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Importance of coupling between specific energy and viscosity in the modeling of twin screw extrusion of starchy products.


Twin screw extrusion is a popular process for transforming starchy products. It has been largely used in the food domain, for example for the extrusion-cooking of flat breads or breakfast cereals (1), (2). It is now developing in non-food applications for producing biobased materials, such as polyolefin/starch or polycaprolactone/starch blends (3), (4). In all cases, starch is submitted into the extruder to high temperatures and mechanical stresses which modify its basic structure: the chains of amylose and amylopectin are broken, the molecular weight is reduced and thus the viscosity of the molten product is lowered. It has been previously shown that starch macromolecular degradation is controlled by the specific mechanical energy (SME) received during the thermomechanical treatment (5). Consequently, the viscosity of a molten starch changes with temperature and shear rate, as a classical synthetic polymer, but also with the SME experienced during the process (6).

To optimize extrusion processes and to perform efficient scale-up between laboratory and industrial machines, it becomes common to use numerical modeling. The specific software Ludovic [c] was developed a few years ago for computing flow conditions along a co-rotating twin screw extruder (7). It is a global 1D model that allows one to calculate the changes of the main thermomechanical parameters (pressure, temperature, residence time, filling ratio, etc.) all along the screws. It has been largely used for modeling extrusion-cooking (8), (9) and more recently to calculate and optimize starch cationization (10), (11). However in these applications, the influence of SME on starch viscosity was not taken into account. In the present article, we have used a specific version of Ludovic [c], implemented for considering reactive extrusion processes (12), to couple all along the screws starch transformation, related to the received SME and starch viscosity, which has evidently a direct effect on the dissipated energy.



We used a wheat starch, with 13 wt% initial moisture content, provided by Chamtor (Bazancourt, France). This starch contained 74% amylopectin and 26% amylose with residual protein and lipid contents less than 0.2% and 0.7%, respectively. Starch was plasticized by 40 wt% of water (on a dry basis).

Extrusion Experiments

The major part of the experiments has been carried out on a laboratory scale twin screw extruder Clextral BC 21. It has a screw diameter of 25 mm and a length to diameter ratio L/D of 36. Three screw profiles were used. They are given in Fig. 1. The first profile is very simple. Besides screw conveying elements, it has only two adjacent blocks of five kneading discs, staggered at -45[degrees], for the melting and the transformation of the starch. The second profile is more restrictive. Compared to Profile 1, a third block of five kneading discs at -45[degrees] has been added after the feeding section for starch melting. The two adjacent blocks at -45[degrees] in Barrel 7 are then expected to induce a more important starch transformation. The third profile is assumed to be the most severe. A fourth block of five kneading discs, always staggered at -45[degrees], has been added in the melting section, adjacent to the first one. For all profiles, the barrel temperature was constant after the feeding section and equal to 80[degrees]C. Starch was introduced in the hopper (first barrel element), whereas water was injected downstream, in the second barrel element, by a pump.


Experiments were conducted by varying screw speed (from 100 to 500 rpm) at constant feed rate (2, 2.7, and 2.9 kg/hr, depending on the profile), and varying feed rate (from 1.3 to 5.5 kg/hr) at constant screw speed (400 rpm). Samples were collected at die exit for subsequent analyses and SME was deduced from torque measurements by:

SME = 1/Q N/[N.sub.max] r C/[C.max] W (1)

where Q is the mass feed rate, N is the screw speed, [N.sub.max] is the maximum screw speed (here, 680 rpm), r is the motor efficiency (0.93), C is the torque, [C.sub.max] is the maximum torque and W is the nominal power (9.2 kW). According to the processing conditions and the screw profile, SME in the range 250-1100 kWh/t were obtained during the experiments.

To validate the results on a larger extruder, complementary experiments have been carried out on a Clextral BC45 (screw diameter = 55 mm, L/D ratio = 22.7). The screw profile is also presented in Fig. 1 (Profile 4). It is made with a left-handed screw element for the melting and a second one close to the die exit, preceded by a block of five kneading discs staggered at 45[degrees]. Similar experiments were performed on this machine, varying screw speed from 100 to 240 rpm at constant feed rate (20 kg/hr) and varying feed rate from 8 to 44 kg/hr at constant screw speed (240 rpm). Barrel temperatures were higher than for laboratory extruder, 130[degrees]C instead of 80[degrees]C. In these conditions, the measured SME was between 370 and 800 kWh/t.

