1
|
Pompa-García I, Castilla R, Metzler R, Dagdug L. First-passage times in conical varying-width channels biased by a transverse gravitational force: Comparison of analytical and numerical results. Phys Rev E 2022; 106:064137. [PMID: 36671151 DOI: 10.1103/physreve.106.064137] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/02/2022] [Accepted: 12/20/2022] [Indexed: 06/17/2023]
Abstract
We study the crossing time statistic of diffusing point particles between the two ends of expanding and narrowing two-dimensional conical channels under a transverse external gravitational field. The theoretical expression for the mean first-passage time for such a system is derived under the assumption that the axial diffusion in a two-dimensional channel of smoothly varying geometry can be approximately described as a one-dimensional diffusion in an entropic potential with position-dependent effective diffusivity in terms of the modified Fick-Jacobs equation. We analyze the channel crossing dynamics in terms of the mean first-passage time, combining our analytical results with extensive two-dimensional Brownian dynamics simulations, allowing us to find the range of applicability of the one-dimensional approximation. We find that the effective particle diffusivity decreases with increasing amplitude of the external potential. Remarkably, the mean first-passage time for crossing the channel is shown to assume a minimum at finite values of the potential amplitude.
Collapse
Affiliation(s)
- Ivan Pompa-García
- Physics Department, Universidad Autónoma Metropolitana-Iztapalapa, San Rafael Atlixco 186, Ciudad de México, 09340, México
| | - Rodrigo Castilla
- Engineering Faculty, Universidad Nacional Autónoma de México, Ciudad Universitaria, Ciudad de México, 04510, México
| | - Ralf Metzler
- Institute of Physics and Astronomy, University of Potsdam, D-14476 Potsdam-Golm, Germany
- Asia Pacific Center for Theoretical Physics, Pohang 37673, Republic of Korea
| | - Leonardo Dagdug
- Physics Department, Universidad Autónoma Metropolitana-Iztapalapa, San Rafael Atlixco 186, Ciudad de México, 09340, México
| |
Collapse
|
2
|
Pompa-García I, Dagdug L. Two-dimensional diffusion biased by a transverse gravitational force in an asymmetric channel: Reduction to an effective one-dimensional description. Phys Rev E 2021; 104:044118. [PMID: 34781435 DOI: 10.1103/physreve.104.044118] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2021] [Accepted: 10/01/2021] [Indexed: 11/07/2022]
Abstract
We focus on the derivation of a general position-dependent effective diffusion coefficient to describe two-dimensional (2D) diffusion in a narrow and smoothly asymmetric channel of varying width under a transverse gravitational external field, a generalization of the symmetric channel case using the projection method introduced earlier by Kalinay and Percus [P. Kalinay and J. K. Percus, J. Chem. Phys. 122, 204701 (2005)10.1063/1.1899150]. To this end, we project the 2D Smoluchowski equation into an effective one-dimensional generalized Fick-Jacobs equation in the presence of constant force in the transverse direction. The expression for the diffusion coefficient given in Eq. (34) is our main result. This expression is a more general effective diffusion coefficient for narrow 2D channels in the presence of constant transverse force, which contains the well-known previous results for a symmetric channel obtained by Kalinay, as well as the limiting cases when the transverse gravitational external field goes to zero and infinity. Finally, we show that diffusivity can be described by the interpolation formula proposed by Kalinay, D_{0}/[1+(1/4)w^{'2}(x)]^{-η}, where spatial confinement, asymmetry, and the presence of a constant transverse force can be encoded in η, which is a function of channel width (w), channel centerline, and transverse force. The interpolation formula also reduces to well-known previous results, namely, those obtained by Reguera and Rubi [D. Reguera and J. M. Rubi, Phys. Rev. E 64, 061106 (2001)10.1103/PhysRevE.64.061106] and by Kalinay [P. Kalinay, Phys. Rev. E 84, 011118 (2011)10.1103/PhysRevE.84.011118].
