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

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 ηhom 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: ηhom=(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.