1
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Antunes GC, Malgaretti P, Harting J. Turning catalytically active pores into active pumps. J Chem Phys 2023; 159:134903. [PMID: 37787144 DOI: 10.1063/5.0160414] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2023] [Accepted: 09/07/2023] [Indexed: 10/04/2023] Open
Abstract
We develop a semi-analytical model of self-diffusioosmotic transport in active pores, which includes advective transport and the inverse chemical reaction that consumes solute. In previous work [Antunes et al., Phys. Rev. Lett. 129, 188003 (2022)], we have demonstrated the existence of a spontaneous symmetry breaking in fore-aft symmetric pores that enables them to function as a micropump. We now show that this pumping transition is controlled by three timescales. Two timescales characterize advective and diffusive transport. The third timescale corresponds to how long a solute molecule resides in the pore before being consumed. Introducing asymmetry to the pore (either via the shape or the catalytic coating) reveals a second type of advection-enabled transition. In asymmetric pores, the flow rate exhibits discontinuous jumps and hysteresis loops upon tuning the parameters that control the asymmetry. This work demonstrates the interconnected roles of shape and catalytic patterning in the dynamics of active pores and shows how to design a pump for optimum performance.
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Affiliation(s)
- G C Antunes
- Helmholtz-Institut Erlangen-Nürnberg für Erneuerbare Energien (IEK-11), Forschungszentrum Jülich, Cauer Str. 1, 91058 Erlangen, Germany
| | - P Malgaretti
- Helmholtz-Institut Erlangen-Nürnberg für Erneuerbare Energien (IEK-11), Forschungszentrum Jülich, Cauer Str. 1, 91058 Erlangen, Germany
| | - J Harting
- Helmholtz-Institut Erlangen-Nürnberg für Erneuerbare Energien (IEK-11), Forschungszentrum Jülich, Cauer Str. 1, 91058 Erlangen, Germany
- Department Chemie- und Bioingenieurwesen und Department Physik, Friedrich-Alexander-Universität Erlangen-Nürnberg, Fürther Straße 248, 90429 Nürnberg, Germany
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2
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Kalinay P, Slanina F. Ratchet effect in an asymmetric two-dimensional system of Janus particles. Phys Rev E 2023; 108:014606. [PMID: 37583160 DOI: 10.1103/physreve.108.014606] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2023] [Accepted: 06/28/2023] [Indexed: 08/17/2023]
Abstract
We consider a disk-like Janus particle self-driven by a force of constant magnitude f, but an arbitrary direction depending on the stochastic rotation of the disk. The particle diffuses in a two-dimensional channel of varying width 2h(x). We applied the procedure mapping the 2+1-dimensional Fokker-Planck equation onto the longitudinal coordinate x; the result is the Fick-Jacobs equation extended by the spatially dependent effective diffusion constant D(x) and an additional effective potential -γ(x), derived recursively within the mapping procedure. Unlike the entropic potential ∼lnh(x), γ(x) becomes an increasing or decreasing function also in periodic channels, depending on the asymmetry of h(x) and thus it visualizes the net force driving the ratchet current. We demonstrate the appearance of the ratchet effect on a trial asymmetric channel; our theory is verified by a numerical solution of the corresponding Fokker-Planck equation. Isotropic driving force f results in the monotonic decrease of the ratchet current with a growing ratio α=D_{R}/D_{T} of the rotation and the translation diffusion constants; asymptotically going ∼1/α^{2}. If we allow anisotropy of the force, we can observe the current reversal depending on α.
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Affiliation(s)
- Pavol Kalinay
- Institute of Physics, Slovak Academy of Sciences, Dúbravska cesta 9, 84511, Bratislava, Slovakia
| | - František Slanina
- Institute of Physics, Czech Academy of Sciences, Na Slovance 2, CZ-18200, Praha, Czech Republic
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3
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Modica KJ, Omar AK, Takatori SC. Boundary design regulates the diffusion of active matter in heterogeneous environments. SOFT MATTER 2023; 19:1890-1899. [PMID: 36790413 DOI: 10.1039/d2sm01421a] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/18/2023]
Abstract
Physical boundaries play a key role in governing the overall transport properties of nearby self-propelled particles. In this work, we develop dispersion theories and conduct Brownian dynamics simulations to predict the coupling between surface accumulation and effective diffusivity of active particles in boundary-rich media. We focus on three models that are well-understood for passive systems: particle transport in (i) an array of fixed volume-excluding obstacles; (ii) a pore with spatially heterogeneous width; and (iii) a tortuous path with kinks and corners. While the impact of these entropic barriers on passive particle transport is well established, we find that these classical models of porous media flows break down due to the unique interplay between activity and the microstructure of the internal geometry. We study the activity-induced slowdown of effective diffusivity by formulating a Smoluchowski description of long-time self diffusivity which contains contributions from the density and fluctuation fields of the active particles. Particle-based and finite element simulations corroborate this perspective and reveal important nonequilibrium considerations of active transport.
