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Recently, it has been shown that entropy can be used to sort Brownian particles according to their size. In particular, a combination of a static and a time-dependent force applied on differently sized particles which are confined in an asymmetric periodic structure can be used to separate them efficiently, by forcing them to move in opposite directions. In this paper, we investigate the optimization of the performance of the "entropic splitter." Specifically, the splitting mechanism and how it depends on the geometry of the channel, and the frequency and strength of the periodic forcing is analyzed. Using numerical simulations, we demonstrate that a very efficient and fast separation with a practically 100% purity can be achieved by a proper optimization of the control variables. The results of this work could be useful for a more efficient separation of dispersed phases such as DNA fragments or colloids dependent on their size.

We propose a mechanism to alter the nature of the potential barriers when a biased brownian particle undergoes a constrained motion in narrow periodic channel. By changing the angle of the external bias, the nature of the potential barriers changes from purely entropic to energetic, which in turn affects the diffusion process in the system. At an optimum angle of the bias, the nonlinear mobility exhibits a striking bell-shaped behavior. Moreover, the enhancement of the scaled effective diffusion coefficient can be efficiently controlled by the angle of the bias. This mechanism enables the proper design of channel structures for transport of molecules and small particles. The approximate analytical predictions have been verified by precise brownian dynamics simulations.

Biased diffusive transport of Brownian particles through irregularly shaped, narrow confining quasi-one-dimensional structures is investigated. The complexity of the higher dimensional diffusive dynamics is reduced by means of the so-called Fick-Jacobs approximation, yielding an effective one-dimensional stochastic dynamics. Accordingly, the elimination of transverse, equilibrated degrees of freedom stemming from geometrical confinements and/or bottlenecks causes entropic potential barriers that the particles have to overcome when moving forward noisily. The applicability and the validity of the reduced kinetic description are tested by comparing the approximation with Brownian dynamics simulations in full configuration space. This non-equilibrium transport in such quasi-one-dimensional irregular structures implies, for moderate-to-strong bias, a characteristic violation of the Sutherland-Einstein fluctuation-dissipation relation.

The dynamics of Brownian motion has widespread applications extending from transport in designed micro-channels up to its prominent role for inducing transport in molecular motors and Brownian motors. Here, Brownian transport is studied in micro-sized, two-dimensional periodic channels, exhibiting periodically varying cross-sections. The particles in addition are subjected to an external force acting alongside the direction of the longitudinal channel axis. For a fixed channel geometry, the dynamics of the two-dimensional problem is characterized by a single dimensionless parameter which is proportional to the ratio of the applied force and the temperature of the particle environment. In such structures entropic effects may play a dominant role. Under certain conditions the two-dimensional dynamics can be approximated by an effective one-dimensional motion of the particle in the longitudinal direction. The Langevin equation describing this reduced, one-dimensional process is of the type of the Fick-Jacobs equation. It contains an entropic potential determined by the varying extension of the eliminated channel direction, and a correction to the diffusion constant that introduces a space dependent diffusion. Different forms of this correction term have been suggested before, which we here compare for a particular class of models. We analyze the regime of validity of the Fick-Jacobs equation, both by means of analytical estimates and the comparisons with numerical results for the full two-dimensional stochastic dynamics. For the nonlinear mobility we find a temperature dependence which is opposite to that known for particle transport in periodic potentials. The influence of entropic effects is discussed for both, the nonlinear mobility and the effective diffusion constant.

Transport of point-size Brownian particles under the influence of a constant and uniform force field through a planar three-dimensional channel with smoothly varying, axis-symmetric periodic side walls is investigated. Here we employ an asymptotic analysis in the ratio between the difference of the widest and the most narrow constriction divided through the period length of the channel geometry. We demonstrate that the leading-order term is equivalent to the Fick-Jacobs approximation. By use of the higher-order corrections to the probability density we show that in the diffusion-dominated regime the average transport velocity is obtained as the product of the zeroth-order Fick-Jacobs result and the expectation value of the spatially dependent diffusion coefficient D(x), which substitutes the constant diffusion coefficient in the common Fick-Jacobs equation. The analytic findings are corroborated with the precise numerical results of a finite element calculation of the Smoluchowski diffusive particle dynamics occurring in a reflection symmetric sinusoidal-shaped channel. [ABSTRACT FROM AUTHOR]

We analyze the diffusive transport of Brownian particles in narrow channels with periodically varying cross-section. The geometrical confinements lead to entropic barriers, the particle have to overcome in order to proceed in transport direction. The transport characteristics exhibit peculiar behaviors which are in contrast to what is observed for the transport in potentials with purely energetic barriers. By adjusting the geometric parameters of the channel one can effectively tune the transport and diffusion properties. A prominent example is the maximized enhancement of diffusion for particular channel parameters. The understanding of the role of channel-shape provides the possibility for a design of stylized channels wherein the quality of the transport can be efficiently optimized. [ABSTRACT FROM AUTHOR]

We demonstrate the existence of stochastic resonance (SR) in confined systems arising from entropy variations associated to the presence of irregular boundaries. When the motion of a Brownian particle is constrained to a region with uneven boundaries, the presence of a periodic input may give rise to a peak in the spectral amplification factor and therefore to the appearance of the SR phenomenon. We have proved that the amplification factor depends on the shape of the region through which the particle moves and that by adjusting its characteristic geometric parameters one may optimize the response of the system. The situation in which the appearance of such entropic stochastic resonance (ESR) occurs is common for small-scale systems in which confinement and noise play an prominent role. The novel mechanism found could thus constitute an important tool for the characterization of these systems and can put to use for controlling their basic properties. [ABSTRACT FROM AUTHOR]

We present a particle separation mechanism which induces the motion of particles of different sizes in opposite directions. The mechanism is based on the combined action of a driving force and an entropic rectification of the Brownian fluctuations caused by the asymmetric form of the channel along which particles proceed. The entropic splitting effect shown could be controlled upon variation of the geometrical parameters of the channel and could be implemented in narrow channels and microfluidic devices. [ABSTRACT FROM AUTHOR]

Abstract: We study the transport of point size particles in micro-sized two-dimensional periodic channels, exhibiting periodically varying cross-sections. The particles are subjected to a constant external force acting alongside the direction of the longitudinal channel axis and a varying force stemming from a periodic potential profile. While particle transport in tilted periodic potentials is facilitated by noise, the transport through pores with periodically varying cross-sections worsens with increasing noise level, i.e. increasing temperature. The competition between the noise-assisted propagation for energetic potentials and the hampered transport in confined structures leads to a striking, non-monotonic behavior which sensitively depends on the phase lag of the periodic channel structure and the periodic potential. By controlling this phase lag the symmetry could be broken and rectification observed. [ABSTRACT FROM AUTHOR]