Tracer Diffusion in Granular Suspensions: Testing the Enskog Kinetic Theory with DSMC and Molecular Dynamics

TL;DR

This study evaluates the accuracy of the Enskog kinetic theory in predicting tracer diffusion in granular suspensions by comparing theoretical results with molecular dynamics and DSMC simulations across various intruder masses.

Contribution

It extends previous kinetic theory by incorporating MD simulations and DSMC results to test the robustness of the Enskog framework for granular suspensions.

Findings

Enskog theory reliably predicts diffusion for certain mass ratios.

Friction parameter significantly influences intruder dynamics.

Results delineate conditions where kinetic theory matches simulations.

Abstract

We investigate the diffusion of an intruder in a granular gas, with both components modeled as smooth hard spheres, both immersed in a low viscosity carrier fluid to form a particle-laden suspension. In this system, dissipative particle collisions coexist with the action of a solvent. The latter is modeled via a viscous drag force and a stochastic Langevin-like force proportional to the background fluid temperature. Building on previous kinetic theory and random-walk results of the tracer diffusion coefficient [R. G\'omez Gonz\'alez, E. Abad, S. Bravo Yuste, and V. Garz\'o, Phys. Rev. E \textbf{108}, 024903 (2023)], where random-walk predictions were compared with Chapman--Enskog results up to the second Sonine approximation, we assess the robustness of the Enskog framework by incorporating molecular dynamics (MD) simulations, using direct simulation Monte Carlo (DSMC) results as an intermediate reference. In particular, we focus on the intruder velocity autocorrelation function, considering intruders different masses (from 0.01 to 100 times the mass of the granular particles), and analyse the behavior of the intruder temperature and diffusion coefficient. Our results clarify the influence of the friction parameter and the conditions under which Enskog kinetic theory reliably describes intruder diffusion in granular suspensions.