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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 $U_0$, and reorienting on a time scale $\tau_R$ 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 $P^\infty = p_f^\infty + \Pi^\infty$, where $p_f^\infty$ is the fluid pressure and $\Pi^\infty$ 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 $\Pi^{wall} = n^\infty(k_B T + \zeta(\Delta) U_0 \ell(\Delta)/6)$, where $\zeta$ is the (Stokes) drag on the swimmer, $\ell = U_0 \tau_R$ is the run length, and $\Delta$ is the minimum gap size between the particle and the wall; as $\Delta \rightarrow \infty$ this is the familiar swim pressure [Takatori \textit{et al., Phys. Rev. Lett.}, 2014, \textbf{113}, 1-5.].

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Publication details

The article was received on 27 Jan 2018, accepted on 08 Apr 2018 and first published on 10 Apr 2018


Article type: Paper
DOI: 10.1039/C8SM00197A
Citation: Soft Matter, 2018, Accepted Manuscript
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    Do hydrodynamic interactions affect the swim pressure?

    E. Burkholder and J. F. Brady, Soft Matter, 2018, Accepted Manuscript , DOI: 10.1039/C8SM00197A

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