Reverse osmotic effect in active matter

Abstract

In nonequilibrium active matter systems, a spatial variation in activity can lead to a spatial variation in concentration of active particles satisfying, at steady state, the condition nU = const [Schnitzer, Phys. Rev. E 48, 2553 (1993); Tailleur and Cates, Phys. Rev. Lett. 100, 218103 (2008)], where n is the number density and U is the active (swim) speed. We show that this condition holds even when the variation is abrupt and when thermal Brownian motion is present provided that the Péclet number is large. This spatial variation in swim speed and concentration produces a fluid pressure distribution that drives a reverse osmotic flow-fluid flows from regions of high concentration to low.

Phoretic motion in active matter

“…We closed the equations by setting . This approximation revealed the essential physics and is expected to have only a quantitative, not qualitative, effect on the results, as has been the case in other studies of forces in active matter (Yan & Brady 2015; Row & Brady 2020; Kjeldbjerg & Brady 2021).…”

“…The hierarchy of equations continues with higher moments, and a truncation is necessary. We shall close here with the first two moments by setting , as this is sufficient to illustrate the basic physics as shown by Yan & Brady (2015), Row & Brady (2020) and Kjeldbjerg & Brady (2021).…”

“…This result predicts a very interesting and surprising behaviour: the phoretic particle moves towards regions of higher bulk concentration even though it is repelled by the active bath particles. Although there are more particles in the bulk on the higher-bulk-concentration side, the actual particle density in the accumulation boundary layer on the lower-bulk-concentration side is higher, leading to a net force up the bulk concentration gradient – a reverse phoretic effect (Row & Brady 2020).…”

Activity-induced propulsion of a vesicle

“…One important intrinsic length scale due to activity is the run or persistence length ℓ = 𝑈 𝑠 𝜏 𝑅 . Previous works have shown that a spatial variation in the swim speed leads to a spatial variation in the concentration (or number density) of active particles (Schnitzer 1993;Tailleur and Cates 2008;Row and Brady 2020). By tuning the swim speed distribution of ABPs confined inside the vesicle, a spherically asymmetric density distribution can emerge and lead to net motion of the vesicle.…”

Snell's Law for Gliders

“…One of the primary modes of directed transport relies on the dynamics of micro-swimmers, or self-propelled particles. A substantial body of work has demonstrated that swimmer density can be spatially modulated using asymmetric barriers [9,10], differing regions of propulsion speed [11][12][13][14], run-and-tumble dynamics [15], motility induced phase separation [16], and dynamic swimmer affinities [17]. However, there are few known mechanisms for controlling the trajectories of swimmers.…”