Pressure of Active Matter

red ball Active matter? Some examples:


Self-propelled colloidal particles                                                               Swimming Cells                            


Shaken Grains

red ball What is the Pressure of a Gas of Active particles? Does it behave like an equilibrium system?

A.P. Solon, J. Stenhammar, R. Wittkowski, M.K., Y. Kafri, M.E. Cates, J. Tailleur, PRL 114, 198301 (2015)

A. P. Solon, Y. Fily, A. Baskaran, M. E. Cates, Y. Kafri, M. Kardar, J. Tailleur, Nature Phys. 11, 673 (2015)

yellow ballTwo common models are Run and Tumble Paticles (RTP), and Active Brownian Particles (ABP):

yellow ballForce and pressure can be measured by introducing a wall potential:


yellow ballReorientation of an active particle close to the wall needs to be separately specified:

yellow ballPressure depends on the wall potential - No equation of state!

yellow ballThere is a net force on a closed box. (Note that there is no momentum conservation.)


red ball In the absence of external torques, averaging active particle equations of motion gives:

yellow ballFor a closed box the total force and current will both be zero independent of wall potential.

yellow ballAre there any remaining surprises in the absence of reorientation (toque) at the wall? E.g. due to

red ball Wall shape and curvature:

N. Nikola, A.P. Solon, Y. Kafri, M. Kardar, J. Tailleur, R. Voiturie, PRL 117, 098001 (2016);

yellow ball  Tangential Ratchet force: Asymmetric walls support a current and net tangential force:

yellow ball  Normal force variations for sinusoidal wall:    

(Density is non-uniform, depending on curvature and potential)


yellow ballThe dependence of pressure on curvature is reminiscent of Laplace's law

red ball Activity-induced line/surface tension                   

red ball Bendable soft boundary:

yellow ballReduction in line tension leads to modulational instability:

yellow ballConfirmation for a granular chain held on a vibrating plate of shaken particles (Physics Viewpoint)

G. Junot, G. Briand, R. Ledesma-Alonso, and O. Dauchot, PRL 119, 028002 (2017)

yellow ballA flexible chain (worm) spontaneously curves and moves:


Active particles at a boundary exert non-intuitive normal (pressure) and tangential (ratchet) forces.