Indirect boundary integral formulation for the solution of shear-thinning flow inside single rotor mixers

Abstract

An efficient indirect boundary integral formulation for the evaluation of inelastic non-Newtonian shearthinning flows at low Reynolds number is presented in this article. The formulation is based on the solution of a homogeneous Stokes flow field and the use of a particular solution for the nonlinear non-Newtonian terms that yields the complete solution to the problem. Matrix multiplications are reduced in comparison to other means of handling nonlinear terms in boundary integral formulations such as the dual reciprocity method. The iterative solution of the nonlinear system of equations has been performed with a modified Newton-Raphson method obtaining accurate results for values of the power law index as low as 0.4 without domain partitioning. Geometries such as Couette flow and a typical industrial polymer mixer have been analyzed with the proposed method obtaining good results with a reduction in computational cost compared with other equivalent formulations.