(655a) Comparison of the Behavior and Distribution of Shear and Extension Rates in a Model Sigma Blade Mixer for a Non-Newtonian Fluid

Internal batch mixers are used in the food, polymer, and pharmaceutical industries to blend different components, to introduce air into the blend and to achieve desirable properties in the final products. The use of mixing in the formation of wheat flour dough, also provide formation of gluten network and the formation of non-covalent bonds. Air introduced during mixing of wheat flour dough become nuclei for carbon dioxide formed in fermentation (Connelly & Kokini, 2007) and determine the cellular foam structure of bread. Numerical simulation allows us to determine the distribution and evaluation of velocity, shear rate, shear stress, extension rate, and temperature, which are effect the cellular foam structure of final product, within the mixer in a non-destructive way.

The objective of the current study is to gain further insights on the evaluation and distribution of shear rate, extension rate and ratio of extension rate to shear rate for mixing non-Newtonian fluid within batch mixer. Three-dimensional (3D) computational fluid dynamics (CFD) of the wheat flour dough having the characteristics of a non-Newtonian fluid in a twin sigma blade model mixer (Brabender Farinograph) is performed using the finite element method (FEM) (Polyflow 19.1 by ANSYS Inc). The two irregular sigma shape paddles are obtained from C.W. Brabender as CAD STEP files. The mixing bowl are created following the methodology as previously described (Connelly & Kokini, 2006). The barrel and the paddles are meshed separately and superimposed in order to use Mesh Super Position Technique (MST). Isothermal flow is considered and in order to do a full mixing analysis a 3D time dependent unsteady state numerical simulation is carried out. The Bird-Carreau constitutive model, which is successfully predicted steady and oscillatory shear properties of wheat flour doughs (Dhanasekharan et al., 1999), is used in the simulation. The local distribution of velocity, shear rate and mixing index are simulated. Extension rates are numerically calculated using second invariant and the third invariant of the rate deformation tensor using the exact derivations of Debbaut and Crochet (1988). Velocity distribution, and evaluation and distribution of shear rate and extension rate are determined.

Three different flow patterns in the mixer are determined during the mixing process. The first flow pattern is a radial flow, which makes the material move with the paddles, the second flow pattern is made up of flow that is parallel to the longitudinal axis caused by the pumping action of the paddles and the third flow pattern is a counter-clock wise circulation that allows exchange of fluid between the paddles, which is generated by the difference in the speed of paddles. The velocity profiles in the non-Newtonian fluid are found to be location and time dependent.

The highest values of the extension rate and local shear rate are determined in two regions; first one is at near the walls of the barrel, which are closely swept by the blades and the other one is at the center of the barrel. The areas, which are just above the paddles show small shear and extension while the areas which are close to the upper boundary of the barrel, show very small or no shear and extension. It is determined that shear rate and extension rate values are time and location dependent. In addition, magnitudes of shear rate are higher than magnitudes of extension rate for all times of the simulation and for the all points,. In the locations that are closer to the center of the mixer have higher extension rate and shear rate values than in the locations closer to the rotation axises due to the rotation points and in the locations in the upper part of the barrel. In these locations, dominant flow type is mixed flow, which is indicating this area has good dispersive and distributive mixing. In addition, shear rate/extension rate ratios are changing between 0 and 0.7 over time and the ratios are not following a pattern.All these results showed that the dispersive and distributive mixing property of the mixer in the center is changing over time, and every point has unique mixing abilities which makes the mixer more effective. This kind of study helps to understand the flow properties of non-Newtonian fluids within the mixer in a non-destructive way and to gain better understanding of the effects of flow properties on the structure of final product.

References

Connelly, R. K., & Kokini, J. L. (2006). 3D numerical simulation of the flow of viscous newtonian and shear thinning fluids in a twin sigma blade mixer. Advances in Polymer Technology, 25(3), 182–194. https://doi.org/10.1002/adv.20071

Connelly, R. K., & Kokini, J. L. (2007). Examination of the mixing ability of single and twin screw mixers using 2D finite element method simulation with particle tracking. Journal of Food Engineering, 79(3), 956–969. https://doi.org/10.1016/j.jfoodeng.2006.03.017

Debbaut, B., & Crochet, M. J. (1988). Extensional effects in complex flows. Journal of Non-Newtonian Fluid Mechanics, 30(2), 169–184. https://doi.org/10.1016/0377-0257(88)85023-7

Dhanasekharan, M., Huang, H., & Kokini, J. L. (1999). Comparison of Observed Rheological Properties of Hard Wheat Flour Dough with Predictions of the Giesekus-Leonov, White-Metzner and Phan-Thien Tanner Models. Journal of Texture Studies, 30(6), 603–623. https://doi.org/10.1111/j.1745-4603.1999.tb00233.x