Normal lubrication force between spherical particles immersed in a shear-thickening fluid

In this work, the inverse bi-viscous model [Physics of Fluids 29, 103104 (2017)] is used to describe a shear-thickening fluid. An analytical velocity profile in a planar Poiseuille flow is utilized to calculate an approximate solution to the generalized lubrication force between two close spheres interacting hydrodynamically in such a medium. This approximate analytical expression is compared to the exact numerical solution.The flow topology of the shear-thickening transition within the interparticle gap is also shown and discussed in relation to the behaviour of the lubrication force. The present result can allow in the future to perform numerical simulations of dense particle suspensions immersed in a shear-thickening matrix based on an effective lubrication force acting between pairwise interacting particles. This model may find additional value in representing experimental systems consisting of suspensions in shear thickening media, polymer coated suspensions, and industrial systems such as concrete