First-order contributions to the partial temperatures in binary granular suspensions at low density

TL;DR

This paper uses the Boltzmann equation and Chapman--Enskog expansion to calculate first-order contributions to partial temperatures in low-density binary granular suspensions, considering gas-particle interactions.

Contribution

It provides a novel analytical approach to quantify first-order temperature contributions and their impact on the cooling rate in granular suspensions.

Findings

First-order temperature contributions can be significant depending on system parameters.

The influence of these contributions on the cooling rate is quantitatively assessed.

The approach extends kinetic theory methods to granular suspensions with gas interactions.

Abstract

The Boltzmann kinetic equation is considered to evaluate the first-order contributions $T_i^{(1)}$ to the partial temperatures in binary granular suspensions at low density. The influence of the surrounding gas on the solid particles is modeled via a drag force proportional to the particle velocity plus a stochastic Langevin-like term. The Boltzmann equation is solved by means of the Chapman--Enskog expansion around the local version of the reference homogeneous base state. To first-order in spatial gradients, the coefficients $T_i^{(1)}$ are computed by considering the leading terms in a Sonine polynomial expansion. In addition, the influence of $T_i^{(1)}$ on the first-order contribution $\zeta^{(1)}$ to the cooling rate is also assessed. Our results show that the magnitude of both $T_i^{(1)}$ and $\zeta^{(1)}$ can be relevant for some values of the parameter space of the system.