Numerical investigation of the rheological behavior of a dense particle suspension in a biviscous matrix using a lubrication dynamics method

Abstract

This paper presents a numerical approach to predict the rheology of dense non-colloidal suspensions with a biviscous matrix. A biviscous matrix is characterized as a fluid with two shear rate dependent viscosities i.e. one above and below a critical shear rate γ˙c. The methodology is based on the lubrication dynamics which dominantly influence the suspension properties at high values of particle concentration. To efficiently handle the singular lubrication forces in the dense suspensions, a semi-implicit splitting integration scheme is employed. Using the presented approach, three dimensional simulations were performed and the predicted rheology of the suspension with a biviscous matrix is discussed under two regimes: (a) γ˙c larger than the macroscopic applied shear rate where fluid slippage effect can be modeled in terms of the non-Newtonian properties of the matrix, and (2) γ˙c smaller than the macroscopic applied shear rate where a biviscous model can be seen as a regularization of an apparent yield stress matrix. The results obtained at high γ˙c show that the shear thinning of the biviscous matrix in the inter-particle gaps, which can be interpreted as an apparent fluid slipping on the particle surface, provides an alternative mechanism to explain the experimentally observed shear-thinning of non-colloidal suspension with Newtonian matrices. At low γ˙c values, the predicted suspension properties and its microstructure corroborates the available experimental results on suspensions with yield stress fluids.