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The diffusion transport coefficients of a binary granular suspension whereone of the components is present in tracer concentration are determined fromthe (inelastic) Enskog kinetic equation. The effect of the interstitial gas onthe solid particles is accounted for in the kinetic equation through twodifferent terms: (i) a viscous drag force proportional to the particle velocityand (ii) stochastic Langevin-like term defined in terms of the backgroundtemperature. The transport coefficients are obtained as the solutions of a setof coupled linear integral equations recently derived for binary granularsuspensions with arbitrary concentration [G\'omez Gonz\'alez \emph{et al.},Phys. Rev. E \textbf{101}, 012904 (2020)]. To achieve analytical expressionsfor the diffusion coefficients, the above integral equations are approximatelysolved by considering the so-called second Sonine approximation. Thetheoretical results for the tracer diffusion coefficient $D_0$ (coefficientconnecting the mass flux with the gradient of density of tracer particles) arecompared with those obtained by numerically solving the Enskog equation bymeans of the direct simulation Monte Carlo method. Although the first-Sonineapproximation to $D_0$ yields in general a good agreement with simulationresults, we show that the second-Sonine approximation leads to an improvementover the first-Sonine correction, especially when the tracer particles are muchlighter than the granular gas. The expressions derived here for the diffusioncoefficients are also used for two different applications. First, the stabilityof the homogeneous steady state is discussed. Second, segregation induced by athermal gradient is studied. As expected, the results show that thecorresponding phase diagrams for segregation clearly differ from those found inprevious works when the effect of gas phase on grains is neglected.

Tracer diffusion coefficients in a moderately dense granular suspension. Stability analysis and thermal diffusion segregation