Numerical Analysis of Non-Newtonian Fluid Effects on the Equilibrium Position of a Suspended Particle and Relative Viscosity in Two-Dimensional Flow

Abstract

A solvent in suspension often has non-Newtonian properties. To date, in order to determine these properties, many constitutive equations have been suggested. In particular, power-law fluid, which describes both dilatant and pseudoplastic fluids, has been used in many previous studies because of its simplicity. Then, the Herschel–Bulkley model is used, which describes fluid with yield stress. In this study, we considered how a non-Newtonian solvent affected the equilibrium position of a particle and relative viscosity using the regularized lattice Boltzmann method for fluid and a two-way coupling scheme for the particle. We focused on these methods so as to evaluate the non-Newtonian effects of a solvent. The equilibrium position in Bingham fluid was closer to the wall than that in Newtonian or power-law fluid. In contrast, the tendency of relative viscosity in Bingham fluid for each position was similar to that in power-law fluid.

Keywords

• rheology
• Bingham fluid
• Herschel–Bulkley model
• regularized lattice Boltzmann method
• virtual flux method
• Segré and Silberberg effect