Starch Transformation

Starch transformation includes the loss of initial granular structure and the reduction of the molecular weight, by degradation of both amylose and amylopectin chains (5), (13-16). It was evaluated by measurements of intrinsic viscosity on an Ubbelhode viscometer. For a polymolecular material, intrinsic viscosity describes the average structure of the sample and thus provides global information on the average size of the macromolecules, i.e., on the average molecular weight. By comparing with the value of the native starch, it gives an idea of the degradation of the macromolecules. However, it is less accurate than size exclusion chromatography (13), (16). Measurements were made as follows: from an initial solution made with 47 ML of water, 2.8 g of potassium hydroxide and 0.5% (0.25 g) of starch (previously ground), four solutions were prepared with 0.1, 0.2, 0.3, and 0.4% starch. Intrinsic viscosity was obtained by extrapolation at zero concentration of the reduced viscosity (at 25[degrees]C).

Starch Viscosity

If SME modifies starch structure, it obviously also affects its rheological behavior. This is known for a long time and it implies to define accurately the relationships between SME and starch viscosity. Anyway, it is a difficult task because the viscosity measurements must be done on a material which has received a well controlled thermomechanical treatment. One of us used previously a specific rheometer with pre-shearing, which allowed for the first time to define a rheological law for starch including the effects of SME (6). He developed also a twin channel system to be operated in line on an extruder (17). This rheometer was largely used for the determination of the rheological behavior of many starchy products (18-21). For the present study, we chose this last system and we designed a new in-line rheometer, adapted to the small size of the extruder (22). It allowed us to quantify the viscous behavior of the molten wheat starch in function of shear rate, temperature, water content, and SME.

Theoretical Modeling

The software Ludovic [c] was developed more than 15 years ago for computing flow conditions along a co-rotating twin screw extruder and is today commercialized by Sciences Computers Consultants company (Saint-Etienne, France). Details on the model and its applications are detailed in previous articles (7), (23). It allows to calculate the main flow parameters (temperature, pressure, shear rate, viscosity, residence time, etc.) all along the screws, from the hopper to the die exit. The flow modeling uses a local one-dimensional approach. Computation of the various parameters is done separately for each type of screw element (partially or totally filled right-handed screw elements, left-handed screw elements and blocks of kneading disks) and for the die components.

For screw elements, pressure/flow rate relationships are computed considering the section of the channel as rectangular, with a constant width. It has been shown by comparing this approximate 1D method with a full 3D computation that the agreement is fairly good, mainly in the usual range of feed rate variations. Flow in kneading disks is modeled considering only the peripheral flow around a disk. Due to the disk geometry and the relative barrel velocity, this flow is characterized by a pressure peak located just before the tip of the disk. As the tips of adjacent disks are staggered, the pressure profiles are also staggered, what creates an axial pressure gradient, parallel to the screw axis and pushing the material in axial direction. The preceding elementary models are linked together to obtain a global description of the flow field along the extruder. Melting is considered either by using a specific model or assuming that it is instantaneous and takes place before the first restrictive element of the screw profile. Afterwards, the material is considered to be fully molten and can fill the screw channel, according to local geometry and flow conditions. As the screws are starve-fed, the filling ratio of the system is not known. Thus, the computation has to start from the die and to proceed backwards. But, as the final product temperature is unknown, an iterative procedure is used.

Recently, a specific version was developed for reactive extrusion (12). In this case, the viscosity can change along the screws in function of the extent of the considered chemical reaction. For example, the cases of controlled degradation (24) or polymerization (25) was successfully considered. For the present study, we have modified this reactive extrusion version, by coupling at each location along the screws the viscosity with the calculated SME.


Starch Transformation

It is known that the starch original structure is completely destroyed when SME is higher than 140-170 kWh/t (26), (27). In our conditions (250 kWh/t < SME < 1100 kWh/t), starch was always completely destructured and transformed at the exit of the extruder. It is also well known that SME increases with screw speed N and decreases with feed rate Q. We show in Fig. 2 that for different feed rates Q and screw speeds N, SME increases linearly with the ratio N/Q. As expected, at same N/Q, the screw profiles are ranked according to their severity: screw Profile 3 provides the highest SME, followed by Profiles 2 and 1. Even if the range of explored N/Q is smaller, the large scale extruder (Clextral BC 45, Profile 4) brings to the starch much more energy than the laboratory scale one.

