Shear viscosity of non-colloidal hard sphere suspensions

To construct a shear viscosity model of colloidal suspensions, it is necessary to have a model that accurately describes the behavior of non-colloidal suspensions and has sufficient mathematical simplicity to extend it to more complex systems. In this paper, we propose a modified cell model of the shear viscosity of a non-colloidal suspension that has both of these properties. It is proposed to represent the viscosity of a suspension as a sum of two contributions. The first one is a consequence of the translational motion of a dispersed particle; its behavior has been studied quite well for small values of the volume fraction of the dispersed phase. The second contribution describes the rotational motion of the particle, making it possible to more naturally match the symmetry of hydrodynamic flows with the spherical shape of the cell, and has the main effect at medium and large values of the volume fraction. The mathematical models of both contributions can be extended to the case of particles with internal structure, non-spherical shape, and an interaction potential different from that of hard spheres. The dependence of the cell radius on the volume fraction is obtained, which is a consequence of the system geometry. A comparison of the calculated values of the shear viscosity and experimental results shows that they are in full agreement up to ϕ < 0.45. Thus, the complication of the proposed model can be used to describe the behavior of the shear viscosity of colloidal suspensions in a wide range of volume fraction changes.