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Affiliation(s)
- Kevin J Modica
- Department of Chemical Engineering, University of California, Santa Barbara, Santa Barbara, CA 93106, USA.
| | - Ahmad K Omar
- Department of Materials Science and Engineering, University of California, Berkeley, Berkeley, CA 94720, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
| | - Sho C Takatori
- Department of Chemical Engineering, University of California, Santa Barbara, Santa Barbara, CA 93106, USA.
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4
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Malgaretti P, Harting J. Closed Formula for Transport across Constrictions. ENTROPY (BASEL, SWITZERLAND) 2023; 25:470. [PMID: 36981357 PMCID: PMC10047801 DOI: 10.3390/e25030470] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/03/2023] [Revised: 03/01/2023] [Accepted: 03/05/2023] [Indexed: 06/18/2023]
Abstract
In the last decade, the Fick-Jacobs approximation has been exploited to capture transport across constrictions. Here, we review the derivation of the Fick-Jacobs equation with particular emphasis on its linear response regime. We show that, for fore-aft symmetric channels, the flux of noninteracting systems is fully captured by its linear response regime. For this case, we derive a very simple formula that captures the correct trends and can be exploited as a simple tool to design experiments or simulations. Lastly, we show that higher-order corrections in the flux may appear for nonsymmetric channels.
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Affiliation(s)
- Paolo Malgaretti
- Helmholtz Institute Erlangen-Nürnberg for Renewable Energy, Forschungszentrum Jülich, 90429 Erlangen, Germany
| | - Jens Harting
- Helmholtz Institute Erlangen-Nürnberg for Renewable Energy, Forschungszentrum Jülich, 90429 Erlangen, Germany
- Department of Chemical and Biological Engineering and Department of Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg, 90429 Erlangen, Germany
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5
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Jain S, Boyer D, Pal A, Dagdug L. Fick-Jacobs description and first passage dynamics for diffusion in a channel under stochastic resetting. J Chem Phys 2023; 158:054113. [PMID: 36754825 DOI: 10.1063/5.0135249] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/09/2023] Open
Abstract
The transport of particles through channels is of paramount importance in physics, chemistry, and surface science due to its broad real world applications. Much insight can be gained by observing the transition paths of a particle through a channel and collecting statistics on the lifetimes in the channel or the escape probabilities from the channel. In this paper, we consider the diffusive transport through a narrow conical channel of a Brownian particle subject to intermittent dynamics, namely, stochastic resetting. As such, resetting brings the particle back to a desired location from where it resumes its diffusive phase. To this end, we extend the Fick-Jacobs theory of channel-facilitated diffusive transport to resetting-induced transport. Exact expressions for the conditional mean first passage times, escape probabilities, and the total average lifetime in the channel are obtained, and their behavior as a function of the resetting rate is highlighted. It is shown that resetting can expedite the transport through the channel-rigorous constraints for such conditions are then illustrated. Furthermore, we observe that a carefully chosen resetting rate can render the average lifetime of the particle inside the channel minimal. Interestingly, the optimal rate undergoes continuous and discontinuous transitions as some relevant system parameters are varied. The validity of our one-dimensional analysis and the corresponding theoretical predictions is supported by three-dimensional Brownian dynamics simulations. We thus believe that resetting can be useful to facilitate particle transport across biological membranes-a phenomenon that can spearhead further theoretical and experimental studies.
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Affiliation(s)
- Siddharth Jain
- Harish-Chandra Research Institute, HBNI, Chhatnag Road, Jhunsi, Allahabad (Prayagraj), UP, 211019, India
| | - Denis Boyer
- Instituto de Física, Universidad Nacional Autónoma de México, Ciudad de México C.P. 04510, Mexico
| | - Arnab Pal
- The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600113, India
| | - Leonardo Dagdug
- Physics Department, Universidad Autónoma Metropolitana-Iztapalapa, San Rafael Atlixco 186, Ciudad de México 09340, Mexico
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6
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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.
