Brownian motion in the presence of a temperature gradient

We analyze the dynamics of Brownian ratchets in a confined environment. The motion of the particles is described by a Fick-Jakobs kinetic equation in which the presence of boundaries is modeled by means of an entropic potential. The cases of a flashing ratchet, a two-state model, and a ratchet under the influence of a temperature gradient are analyzed in detail. We show the emergence of a strong cooperativity between the inherent rectification of the ratchet mechanism and the entropic bias of the fluctuations caused by spatial confinement. Net particle transport may take place in situations where none of those mechanisms leads to rectification when acting individually. The combined rectification mechanisms may lead to bidirectional transport and to new routes to segregation phenomena. Confined Brownian ratchets could be used to control transport in mesostructures and to engineer new and more efficient devices for transport at the nanoscale. © 2013 AIP Publishing LLC.

Section: Thermal Ratchetmentioning

confidence: 99%

Confined Brownian ratchets

Malgaretti

Pagonabarraga

Rubı́

2013

“…Thermophoretic forces caused by a temperature gradient give rise to dust structures, are of central interest in the scavenging of aerosol particles in clouds, when droplets and/or ice crystals grow or evaporate, during the fall of hydrometeors, 1,2 and have been discussed in the context of nonequilibrium thermodynamics, 3,4 and in terms of a kinetic description, leading to a stochastic differential equation for a tracer particle in a solvent. 5 In contrast to thermophoretic forces, barophoretic effects caused by pressure gradients 6 and rheophoretic forces caused by velocity field gradients have been considered less frequently and not yet elaborated in an extensive, complete, or unifying fashion.…”

Section: Introductionmentioning

confidence: 99%

Phoretic forces on convex particles from kinetic theory and nonequilibrium thermodynamics

Hütter

Kröger

2006

In this article we derive the phoretic forces acting on a tracer particle, which is assumed to be small compared to the mean free path of the surrounding nonequilibrium gas, but large compared to the size of the surrounding gas molecules. First, we review and extend the calculations of Waldmann ͓Z. Naturforsch. A 14A, 589 ͑1959͔͒ using half-sphere integrations and an accommodation coefficient characterizing the collision process. The presented methodology is applied to a gas subject to temperature, pressure, and velocity gradients. Corresponding thermophoretic, barophoretic, and rheophoretic forces are derived, and explicit expressions for spherical particles are compared to known results. Second, nonequilibrium thermodynamics is used to join the diffusion equation for the tracer particle with the continuum equations of nonisothermal hydrodynamics of the solvent. So doing, the distinct origin of the thermophoretic and barophoretic forces is demonstrated. While the latter enters similarly to an interaction potential, the former is given by flux-flux correlations in terms of a Green-Kubo relation, as shown in detail.

“…1 Thermophoretic forces caused by a temperature gradient induce dust structures, are of central interest in the scavenging of aerosol particles in clouds, when droplets and/or ice crystals grow or evaporate, during the fall of hydrometeors, 2,3 influence the velocity measurements in particle image velocimetry measurements, 4 and have been discussed in the context of nonequilibrium thermodynamics, 1,5,6 and in terms of a kinetic description, [7][8][9][10] leading to a stochastic differential equation for a tracer particle in a solvent. 1,11 In contrast to thermophoretic forces, barophoretic effects caused by pressure gradients, 12,13 and rheophoretic forces caused by velocity field gradients have been considered less frequently and not yet elaborated in an extensive, complete, or unifying fashion for nonspherical tracers.…”

Section: Introductionmentioning

confidence: 99%

Unifying kinetic approach to phoretic forces and torques onto moving and rotating convex particles

Kröger

Hütter

2006

We derive general expressions and present several examples for the phoretic forces and torques acting on a translationally moving and rotating convex tracer particle, usually a submicrosized aerosol particle, assumed to be small compared to the mean free path of the surrounding nonequilibrium gas. Point of departure is an expression of the stress tensor in terms of half-sphere integrals to be evaluated with the inhomogeneous velocity distribution function of the surrounding gas, more specifically, its approximation in terms of a finite number of moments. A worked out example covers Grad’s 13 moment approximation in and out of the so-called hydrodynamic approximation. We implement an accommodation coefficient characterizing the collision process in order to derive the tracer particle’s complete equations of motion in a form which offers the possibility for immediate numerical implementation, and the analytical exploration of the effect of particle shape and size on phoretic drift velocity. Explicit expressions for axisymmetric, spherical, cylindrical, and also cuboidal particles are presented, discussed, and successfully compared with the rarely available, previously treated special cases, thus supporting the unifying approach presented in this manuscript.