# Shear-rate dependent transport coefficients in granular suspensions

## TL;DR

This paper investigates how shear rate influences transport coefficients in granular suspensions using a kinetic model based on the inelastic Boltzmann equation, providing explicit forms and analyzing shear-rate dependence.

## Contribution

It introduces a Chapman-Enskog-like expansion for granular suspensions near simple shear flow, deriving shear-rate dependent transport coefficients with explicit solutions.

## Key findings

- Transport coefficients depend on shear rate and restitution coefficient.
- Explicit forms of generalized transport coefficients are obtained under steady-state conditions.
- Shear-rate dependence of transport coefficients is illustrated for various restitution coefficients.

## Abstract

A recent model for monodisperse granular suspensions is used to analyze transport properties in spatially inhomogeneous states close to the simple (or uniform) shear flow. The kinetic equation is based on the inelastic Boltzmann (for low density gases) with the presence of a viscous drag force that models the influence of the interstitial gas phase on the dynamics of grains. A normal solution is obtained via a Chapman-Enskog-like expansion around a (local) shear flow distribution which retains all the hydrodynamic orders in the shear rate. To first-order in the expansion, the transport coefficients characterizing momentum and heat transport around shear flow are given in terms of the solutions of a set of coupled linear integral equations which are approximately solved by using a kinetic model of the Boltzmann equation. To simplify the analysis, the steady-state conditions when viscous heating is compensated by the cooling terms arising from viscous friction and collisional dissipation are considered to get the explicit forms of the set of generalized transport coefficients. The shear-rate dependence of some of the transport coefficients of the set is illustrated for several values of the coefficient of restitution.