Rheology of concentrated suspension of fibers with load dependent friction coefficient

Abstract

We numerically investigate the effects of fiber aspect ratio, roughness, flexibility, and flow inertia on the rheology of concentrated suspensions. We perform direct numerical simulations modeling the fibers, suspended in an incompressible Newtonian fluid, as continuous flexible slender bodies obeying the Euler-Bernoulli beam equation. An immersed Boundary Method (IBM) is employed to solve for the motion of fibers. In concentrated suspensions, fibers come into contact due to the presence of asperities on their surface. We assume a normal load-dependent friction coefficient to model contact dynamics and friction, which successfully recovers the shear-thinning behaviour observed in experiments. First, we report the shear rate dependent behavior and the increase in the suspension viscosity with the increasing volume fraction of fibers, fiber roughness, and rigidity. The increase in the viscosity is stronger at a lower shear rate and finite inertia. Simulation results indicate that for the concentrated suspensions, contact stresses between fibers form the dominant contribution to the viscosity. Moreover, we find the first normal stress difference to be positive and to increase with the Reynolds number for flexible fibers. Lastly, we explore the divergence of viscosity for different aspect ratios and roughness of the fibers and predict the jamming volume fraction by fitting the data to the Maron-Pierce law. The jamming volume fraction decreases with increasing the aspect ratio and roughness. We conclude that the contact forces and interparticle friction become one of the crucial factors governing the rheology of flexible fiber suspensions at high concentrations.