(54d) The Force on a Body in Active Matter

The statistical mechanics and microhydrodynamics of active matter systems have seen a dramatic increase in interest in the past several years. Much attention has focused on the fascinating nonequilibrium behaviors of active matter not observed in equilibrium thermodynamic systems, such as spontaneous collective motion and swarming. Even minimal kinetic models of active Brownian particles exhibit self-assembly that resembles a gas-liquid phase separation. Self propulsion allows active systems to generate internal stresses that enable them to control and direct their own behavior and that of their surroundings. Recent work involving the unique â??swim pressureâ?? exerted by active systems offers a perspective on the basic underlying physical mechanism responsible for self-assembly and pattern formation in active matter [1-3].

In this work we take a more microscopic view and present a general theory for determining the force (and torque) exerted on a body (or boundary) in active matter [4]. The theory extends the description of passive Brownian colloids to self-propelled active particles and applies for all ratios of the thermal energy k_BT to the swimmerâ??s activity k_sT_s = ζU²₀Ï?R/6, where ζ is the Stokes drag coefficient, U₀ is the swim speed and Ï?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 behavior when the body size is large compared to the swimmerâ??s run length l = U₀Ï?R. The theory is used to predict the motion of bodies of all sizes immersed in active matter.

References
[1] S.C. Takatori, W. Yan and J.F. Brady, Phys. Rev. Lett. 113, 028103 (2014)
[2] S.C. Takatori and J.F. Brady, Phys. Rev. E 91, 032117 (2015)
[3] S.C. Takatori and J.F. Brady, Current Opinion in Colloid & Interface Science, 21, 24 (2016)
[4] W. Yan and J.F. Brady, J. Fluid Mech. 785, R1 (2015)