Stress and strain amplification in a dilute suspension of spherical particles based on a Bird–Carreau model

Abstract A numerical study of a dilute suspension based on a non-Newtonian matrix fluid and rigid spherical particles was performed. In particular, an elongational flow of a Bird–Carreau fluid around a sphere was simulated and numerical homogenization has been used to obtain the effective viscosity of the dilute suspension η hom for different applied rates of deformation and different thinning exponents. In the Newtonian regime the well-known Einstein result for the viscosity of dilute suspension is obtained: η hom = ( 1 + [ η ] φ ) η with the intrinsic viscosity [ η ] = 2.5 . Here φ is the volume fraction of particles and η is the viscosity of the matrix fluid. However in the transition region from Newtonian to non-Newtonian behavior lower values of the intrinsic viscosity [ η ] are obtained, which depend on both the applied rate of deformation and the thinning exponent. In the power-law regime of the Bird–Carreau model, i.e. at high deformation rates, it is found that the intrinsic viscosity [ η ] depends only on the thinning exponent. Utilizing the simulation results a modification of the Bird–Carreau model for dilute suspensions with a non-Newtonian matrix fluid is proposed.