Osmosis with active solutes

Lion, Thomas; Allen, Rosalind J.

doi:10.1209/0295-5075/106/34003

Cited by 12 publications

(17 citation statements)

References 47 publications

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“…1. It consists of N identical self-propelled dumbbells [5,[20][21][22][23][24][25][26] . A mobile wall of thickness e 2 separates this area into two non-communicating chambers.…”

Section: -Description Of the Modelmentioning

confidence: 99%

“…(II-4) implies that the medium surrounding the dumbbells contributes to the damping of the motion of the mobile wall and of the dumbbells but does not directly contribute to pressure forces (its contribution to pressure is only indirect, through its action on dumbbell dynamics). The wall is therefore assumed to be permeable to this medium and the pressure exerted by active dumbbells must be considered as an osmotic pressure [5,7]. Note also that some of the numerical simulations reported in [5] were done with inertial dumbbells, but comparisons with the present model are not straightforward because the model of [5] used a Nosé-Hoover thermostat, instead of a simple viscous friction term to dissipate the energy injected by the self-propulsion force.…”

Section: -Description Of the Modelmentioning

confidence: 99%

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Pressure of a gas of underdamped active dumbbells

Joyeux

Bertin

2016

Phys. Rev. E

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Abstract:The pressure exerted on a wall by a gas at equilibrium does not depend on the shape of the confining potential defining the walls. In contrast, it has been shown recently [A.P. Solon et.al., Nat. Phys. 11, 673 (2015)] that a gas of overdamped active particles exerts on a wall a force that depends on the confining potential, resulting in a net force on an asymmetric wall between two chambers at equal densities. Here, considering a model of underdamped self-propelled dumbbells in two dimensions, we study how the behavior of the pressure depends on the damping coefficient of the dumbbells, thus exploring inertial effects.We find in particular that the force exerted on a moving wall between two chambers at equal density continuously vanishes at low damping coefficient, and exhibits a complex dependence on the damping coefficient at low density, when collisions are scarce. We further show that this behavior of the pressure can to a significant extent be understood in terms of the trajectories of individual particles close to and in contact with the wall. 02.70.Ns (Molecular dynamics and particle methods) (#)

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“…1. It consists of N identical self-propelled dumbbells [5,[20][21][22][23][24][25][26] . A mobile wall of thickness e 2 separates this area into two non-communicating chambers.…”

Section: -Description Of the Modelmentioning

confidence: 99%

Section: -Description Of the Modelmentioning

confidence: 99%

Pressure of a gas of underdamped active dumbbells

Joyeux

Bertin

2016

Phys. Rev. E

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“…1. It consists of N identical self-propelled dumbbells [5,19,[21][22][23][24][25][26] moving in a 2-dimensional space and enclosed between fixed walls with gross size…”

Section: A Model With Two Confinement Chambersmentioning

confidence: 99%

Recovery of mechanical pressure in a gas of underdamped active dumbbells with Brownian noise

Joyeux

2017

Phys. Rev. E

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Abstract:In contrast with a gas at thermodynamic equilibrium, the mean force exerted on a wall by a gas of active particles usually depends on the confining potential, thereby preventing a proper definition of mechanical pressure. In this paper, we investigate numerically the properties of a gas of underdamped self-propelled dumbbells subject to Brownian noise of increasing intensity, in order to understand how the notion of pressure is recovered as noise progressively masks the effects of self-propulsion and the system approaches thermodynamic equilibrium. The simulations performed for a mobile asymmetric wall separating two chambers containing an equal number of active dumbbells highlight some subtle and unexpected properties of the system. First, Brownian noise of moderate intensity is sufficient to let mean forces equilibrate for small values of the damping coefficient, while much stronger noise is required for larger values of the damping coefficient. Moreover, the displacement of the mean position of the wall upon increase of the intensity of the noise is not necessarily monotonous and may instead display changes of direction. Both facts actually reflect the existence of several mechanisms leading to the rupture of force balance, which tend to displace the mean position of the wall towards different directions and display different robustness against an increase of the intensity of Brownian noise. This work therefore provides a clear illustration of the fact that driving an autonomous system towards (or away from) thermodynamic equilibrium may not be a straightforward process, but may instead proceed through the variations of the relative weights of several conflicting mechanisms.

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“…Even the definition of basic thermodynamic variables such as temperature and pressure is problematic. While "effective temperature" is a widely used concept outside equilibrium [7], the discussion of pressure P in active matter has been neglected until recently [8][9][10][11][12][13][14]. At first sight, because P can be defined mechanically as the force per unit area on a confining wall, its computation as a statistical average looks unproblematic.…”

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confidence: 99%

“…(When immersed in a space-filling solvent, this becomes an osmotic pressure [8,10].) Less clear is how to calculate P; several suggestions have been made [9][10][11][12] whose interrelations are, as yet, uncertain.…”

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confidence: 99%

An Equation of State for Active Matter

Bertin

2015

Physics

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We derive a microscopic expression for the mechanical pressure P in a system of spherical active Brownian particles at density ρ. Our exact result relates P, defined as the force per unit area on a bounding wall, to bulk correlation functions evaluated far away from the wall. It shows that (i) PðρÞ is a state function, independent of the particle-wall interaction; (ii) interactions contribute two terms to P, one encoding the slow-down that drives motility-induced phase separation, and the other a direct contribution well known for passive systems; and (iii) P is equal in coexisting phases. We discuss the consequences of these results for the motility-induced phase separation of active Brownian particles and show that the densities at coexistence do not satisfy a Maxwell construction on P. Much recent research addresses the statistical physics of active matter, whose constituent particles show autonomous dissipative motion (typically self-propulsion), sustained by an energy supply. Progress has been made in understanding spontaneous flow [1] and phase equilibria in active matter [2-6], but as yet there is no clear thermodynamic framework for these systems. Even the definition of basic thermodynamic variables such as temperature and pressure is problematic. While "effective temperature" is a widely used concept outside equilibrium [7], the discussion of pressure P in active matter has been neglected until recently [8][9][10][11][12][13][14]. At first sight, because P can be defined mechanically as the force per unit area on a confining wall, its computation as a statistical average looks unproblematic. Remarkably, though, it was recently shown that for active matter the force on a wall can depend on details of the wall-particle interaction so that P is not, in general, a state function [15].Active particles are nonetheless clearly capable of exerting a mechanical pressure P on their containers. (When immersed in a space-filling solvent, this becomes an osmotic pressure [8,10].) Less clear is how to calculate P; several suggestions have been made [9][10][11][12] whose interrelations are, as yet, uncertain. Recall that for systems in thermal equilibrium, the mechanical and thermodynamic definitions of pressure [force per unit area on a confining wall, and −ð∂F =∂VÞ N for N particles in volume V, with F the Helmholtz free energy] necessarily coincide. Accordingly, various formulas for P (involving, e.g., the density distribution near a wall [16], or correlators in the bulk [17,18]) are always equivalent. This ceases to be true, in general, for active particles [11,15].In this Letter we adopt the mechanical definition of P. We first show analytically that P is a state function, independent of the wall-particle interaction, for one important and well-studied class of systems: spherical active Brownian particles (ABPs) with isotropic repulsions. By definition, such ABPs undergo overdamped motion in response to a force that combines an arbitrary pair interaction with an external forcing term of constant magnitude along a...

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Osmosis with active solutes

Cited by 12 publications

References 47 publications

Pressure of a gas of underdamped active dumbbells

Pressure of a gas of underdamped active dumbbells

Recovery of mechanical pressure in a gas of underdamped active dumbbells with Brownian noise

An Equation of State for Active Matter

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