Velocity Distribution and Diffusion of an Athermal Inertial Run-and-Tumble Particle in a Shear-Thinning Medium

Sayantan Mondal; Prasenjit Das

doi:10.1063/5.0261651

paper

Velocity Distribution and Diffusion of an Athermal Inertial Run-and-Tumble Particle in a Shear-Thinning Medium

arXiv:2504.11683 · doi:10.1063/5.0261651

Abstract

We study the dynamics of an athermal inertial active particle moving in a shear-thinning medium in $d = 1$ . The viscosity of the medium is modeled using a Coulomb-tanh function, while the activity is represented by an asymmetric dichotomous noise with strengths $- Δ$ and $μ Δ$ , transitioning between these states at a rate $λ$ . Starting from the Fokker-Planck~(FP) equation for the time-dependent probability distributions $P (v, - Δ, t)$ and $P (v, μ Δ, t)$ of the particle's velocity $v$ at time $t$ , moving under the influence of active forces $- Δ$ and $μ Δ$ respectively, we analytically derive the steady-state velocity distribution function $P_{s} (v)$ , explicitly dependent on $μ$ . Also, we obtain a quadrature expression for the effective diffusion coefficient $D_{e}$ for the symmetric active force case~( $μ = 1$ ). For a given $Δ$ and $μ$ , we show that $P_{s} (v)$ exhibits multiple transitions as $λ$ is varied. Subsequently, we numerically compute $P_{s} (v)$ , the mean-squared velocity $⟨ v^{2} ⟩ (t)$ , and the diffusion coefficient $D_{e}$ by solving the particle's equation of motion, all of which show excellent agreement with the analytical results in the steady-state. Finally, we examine the universal nature of the transitions in $P_{s} (v)$ by considering an alternative functional form of medium's viscosity that also capture the shear-thinning behavior.

arXiv comment20 Pages, 7 Figures, Accepted to Physics of Fluids

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Velocity Distribution and Diffusion of an Athermal Inertial Run-and-Tumble Particle in a Shear-Thickening Medium