Drift ratchet

Kettner, Christiane; Reimann, Peter; Hänggi, Peter; Müller, Frank

doi:10.1103/physreve.61.312

Cited by 167 publications

(197 citation statements)

References 41 publications

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“…Applying an oscillating electric field or even a mechanical vibration disrupts the contact lines between the fluid and the walls, and the asymmetry of the structured surface rectifies the motion of the drop. Along similar lines, functional drift ratchets in which the fluid in pumped back and forth in asymmetric pores in order to separate suspended particles have been built [60].…”

Section: Ratchetsmentioning

confidence: 99%

Theory of DNA electrophoresis (∼ 1999 –2002 ½)

et al. 2002

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Over the last two decades, the introduction of new methods such as pulsed-field gel electrophoresis and capillary array electrophoresis has made it possible to map and sequence entire genomes, including our own. The development of these experimental methods has been helped by the progress of theoretical and computational sciences, and the interactions between these three modi operandi of modern science are still pushing the limits of our technologies. We now see a clear trend towards proteomics and microfluidic (even nanofluidic!) devices. In this review, we take a look at the progress of the field over the last 3 years using the glasses of the theoretical scientist and focusing mostly on new ideas and concepts. About a dozen different subfields are discussed and reviewed. We conclude by giving a commented list of some of the best review articles published over the last 2-3 years.

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Section: Ratchetsmentioning

confidence: 99%

Theory of DNA electrophoresis (∼ 1999 –2002 ½)

et al. 2002

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“…Diffusion of Brownian particles through narrow, tortuous confining structures such as micropores and nanopores, zeolites, biological cells and microfluidic devices plays a prominent role in the dynamical characterization of these systems (Barrer 1978;Volkmuth & Austin 1992;Liu et al 1999;Kettner et al 2000;Müller et al 2000;Hille 2001;Nixon & Slater 2002;Matthias & Müller 2003;Berezhkovskii & Bezrukov 2005;Siwy et al 2005). Effective control schemes for transport in these systems require a detailed understanding of the diffusive mechanisms involving small objects and, in this regard, an operative measure to gauge the role of fluctuations.…”

Section: Introductionmentioning

confidence: 99%

Entropic transport: a test bed for the Fick–Jacobs approximation

Burada

Schmid

Hänggi

2009

Phil. Trans. R. Soc. A.

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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.

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“…The geometric restrictions to the system's dynamics results in entropic barriers and regulate the transport of particles yielding important effects exhibiting peculiar properties. The results have prominent implications in processes such as catalysis, osmosis and particle separation [1][2][3][4][5][6][7][8][9][10][11][12] and, as well, for the noise-induced transport in periodic potential landscapes that lack reflection symmetry (Brownian ratchet systems) [13][14][15] or Brownian motor transport occurring in arrays of periodically arranged asymmetric obstacles, termed "entropic" ratchet devices [16][17][18][19][20]. Motion in these systems can be induced by imposing different concentrations at the ends of the channel, or by the presence of external driving forces supplying the particles with the energy necessary to proceed.…”

Section: Introductionmentioning

confidence: 99%

Rectification Through Entropic Barriers

Schmid

Burada

Talkner

et al. 2009

Advances in Solid State Physics

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Abstract. 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 a constant 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 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 transversal channel direction, and a correction to the diffusion constant that introduces a space dependent diffusion. We analyze the influence of broken channel symmetry and the validity of the FickJacobs equation. For the nonlinear mobility we find a temperature dependence which is opposite to that known for particle transport in periodic energetic potentials. The influence of entropic effects is discussed for both, the nonlinear mobility, and the effective diffusion constant. In case of broken reflection symmetry rectification occurs and there is a favored direction for particle transport. The rectification effect could be maximized due to the optimal chosen absolute value of the applied bias.

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Drift ratchet

Cited by 167 publications

References 41 publications

Theory of DNA electrophoresis (∼ 1999 –2002 ½)

Theory of DNA electrophoresis (∼ 1999 –2002 ½)

Entropic transport: a test bed for the Fick–Jacobs approximation

Rectification Through Entropic Barriers

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