Inertial hydrodynamic ratchet: Rectification of colloidal flow in tubes of variable diameter

Abstract

We investigate analytically a microfluidic device consisting of a tube with non-uniform but spatially periodic diameter, where a fluid driven back and forth by a pump carries colloidal particles. Although the net flow of the fluid is zero, the particles move preferentially in one direction due to ratchet mechanism, which occurs by simultaneous effect of inertial hydrodynamics and Brownian motion. We show that the average current is strongly sensitive to particle size, thus facilitating colloidal particle sorting.

Dimensional reduction of a general advection–diffusion equation in 2D channels

“…The effective 1D equations appeared useful in description of transport through biological structures [9], or artificial nano pores [10][11][12]. Special attention was paid to rectification effects in Brownian motors [13,14], Brownian pumps [15][16][17], entropic particle separators [18][19][20] in electrophoretic [21], gravitational, [22] or optical [23] ratchets [24,25], or hybrid schemes based on interplay between hydrodynamics and diffusion [26][27][28][29][30][31][32].…”

Thermal Ratchet Effect in Confining Geometries

“…In these, and in the subsequent works, the originally phenomenological approach was generalized and put on solid mathematical grounds . In particular, various many-dimensional Brownian ratchets have been studied with the aid of the Fick-Jacobs approximation including flashing and rocking ratchets [37][38][39], ratchets driven by a temperature gradient [39], and hydrodynamic ratchets [22,40]. Possible application to separation of particles according to their size can be found in Refs.…”

Diffusion of colloidal rods in corrugated channels

“…We further show how to extend the standard Fick-Jacobs theory to incorporate combined hydrodynamic and entropic effects, so as, for instance, to accurately predict experimentally measured mean first passage times along the channel. Our approach can be used as a generic method to describe translational diffusion of anisotropic particles in corrugated channels.1 Diffusive transport through micro-structures such as occurring in porous media [1,2], micro/nano-fluidic channels [3][4][5][6][7] and living tissues [8,9], is ubiquitous and attracts evergrowing attention from physicists [10,11], mathematicians [12], engineers [1], and biologists [8,9,13]. A common feature of these systems are confining boundaries of irregular shapes.Spatial confinement can fundamentally change equilibrium and dynamical properties of a system by both limiting the configuration space accessible to its diffusing components [10] and increasing the hydrodynamic drag [14] on them.An archetypal model to study confinement effects consists of a spherical particle diffusing in a corrugated narrow channel, which mimics directed ionic channels [15], zeolites [16], and nanopores [17].…”

“…Diffusive transport through micro-structures such as occurring in porous media [1,2], micro/nano-fluidic channels [3][4][5][6][7] and living tissues [8,9], is ubiquitous and attracts evergrowing attention from physicists [10,11], mathematicians [12], engineers [1], and biologists [8,9,13]. A common feature of these systems are confining boundaries of irregular shapes.…”