2,935 research outputs found
How entropy and hydrodynamics cooperate in rectifying particle transport
Using the analytical Fick-Jacobs approximation formalism and extensive
Brownian dynamics simulations we study particle transport through
two-dimensional periodic channels with triangularly shaped walls. Directed
motion is caused by the interplay of constant bias acting along the channel
axis and a pressure-driven flow. In particular, we analyze the particle
mobility and the effective diffusion coefficient. The mechanisms of entropic
rectification is revealed in channels with a broken spatial reflection symmetry
in presence of hydrodynamically enforced entropic trapping. Due to the combined
action of the forcing and the pressure-driven flow field, efficient
rectification with a drastically reduced diffusivity is achieved.Comment: 11 pages, 7 figure
Entropic transport - A test bed for the Fick-Jacobs approximation
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
cause entropic potential barriers which the particles have to overcome when
moving forward noisily. The applicability and the validity of the reduced
kinetic description is 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.Comment: 15 pages, 6 figures ; Phil. Trans. R. Soc. A (2009), in pres
Entropy production and rectification efficiency in colloids transport along a pulsating channel
We study the current rectification of particles moving in a pulsating channel
under the in uence of an applied force. We have shown the existence of diferent
rectification scenarios in which entropic and energetic effects compete. The
effect can be quantified by means of a rectification coefficient that is
analyzed in terms of the force, the frequency and the diffusion coefficient.
The energetic cost of the motion of the particles expressed in terms of the
entropy production depends on the importance of the entropic contribution to
the total force. Rectification is more important at low values of the applied
force when entropic effects become dominant. In this regime, the entropy
production is not invariant under reversal of the applied force. The phenomenon
observed could be used to optimize transport in microfluidic devices or in
biological channels
Hydrodynamic and entropic effects on colloidal diffusion in corrugated channels
In the absence of advection, confined diffusion characterizes transport in
many natural and artificial devices, such as ionic channels, zeolites, and
nanopores. While extensive theoretical and numerical studies on this subject
have produced many important predictions, experimental verifications of the
predictions are rare. Here, we experimentally measure colloidal diffusion times
in microchannels with periodically varying width and contrast results with
predictions from the Fick-Jacobs theory and Brownian dynamics simulation. While
the theory and simulation correctly predict the entropic effect of the varying
channel width, they fail to account for hydrodynamic effects, which include
both an overall decrease and a spatial variation of diffusivity in channels.
Neglecting such hydrodynamic effects, the theory and simulation underestimate
the mean and standard deviation of first passage times by 40\% in channels with
a neck width twice the particle diameter. We further show that the validity of
the Fick-Jakobs theory can be restored by reformulating it in terms of the
experimentally measured diffusivity. Our work thus demonstrates that
hydrodynamic effects play a key role in diffusive transport through narrow
channels and should be included in theoretical and numerical models.Comment: 7 pages, 4 figure
Giant enhancement of hydrodynamically enforced entropic trapping in thin channels
Using our generalized Fick-Jacobs approach [Martens et al., PRL 110, 010601
(2013); Martens et al., Eur. Phys. J. Spec. Topics 222, 2453-2463 (2013)] and
extensive Brownian dynamics simulations, we study particle transport through
three-dimensional periodic channels of different height. Directed motion is
caused by the interplay of constant bias acting along the channel axis and a
pressure-driven flow. The tremendous change of the flow profile shape in
channel direction with the channel height is reflected in a crucial dependence
of the mean particle velocity and the effective diffusion coefficient on the
channel height. In particular, we observe a giant suppression of the effective
diffusivity in thin channels; four orders of magnitude compared to the bulk
value.Comment: 16 pages, 8 figure
Controlling diffusive transport in confined geometries
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 has 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.Comment: accepted for publication in Acta Physica Polonica
Driven Brownian transport through arrays of symmetric obstacles
We numerically investigate the transport of a suspended overdamped Brownian
particle which is driven through a two-dimensional rectangular array of
circular obstacles with finite radius. Two limiting cases are considered in
detail, namely, when the constant drive is parallel to the principal or the
diagonal array axes. This corresponds to studying the Brownian transport in
periodic channels with reflecting walls of different topologies. The mobility
and diffusivity of the transported particles in such channels are determined as
functions of the drive and the array geometric parameters. Prominent transport
features, like negative differential mobilities, excess diffusion peaks, and
unconventional asymptotic behaviors, are explained in terms of two distinct
lengths, the size of single obstacles (trapping length) and the lattice
constant of the array (local correlation length). Local correlation effects are
further analyzed by continuously rotating the drive between the two limiting
orientations.Comment: 10 pages 13 figure
Biased diffusion in confined media: Test of the Fick-Jacobs approximation and validity criteria
We study biased, diffusive transport of Brownian particles through narrow,
spatially periodic structures in which the motion is constrained in lateral
directions. The problem is analyzed under the perspective of the Fick-Jacobs
equation which accounts for the effect of the lateral confinement by
introducing an entropic barrier in a one dimensional diffusion. The validity of
this approximation, being based on the assumption of an instantaneous
equilibration of the particle distribution in the cross-section of the
structure, is analyzed by comparing the different time scales that characterize
the problem. A validity criterion is established in terms of the shape of the
structure and of the applied force. It is analytically corroborated and
verified by numerical simulations that the critical value of the force up to
which this description holds true scales as the square of the periodicity of
the structure. The criterion can be visualized by means of a diagram
representing the regions where the Fick-Jacobs description becomes inaccurate
in terms of the scaled force versus the periodicity of the structure.Comment: 20 pages, 7 figure
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