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The Enskog kinetic theory is applied to compute the mean square displacementof intruders immersed in a granular gas of smooth inelastic hard spheres(grains). Both species (intruders and grains) are surrounded by an interstitialmolecular gas (background) that plays the role of a thermal bath. The influenceof the latter on the motion of intruders and grains is modeled via a standardviscous drag force supplemented by a stochastic Langevin-like forceproportional to the background temperature. We solve the correspondingEnskog--Lorentz kinetic equation by means of the Chapman--Enskog expansiontruncated to first order in the gradient of the intruder number density. Theintegral equation for the diffusion coefficient is solved by considering thefirst two Sonine approximations. To test these results, we also compute thediffusion coefficient from the numerical solution of the inelastic Enskogequation by means of the direct simulation Monte Carlo method. We find that thefirst Sonine approximation generally agrees well with the simulation results,although significant discrepancies arise when the intruders become lighter thanthe grains. Such discrepancies are largely mitigated by the use of thesecond-Sonine approximation, in excellent agreement with computer simulationseven for moderately strong inelasticities and/or dissimilar mass and diameterratios. We invoke a random walk picture of the intruders' motion to shed lighton the physics underlying the intricate dependence of the diffusion coefficienton the main system parameters. This approach, recently employed to study thecase of an intruder immersed in a granular gas, also proves useful in thepresent case of a granular suspension. Finally, we discuss the applicability ofour model to real systems in the self-diffusion case. We conclude thatcollisional effects may strongly impact the diffusion coefficient of thegrains.

Diffusion of intruders in granular suspensions: Enskog theory and random walk interpretation