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)U_0ℓ(Δ)/6), where ζ is the (Stokes) drag on the swimmer, ℓ = U_0τ_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].