Collapse
Affiliation(s)
- Ivan Pompa-García
- Physics Department, Universidad Autónoma Metropolitana-Iztapalapa, San Rafael Atlixco 186, Ciudad de México 09340, Mexico
| | - Leonardo Dagdug
- Physics Department, Universidad Autónoma Metropolitana-Iztapalapa, San Rafael Atlixco 186, Ciudad de México 09340, Mexico
| |
Collapse
|
3
|
Nagarajan K, Chen SB. Polyelectrolyte Translocation through a Corrugated Nanopore. MACROMOL THEOR SIMUL 2020. [DOI: 10.1002/mats.202000042] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023]
Affiliation(s)
- Karthik Nagarajan
- Department of Chemical & Biomolecular EngineeringNational University of Singapore Singapore 117585 Singapore
| | - Shing Bor Chen
- Department of Chemical & Biomolecular EngineeringNational University of Singapore Singapore 117585 Singapore
| |
Collapse
|
4
|
|
5
|
Das M, Ray DS. Landauer's blow-torch effect in systems with entropic potential. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:052133. [PMID: 26651672 DOI: 10.1103/physreve.92.052133] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/17/2015] [Indexed: 06/05/2023]
Abstract
We consider local heating of a part of a two-dimensional bilobal enclosure of a varying cross section confining a system of overdamped Brownian particles. Since varying cross section in higher dimension results in an entropic potential in lower dimension, local heating alters the relative stability of the entropic states. We show that this blow-torch effect modifies the entropic potential in a significant way so that the resultant effective entropic potential carries both the features of variation of width of the confinement and variation of temperature along the direction of transport. The reduced probability distribution along the direction of transport calculated by full numerical simulations in two dimensions agrees well with our analytical findings. The extent of population transfer in the steady state quantified in terms of the integrated probability of residence of the particles in either of the two lobes exhibits interesting variation with the mean position of the heated region. Our study reveals that heating around two particular zones of a given lobe maximizes population transfer to the other.
Collapse
Affiliation(s)
- Moupriya Das
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata-700032, India
| | - Deb Shankar Ray
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata-700032, India
| |
Collapse
|
6
|
Kalinay P. Generalized method calculating the effective diffusion coefficient in periodic channels. J Chem Phys 2015; 142:014106. [DOI: 10.1063/1.4905079] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
7
|
|
8
|
Bernate JA, Drazer G. Stochastic and deterministic vector chromatography of suspended particles in one-dimensional periodic potentials. PHYSICAL REVIEW LETTERS 2012; 108:214501. [PMID: 23003265 DOI: 10.1103/physrevlett.108.214501] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/12/2011] [Indexed: 06/01/2023]
Abstract
We present a comprehensive description of vector chromatography (VC) that includes deterministic and stochastic transport in one-dimensional periodic free-energy landscapes, with both energetic and entropic contributions, and identifies the parameters governing the deflection angle. We also investigate the dependence of the deflection angle on the shape of the free-energy landscape by varying the width of the linear transitions in an otherwise dichotomous potential. Finally, we present experimental results obtained in a microfluidic system in which gravity drives the suspended particles and, in combination with a bottom surface patterned with shallow rectangular grooves, creates a periodic landscape of (potential) energy barriers. The experiments validate the model and demonstrate that a simple, passive microdevice can lead to VC of colloidal particles based on both size and density. More generally, other fields, e.g., electric, dielectrophoretic, or magnetic, can play or enhance the role of gravity, potentially leading to a versatile technique.
Collapse
Affiliation(s)
- Jorge A Bernate
- Department of Chemical and Biomolecular Engineering, Johns Hopkins University, Baltimore, Maryland 21218, USA.
| | | |
Collapse
|
9
|
Mondal D, Das M, Ray DS. Entropic dynamical hysteresis in a driven system. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:031128. [PMID: 22587059 DOI: 10.1103/physreve.85.031128] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/04/2012] [Indexed: 05/31/2023]
Abstract
We show that the application of a time periodic field driving a Brownian particle between the two lobes of a two-dimensional bilobal enclosure results in a hysteresis loop in the variation of integrated probability of residence of the particle as a function of the field. The confinement of the particle is characterized by symmetry breaking of the hysteresis loop, and the area of the loop exhibits a turnover with variation of frequency of the field. This dynamical hysteresis is geometry controlled, entropic in nature, and amenable to theoretical analysis with a two-state model.
Collapse
Affiliation(s)
- Debasish Mondal
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata, India
| | | | | |
Collapse
|
10
|
Martens S, Schmid G, Schimansky-Geier L, Hänggi P. Biased Brownian motion in extremely corrugated tubes. CHAOS (WOODBURY, N.Y.) 2011; 21:047518. [PMID: 22225392 DOI: 10.1063/1.3658621] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
Biased Brownian motion of point-size particles in a three-dimensional tube with varying cross-section is investigated. In the fashion of our recent work, Martens et al. [Phys. Rev. E 83, 051135 (2011)] we employ an asymptotic analysis to the stationary probability density in a geometric parameter of the tube geometry. We demonstrate that the leading order term is equivalent to the Fick-Jacobs approximation. Expression for the higher order corrections to the probability density is derived. Using this expansion orders, we obtain that in the diffusion dominated regime the average particle current equals the zeroth order Fick-Jacobs result corrected by a factor including the corrugation of the tube geometry. In particular, we demonstrate that this estimate is more accurate for extremely corrugated geometries compared with the common applied method using a spatially-dependent diffusion coefficient D(x, f) which substitutes the constant diffusion coefficient in the common Fick-Jacobs equation. The analytic findings are corroborated with the finite element calculation of a sinusoidal-shaped tube.