Starch intrinsic viscosity has been evaluated for the different trials. It can be seen in Fig. 3 that it decreases regularly when SME increases, independently of the flow conditions (feed rate, screw speed) and of the screw profile. These results are in agreement with those published in the literature for other starches (5), (20). According to this figure, it is clear that starch transformation (and thus starch properties) can be evaluated as soon as SME is correctly predicted. Despite the fact that intrinsic viscosity [eta] and SME are usually related by exponential or power law relationships (28-30), in our case, in the range 200-800 kWh/t, intrinsic viscosity [eta] can be correctly estimated by a simple linear relationship:

[eta] = A SME + B (2)

where A = -0.05 and B = 140, for SME expressed in kWh/t and [eta] in ML/g.

Starch Viscosity





As an example, Fig. 4 shows the viscosity curves at 85[degrees]C and 40% water content, for three different values of SME, ranging from 185 to 466 kWh/t. Each curve can be correctly fitted by a power law. As expected, the viscosity decreases when SME increases, in relationship with the macromolecular degradation (6). The detailed study of the characterization of starch rheological behavior can be found elsewhere (22). To summarize, the viscous behavior of wheat starch can be written as a power law of the form:

[eta] = K exp[n[E/R[1/T - 1/[T.sub.0]] + [beta](SME - [SME.sub.0]) + [gamma](WC - [WC.sub.0])]] * [[gamma].sup.n-1] (3) (3)


where K is the consistency, n is the power law index, E is the activation energy, R is the gas constant, T is the absolute temperature, WC is the water content. [T.sub.0], [SME.sub.0], and [WC.sub.0] are reference values, [beta] and [gamma] are parameters. From our experiments, we obtained: K = 1920 Pa s, n = 0.53, E/R = 5150 K, [T.sub.0] = 363 K, [beta] = -0.0028 t k[Wh.sup.-1], [SME.sub.0] = 325 k[Wh t.sup.-1], [gamma] = -10.91 and [WC.sub.0] = 0.40. Once again, these values compare well with those of the literature on similar products (6), (31).


The software Ludovic [c] has been used for calculating the parameters of the wheat starch extrusion process, using the viscous law defined by Eq. 3. For the coupling between SME and viscosity, the following procedure is adopted: a first simulation is made (from die to hopper) at a fixed value of SME (here, 325 kWh/t) to obtain a first guess of the pressure and temperature distribution along the extruder. For that, the extruder is divided into adjacent slabs, in which the different parameters are successively calculated (7). Then, a second simulation is carried out (from hopper to die), by coupling step by step calculations of flow, SME, and viscosity: temperature [T.sub.i], shear rate [[gamma].sub.i], cumulative energy [SME.sub.i], and viscosity [[eta].sub.i] are supposed to be known in slab i; then, from viscosity in slab i and processing conditions, temperature and SME changes, [DELTA]T and [DELTA]SME, as well as average shear rate [[gamma].sub.i-1] are calculated in slab i + 1; new values of temperature and cumulative SME are then calculated: [T.sub.i+1] = [T.sub.i] + [DELTA]T and [SME.sub.i+1] = [SME.sub.i] + [DELTA]SME; Eq. 3 is used to calculate the new viscosity [[eta].sub.i+1] in slab i + 1, and the procedure is repeated until reaching the extruder end.


In the first step, we focused on screw Profile 1 and performed calculations without coupling, i.e., assuming a constant value of SME for estimating the viscosity. The chosen value (325 kWh/t) corresponds to the reference value of the rheological measurements. It can be considered as an average value for the experiments made on the large scale extruder and in the low range of SME for the laboratory extruder. Figures 5 and 6 present the comparison between calculated and experimental values of SME and product temperature at the die exit, in the cases where screw speed and feed rate are varied. As expected, we observe in Fig. 5 that SME increases with screw speed and decreases with feed rate. The simulations provide correct tendencies, but the calculated results overestimate the experimental values, whatever the conditions. The differences are more important at high screw speed and low feed rate, i.e., at high SME, apparently because a too moderate SME value was chosen to calculate the viscosity. At 400 rpm and 2.9 kg/hr, the calculation of starch transformation using Eq. 2 would predict an intrinsic viscosity of 97 ML/g, instead of 116 ML/g in the reality.



