-law consistency K has no effect on the flow kinematics [equations (8) and (9)] whereas the dynamic properties (F, T, Pmax) are proportional to the consistency [equations (10) –(12)]. The roll speed has no effect on the sheet thickness, while the flow rate scales proportionally with the roll speed v and the dynamic properties increase with the roll speed raised to the power of n. Exact or approximate solutions of the model equations therefore provide only additional information concerning the effect of the four dimensionless variables: reduction ratio, radius-to-gap-ratio, flow index and gas content. Model solutions were generated for parameters lying within the parameter range relevant to our experimental data, and the results are now presented and discussed. Figures 11 and 12 show that the sheeted thickness (relative to gap width) is not very sensitive to gap width/roller ratio R/h0 or flow index n, but depends more strongly on the reduction ratio, RR. The dependence on R/h0 arises from the use of equation (6), whereas the commonly used
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Figure 11. Dependence of sheeted thickness on ratio of roller radius to gap width. Circles, RR ¼ 2; triangles, RR ¼ 4.
parabolic approximation to (6) would yield a sheeted thickness independent of R/h0. However, it must again be pointed out that the accuracy of the lubrication approximation contained in (1) and (2) deteriorates rapidly for small values of R/h0. The dependency of the flow rate on n and RR is essentially the same as for the sheeted thickness since they are related via the exit velocity, which depends only very weakly on the location of the detachment point. The very large values of RR in Figure 12 are unlikely to be achievable in practice, so the plot indicates that the strong dependence of h /h0 on RR is likely to be observed over all practical reductions. Figure 13(a) shows that the (dimensionless) maximum depends strongly on the surface normal stress Pmax reduction ratio and weakly on the flow index, while the curves flatten out at higher reduction ratios. Similar behaviour was predicted for the roll separating force, plotted in Figure 13(b). Compressibility can be included in this approximation without much additional effort: the local flow rate from which the pressure gradient is calculated simply needs to be corrected with the local dough density, which depends on the local pressure. The initial gas content of the dough is unknown, but a value of 20% can be expected to represent a realistic upper limit (Campbell et al., 1998; Campbell, 2003). For this value of initial gas content, Figure 12 shows that the sheeted thickness and ‘swell’
Figure 12. Effect of flow index and reduction ratio on sheeted thickness, including compressibility. Solid circles, n ¼ 0.2; triangles, n ¼ 0.3. Open circles, n ¼ 0.2 with compressibility effect (for f ¼ 0.2).
Figure 13. Effect of reduction ratio on (a) maximum surface normal stress [non-dimensionalized as in equation (12)] and (b) roll separating force [non-dimensionalized as in equation (10)]. Solid lines, n ¼ 0.2; dashed line, n ¼ 0.3.
increase slightly. Calculations also showed that there was only a marginal effect on roll separating force and on Pmax.
COMPARISON OF MODEL AND EXPERIMENTS Figure 14 shows that the degree of swelling in the experiments increased with reduction ratio, as predicted by the model. At a fixed roll speed, the incompressible model underpredicted the degree of swelling by approximately a factor of two, and the compressible model improved the prediction only slightly. There are several possible explanations for this discrepancy. Adherence of the dough to the rolls (as mentioned above, the sheets always stuck to one of the rolls after passing through the apparatus) or non-Newtonian flow effects between the rolls could lead to later detachment and hence a greater sheet thickness. This should be indicated by the surface pressure transducer data. However, when determining the point where the surface normal stress recorded by the pressure transducer reaches zero, as illustrated in Figure 15, and calculating the gap between the rolls at this point, the detachment gap width agreed quite well with the predicted sheeted thickness, shown in Figure 14. It seems therefore likely that the observed greater final sheet thicknesses arise from the viscoelasticity of the dough (as previously observed by Morgenstern et al. 2000), causing residual
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Moreover, the experimental roll torque data were an order of magnitude smaller than the model estimates, if the power-law consistency was chosen such that the roll separating forces were best fitted. The simple lubrication model is therefore unable to quantify the gross behaviour of the system (reflected in torque and separating forces) accurately.
CONCLUSIONS
Figure 14. Effect of thickness reduction ratio (RR) on sheet thickness. Solid circles, calculated from detachment via surface normal stress profile; open circles, measured from sheet on roll; solid line, model prediction; dashed line, compressible dough model with f ¼ 0.20.
stresses in the sheet along the direction of sheeting and delayed recoil after detachment from one of the rolls. The experimental data also showed a weak dependence of sheet thickness on roll speed (not explicitly shown) whereas the model predicted no roll speed dependence because it has no time dependence. This indicates that there must be another time-dependent physical mechanism occurring in the sheeting process. When comparing the trends in roll separating force and surface normal stress in Figures 7(a) and (c) and 13(a) and (b), respectively, it is apparent that the model cannot correctly describe the dependence of the roll separating force and maximum surface normal stress on the reduction ratio, particularly for reduction ratios larger than three. While the model suggests convergence towards a finite value, the experimental data show a strong increase of the maximum stress with RR. This conclusion holds independently of the value of the power-law consistency K, which changes only the absolute values, but not the shape of the curves, as follows from equation (12). The strong increase of the normal stresses observed experimentally at high reduction ratios may be due to elastic stresses arising from the stretching of polymeric molecules (gluten proteins) in the dough, which is not accounted for by the simple inelastic model.
Comparison of experimental data from the model sheeting system with predictions from an inelastic lubrication model, similar to the one described previously by Levine, showed that this model can correctly predict the detachment point for (at least some) viscoelastic bread doughs, but fails to predict the final sheeted thickness accurately. The thicknesses of the final sheets are significantly larger, therefore the disagreement between model and experiment is most likely due to substantial viscoelastic recoil after detachment, as was for the first time experimentally supported in this study via measurements of normal stresses directly at the roll surface. The agreement between experiment and model for the dynamic variables (surface normal stress, roll separating force and roll torque) is poor and may be attributed to the use of too simple a rheological model to describe a complex material such as bread dough. It is therefore of major interest to explore the consequences of more complex rheological models, even although this requires a much larger mathematical effort.
NOMENCLATURE hf h0 he h F F K n P Pmax Pmax Q R RR T u us,x V W x y
initial sheet half-thickness, m roller gap half-thickness, m rolled sheet final half-thickness, m final sheet half-thickness at detachment point, m roll separating force (per unit width), N m21 dimensionless roll separating force dough (shear) consistency, Pa sn dough shear index pressure, Pa maximum surface normal stress, Pa dimensionless maximum surface normal stress flow rate, m3 s21 roller radius, m reduction ratio normalized torque (per unit width), N m21 velocity, m s21 velocity in x direction at roller surface, m s21 volume, m3 sheet width, m cartesian co-ordinate, m cartesian co-ordinate, m
Greek symbols f initial relative volume of gas in dough r dough density, kg m23 t shear stress, Pa v roller rotational speed, rad s21
Figure 15. Surface normal stress profile during dough rolling. Roller position of zero corresponds to roll nip; negative values to feed side. Dashed line indicates detachment point (D in Figure 1).
Subscripts f feed condition 0 roll gap location
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ACKNOWLEDGEMENTS We are grateful to Nestec S.A., Switzerland, for permission to publish this work and to the reviewers of the manuscript for their insightful comments and suggestions. The support of Dr Simon Butler and Prof. Malcolm Mackley in generating rheological data is also gratefully acknowledged. The manuscript was received 7 July 2004 and accepted for publication after revision 15 April 2005.
Trans IChemE, Part C, Food and Bioproducts Processing, 2005, 83(C3): 175–184