Do hydrodynamic interactions affect the swim pressure?

Abstract

We study the motion of a spherical active Brownian particle (ABP) of size a, moving with a fixed speed U₀, and reorienting on a time scale τ_R in the presence of a confining boundary. Because momentum is conserved in the embedding fluid, we show that the average force per unit area on the boundary equals the bulk mechanical pressure P^∞ = p^∞_f + Π^∞, where p^∞_f is the fluid pressure and Π^∞ is the particle pressure; this is true for active and passive particles alike regardless of how the particles interact with the boundary. As an example, we investigate how hydrodynamic interactions (HI) change the particle-phase pressure at the wall, and find that Π^wall = n^∞(k_BT + ζ(Δ)U₀(Δ)/6), where ζ is the (Stokes) drag on the swimmer, = U₀τ_R is the run length, and Δ is the minimum gap size between the particle and the wall; as Δ → ∞ this is the familiar swim pressure [Takatori et al., Phys. Rev. Lett., 2014, 113, 1–5].