An improved constitutive model for concentrated suspensions accounting for shear-induced particle migration rate dependence on particle radius

Several rheological constitutive equations for the modeling of dense suspensions in nonlinear shear flows have been developed over the last three decades. Although these models have been able to predict the correct steady-state solid-phase concentration profile, none have been able to follow the transient experimentally measured concentration profile over a range of suspended particle radii with a consistent set of diffusion coefficients. In this research, two improvements are made to the diffusive-flux model, namely, modeling the diffusion coefficients as linear functions of the so-called nonlinearity parameter and adding slip boundary conditions at the wall. A particle-level explanation for the linear dependence of the diffusion coefficients on the nonlinearity parameter is provided. With these two improvements, it is shown that the modified diffusive flux model can accurately predict the transient solid-phase concentration profile in a Couette device over a wide range of particle radii.