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The force on a boundary in active matter

Published online by Cambridge University Press:  13 November 2015

Wen Yan Open the ORCID record for Wen Yan [Opens in a new window]  and
John F. Brady
Wen Yan
Affiliation:
Department of Mechanical and Civil Engineering, California Institute of Technology, Pasadena, CA 91125, USA
John F. Brady*
Affiliation:
Division of Chemistry and Chemical Engineering and Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, USA
*
†Email address for correspondence: jfbrady@caltech.edu
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Abstract

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.

JFM classification

Complex Fluids: Colloids Biological Fluid Dynamics: Micro-organism dynamics Low-Reynolds-number flows: Stokesian dynamics
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 785 , 25 December 2015 , R1
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Copyright
© 2015 Cambridge University Press 

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