Collapse
Affiliation(s)
- S Martens
- Department of Physics, Humboldt-Universität zu Berlin, Newtonstr. 15, 12489 Berlin, Germany.
| | | | | | | |
Collapse
|
11
|
Kalinay P. Effective one-dimensional description of confined diffusion biased by a transverse gravitational force. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:011118. [PMID: 21867124 DOI: 10.1103/physreve.84.011118] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/14/2011] [Indexed: 05/31/2023]
Abstract
Diffusion of pointlike noninteracting particles in a two-dimensional channel of varying cross section is considered. The particles are biased by a constant force in the transverse direction. A recurrence mapping procedure is applied, which enables the derivation of an effective one-dimensional (1D) evolution equation that governs the 1D density of the particles in the channel. In the limit of stationary flow, an extended Fick-Jacobs equation is reached, which is corrected by an effective diffusion coefficient D(x) that depends on the longitudinal coordinate x. The result is an approximate formula for D(x) that also involves the influence of the transverse force. The calculations are verified by the stationary diffusion in a linear cone, which is exactly solvable.
Collapse
Affiliation(s)
- Pavol Kalinay
- Institute of Physics, Slovak Academy of Sciences, Dúbravska cesta 9, 84511 Bratislava, Slovakia
| |
Collapse
|
12
|
Mondal D. Enhancement of entropic transport by intermediates. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:011149. [PMID: 21867154 DOI: 10.1103/physreve.84.011149] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/21/2010] [Revised: 04/08/2011] [Indexed: 05/31/2023]
Abstract
Brownian particles confined in a two-dimensional enclosure that give rise to a bistable entropic potential are considered. With the introduction of an intermediate lobe, the mean first passage time from one lobe to another through the intermediate shows a turnover behavior with the variation of the stability of the entropic intermediate. The mean escape time shows a minimum for an optimal value of the barrier height of the intermediate state. A three-state model is proposed to explain the nonmonotonic behavior of the entropic transport.
Collapse
Affiliation(s)
- Debasish Mondal
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700-032, India.
| |
Collapse
|
13
|
Martens S, Schmid G, Schimansky-Geier L, Hänggi P. Entropic particle transport: higher-order corrections to the Fick-Jacobs diffusion equation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:051135. [PMID: 21728518 DOI: 10.1103/physreve.83.051135] [Citation(s) in RCA: 46] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/24/2011] [Indexed: 05/31/2023]
Abstract
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.
Collapse
Affiliation(s)
- S Martens
- Department of Physics, Humboldt-Universität zu Berlin, Berlin, Germany.
| | | | | | | |
Collapse
|
14
|
Berezhkovskii AM, Dagdug L. Analytical treatment of biased diffusion in tubes with periodic dead ends. J Chem Phys 2011; 134:124109. [PMID: 21456647 PMCID: PMC3078163 DOI: 10.1063/1.3567187] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2011] [Accepted: 02/25/2011] [Indexed: 11/14/2022] Open
Abstract
Effective mobility and diffusion coefficient of a particle in a tube with identical periodic dead ends characterize the motion on large time scale, when the particle displacement significantly exceeds the tube period. We derive formulas that show how these transport coefficients depend on the driving force and the geometric parameters of the system. Numerical tests show that values of the transport coefficients obtained from Brownian dynamics simulations are in excellent agreement with our theoretical predictions.
Collapse
Affiliation(s)
- Alexander M Berezhkovskii
- Mathematical and Statistical Computing Laboratory, Division of Computational Bioscience, Center for Information Technology, National Institutes of Health, Bethesda, Maryland 20892, USA
| | | |
Collapse
|
15
|
Dagdug L, Berezhkovskii AM, Makhnovskii YA, Zitserman VY, Bezrukov SM. Communication: Turnover behavior of effective mobility in a tube with periodic entropy potential. J Chem Phys 2011; 134:101102. [PMID: 21405148 PMCID: PMC3069984 DOI: 10.1063/1.3561680] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/14/2011] [Accepted: 02/12/2011] [Indexed: 11/14/2022] Open
Abstract
Using Brownian dynamics simulations, we study the effective mobility and diffusion coefficient of a point particle in a tube formed from identical compartments of varying diameter, as functions of the driving force applied along the tube axis. Our primary focus is on how the driving force dependences of these transport coefficients are modified by the changes in the compartment shape. In addition to monotonically increasing or decreasing behavior of the effective mobility in periodic entropy potentials reported earlier, we now show that the effective mobility can even be nonmonotonic in the driving force.
Collapse
Affiliation(s)
- Leonardo Dagdug
- Division of Computational Bioscience, Center for Information Technology, National Institutes of Health, Bethesda, Maryland 20892, USA
| | | | | | | | | |
Collapse
|