Figure 6 presents the results for the product temperature at the die exit. Experimentally, it increases quite linearly with the screw speed, what is correctly predicted by the simulation. However, the calculation tends also to overestimate the value, for the same reason than previously: the viscosity being overestimated, the calculated viscous dissipation is more important, mainly at high screw speed. If we consider the effect of feed rate (Fig. 6b), the results are different. Calculations overestimate again the real temperature, but now the tendencies are no more correct. When increasing feed rate, we observe a slight increase of the experimental temperature but a slight decrease of the computed one.



Similar results and same tendencies were obtained with the other screw profiles (see Fig. 7). For SME results obtained on the laboratory extruder, we do not see any influence of the screw profile. However, the results concerning the large scale extruder show a larger discrepancy compared to experiments. Concerning product temperature, the calculated values are generally close to the experimental ones, but the wrong tendency observed when varying feed rate is confirmed on the different profiles (points with negative slope).

In the second step, we implemented the coupling between SME and viscosity, as explained previously. The comparison of the evolutions of the temperature, the SME and the viscosity along the screws, with and without coupling, is presented in Fig. 8, in the case of Profile 2 at 250 rpm and 2.9 kg/hr. For each parameter, we observe a crossover between the curves: before this point, values obtained without coupling are lower than values obtained with coupling; after, it is the opposite. It can be seen in Fig. 8b that the crossover point corresponds to the SME value that has been chosen for defining the viscosity without coupling. It can be pointed out that, in the presented case, the coupling induces a reduction of viscosity by a factor around two in the final part of the extruder.

As a consequence of coupling, it can be seen in Figs. 9 and 10 that the theoretical results (Profile 1.) are largely improved. SME follows the same tendencies, but much closer to the experimental values, even at high screw speed or low feed rate. The evolution of temperature with screw speed is now perfectly predicted (Fig. 10a). Moreover, the evolution with the feed rate is now in agreement with the experiments (Fig. 10b): calculated temperature increases now with the feed rate, with an error of maximum 2%. Once again, these improvements of the theoretical results are observed whatever the screw profile. Figure 11 shows that SME and exit temperature are correctly estimated on the whole range of experimental data when the coupling is taken into account.


One of the objectives of the twin screw modeling is to be able to predict starch transformation. According to Eq. 2, we have calculated the intrinsic viscosity for the different screw profiles and the various processing conditions, with and without coupling between viscosity and SME. Results are presented in Fig. 12. The advantage to take into account the specific effect of SME on starch viscosity is clearly shown on this figure. Whatever the processing conditions, the starch transformation is estimated with an error inferior to 10%, when it could reach more than 30% without coupling.


In this article, we present a computation of wheat starch twin screw extrusion, in which the influence of SME on starch viscosity is considered. Relationships between SME and starch degradation (estimated by intrinsic viscosity) and SME and starch viscosity are experimentally established. The calculation is then carried out, using a software dedicated to twin screw reactive extrusion. The results show that the fact to neglect the coupling between SME and viscosity leads to an overestimation of calculated SME, product temperature, and predicted starch transformation. If the coupling is taken into account, results are largely improved and starch transformation can be predicted with an error inferior to 10%.


The authors thank G. Della Valle from INRA-BIA (Nantes, France) for allowing to perform the experiments with the Clextral BC45.


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Francoise Berzin, (1) Ahmed Tara, (1) Lan Tighzert, (1) Bruno Vergnes (2)

(1) GRESPI, Universite de Reims Champagne Ardenne, Reims, France

(2) Mines ParisTech, CEMEF, UMR CNRS 7635, Sophia-Antipolis, France

Correspondence to: Francoise Berzin: e-mail:

DOI 10.1002/pen.21702

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Author:Berzin, Francoise; Tara, Ahmed; Tighzert, Lan; Vergnes, Bruno
Publication:Polymer Engineering and Science
Article Type:Report
Geographic Code:4EUFR
Date:Sep 1, 2010
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