Introduction of a chaotic dough mixer, part A: mathematical modeling and numerical simulation

The motivation of this work is to propose a special dough mixer with chaotic advection to take advantage of high performance mixing in chaotic mixers and to develop typical dough mixers. In order to prevent common difficulties encountered due to the dynamic mesh, a mathematical model was employed based on neglecting the transient term of the momentum equation using conceptual features from creeping flow. Then, the numerical simulation was performed using the bird Carreau dough model of Dhanasekharan. The mathematical model was further developed to complete the numerical procedure in order to find the required material point trajectories for assessing the presence of chaotic advection in the proposed mixer. In this approach, Lyapunov exponents were also calculated which quantify the exponential divergence of the initially close state-space trajectories and identify chaotic behavior of the system as well. The results indicated that the flow field was a combination of both chaotic and non-chaotic zones.