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The force on a boundary in active matter

Published online by Cambridge University Press:  13 November 2015

Wen Yan
Department of Mechanical and Civil Engineering, California Institute of Technology, Pasadena, CA 91125, USA
John F. Brady
Division of Chemistry and Chemical Engineering and Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, USA
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We present a general theory for determining the force (and torque) exerted on a boundary (or body) in active matter. The theory extends the description of passive Brownian colloids to self-propelled active particles and applies for all ratios of the thermal energy $k_{B}T$ to the swimmer’s activity $k_{s}T_{s}={\it\zeta}U_{0}^{2}{\it\tau}_{R}/6$ , where ${\it\zeta}$ is the Stokes drag coefficient, $U_{0}$ is the swim speed and ${\it\tau}_{R}$ is the reorientation time of the active particles. The theory, which is valid on all length and time scales, has a natural microscopic length scale over which concentration and orientation distributions are confined near boundaries, but the microscopic length does not appear in the force. The swim pressure emerges naturally and dominates the behaviour when the boundary size is large compared to the swimmer’s run length $\ell =U_{0}{\it\tau}_{R}$ . The theory is used to predict the motion of bodies of all sizes immersed in active matter.

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