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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
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7
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Kalinay P. Transverse dichotomic ratchet in a two-dimensional corrugated channel. Phys Rev E 2022; 106:044126. [PMID: 36397573 DOI: 10.1103/physreve.106.044126] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/29/2022] [Accepted: 09/23/2022] [Indexed: 06/16/2023]
Abstract
A particle diffusing in a two-dimensional channel of varying width h(x) is considered. It is driven by a force of constant magnitude f, but random orientation across the channel. We suggest the projection technique to study the ratchet effect appearing in this system. Reducing the transverse coordinate, as well as the orientation of the force in the full-dimensional Fokker-Planck equation, we arrive at the generalized Fick-Jacobs equation, describing dynamics of the system in the longitudinal coordinate x only. The additional effective potential -γ(x), calculated within the mapping procedure, exhibits an increasing or decreasing part in the channel shaped by an asymmetric periodic h(x), which determines the appearing ratchet current. As shown on a specific example, random driving in the transverse direction is much more effective than that in the longitudinal direction, at least for quickly flipping orientation of the force. Also, the transverse and the longitudinal driving push the rectified current in opposite directions along the same channel.
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Affiliation(s)
- Pavol Kalinay
- Institute of Physics, Slovak Academy of Sciences, Dúbravska cesta 9, 84511, Bratislava, Slovakia
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8
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Kalinay P, Slanina F. Dichotomic ratchet in a two-dimensional corrugated channel. Phys Rev E 2021; 104:064115. [PMID: 35030943 DOI: 10.1103/physreve.104.064115] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/04/2021] [Accepted: 11/29/2021] [Indexed: 06/14/2023]
Abstract
We consider a particle diffusing in a two-dimensional (2D) channel of varying width h(x). It is driven by a force of constant magnitude f but random orientation there or back along the channel. We derive the effective generalized Fick-Jacobs equation for this system, which describes the dynamics of such a particle in the longitudinal coordinate x. Aside from the effective diffusion coefficient D(x), our mapping also generates an additional effective potential -γ(x) added to the entropic potential -log[h(x)]. It acquires an increasing or decreasing component in asymmetric periodic channels, and thus it explains appearance of the ratchet current. We study this effect on a trial example and compare the results of our true 2D theory with a commonly used effective one-dimensional description; the data are verified by the numerical solution of the full 2D problem.
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Affiliation(s)
- Pavol Kalinay
- Institute of Physics, Slovak Academy of Sciences, Dúbravska cesta 9, 84511, Bratislava, Slovakia
| | - František Slanina
- Institute of Physics, Czech Academy of Sciences, Na Slovance 2, CZ-18221, Prague, Czech Republic
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9
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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].
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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
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10
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Kalinay P. Reduced dynamics of a one-dimensional Janus particle. Phys Rev E 2021; 104:014608. [PMID: 34412275 DOI: 10.1103/physreve.104.014608] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2021] [Accepted: 07/08/2021] [Indexed: 11/07/2022]
Abstract
A Janus particle diffusing on a line is considered. Aside from its own driving force f acting forward or backward according to its stochastic orientation, it moves in a position-dependent potential U(x). We propose here the mapping scheme generating the effective generalized Fick-Jacobs equation, describing motion of the particle in the spatial coordinate x only; the orientation is understood as the transverse coordinate. The self-propulsion, driving the system out of equilibrium, is reflected as an additional effective potential -γ(x) in the reduced picture. It enables us to understand peculiarities of this system in a handy way. The additionally corrected potential redistributes the confined particles in quasiequilibrium causing their piling at the walls. In periodic asymmetric channels, it acquires a growing contribution, responsible for driving the ratchet effect.
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Affiliation(s)
- Pavol Kalinay
- Institute of Physics, Slovak Academy of Sciences, Dúbravska cesta 9, 84511 Bratislava, Slovakia
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11
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Caprini L, Cecconi F, Marini Bettolo Marconi U. Transport of active particles in an open-wedge channel. J Chem Phys 2019; 150:144903. [DOI: 10.1063/1.5090104] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Lorenzo Caprini
- Gran Sasso Science Institute (GSSI), Via F.Crispi 7, I-67100 L’Aquila, Italy
| | - Fabio Cecconi
- Istituto dei Sistemi Complessi (CNR), Via Taurini 19, I-00185 Roma, Italy
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12
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Puertas AM, Malgaretti P, Pagonabarraga I. Active microrheology in corrugated channels. J Chem Phys 2018; 149:174908. [DOI: 10.1063/1.5048343] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
Affiliation(s)
- Antonio M. Puertas
- Department of Applied Physics, Universidad de Almería, 04120 Almería, Spain
| | - Paolo Malgaretti
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstr. 3, D-70569 Stuttgart, Germany and IV. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany
| | - Ignacio Pagonabarraga
- CECAM, Centre Européen de Calcul Atomique et Moléculaire, École Polytechnique Fédérale de Lasuanne, Batochime, Avenue Forel 2, 1015 Lausanne, Switzerland
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13
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Abstract
We derive a general closed expression for the local pressure exerted onto the corrugated walls of a channel confining a fluid medium. When the fluid medium is at equilibrium, the local pressure is a functional of the shape of the walls. It is shown that, due to the intrinsic nonlocal character of the interactions among the particles forming the fluid, the applicability of approximate schemes such as the concept of a surface of tension or morphometric thermodynamics is limited to wall curvatures that are small compared to the range of particle-particle interactions.
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Affiliation(s)
- Paolo Malgaretti
- Max Planck Institute for Intelligent Systems, Heisenbergstrasse 3, 70569 Stuttgart, Germany and Institute for Theoretical Physics IV, University of Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
| | - Markus Bier
- Max Planck Institute for Intelligent Systems, Heisenbergstrasse 3, 70569 Stuttgart, Germany and Institute for Theoretical Physics IV, University of Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
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14
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Malgaretti P, Stark H. Model microswimmers in channels with varying cross section. J Chem Phys 2017; 146:174901. [DOI: 10.1063/1.4981886] [Citation(s) in RCA: 33] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023] Open
Affiliation(s)
- Paolo Malgaretti
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstr. 3, D-70569 Stuttgart, Germany
- IV. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany
| | - Holger Stark
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany
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16
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Sosa-Hernández JE, Santillán M, Santana-Solano J. Motility of Escherichia coli in a quasi-two-dimensional porous medium. Phys Rev E 2017; 95:032404. [PMID: 28415239 DOI: 10.1103/physreve.95.032404] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/07/2016] [Indexed: 06/07/2023]
Abstract
Bacterial migration through confined spaces is critical for several phenomena, such as biofilm formation, bacterial transport in soils, and bacterial therapy against cancer. In the present work, E. coli (strain K12-MG1655 WT) motility was characterized by recording and analyzing individual bacterium trajectories in a simulated quasi-two-dimensional porous medium. The porous medium was simulated by enclosing, between slide and cover slip, a bacterial-culture sample mixed with uniform 2.98-μm-diameter spherical latex particles. The porosity of the medium was controlled by changing the latex particle concentration. By statistically analyzing several trajectory parameters (instantaneous velocity, turn angle, mean squared displacement, etc.), and contrasting with the results of a random-walk model developed ad hoc, we were able to quantify the effects that different obstacle concentrations have upon bacterial motility.
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Affiliation(s)
- Juan Eduardo Sosa-Hernández
- Centro de Investigación y de Estudios Avanzados del IPN, Unidad Monterrey, Vía del Conocimiento 201, Parque PIIT, 66600 Apodaca NL, Mexico
| | - Moisés Santillán
- Centro de Investigación y de Estudios Avanzados del IPN, Unidad Monterrey, Vía del Conocimiento 201, Parque PIIT, 66600 Apodaca NL, Mexico
| | - Jesús Santana-Solano
- Centro de Investigación y de Estudios Avanzados del IPN, Unidad Monterrey, Vía del Conocimiento 201, Parque PIIT, 66600 Apodaca NL, Mexico
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17
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Verdel R, Dagdug L, Berezhkovskii AM, Bezrukov SM. Unbiased diffusion in two-dimensional channels with corrugated walls. J Chem Phys 2016; 144:084106. [PMID: 26931680 DOI: 10.1063/1.4942470] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
This paper deals with diffusion of point particles in linearly corrugated two-dimensional channels. Such geometry allows one to obtain an approximate analytical expression that gives the particle effective diffusivity as a function of the geometric parameters of the channel. To establish its accuracy and the range of applicability, the expression is tested against Brownian dynamics simulation results. The test shows that the expression works very well for long channel periods, but fails when the period is not long enough compared to the minimum width of the channel. To fix this deficiency, we propose a simple empirical correction to the analytical expression. The resulting corrected expression for the effective diffusivity is in excellent agreement with the simulation results for all values of the channel period.
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Affiliation(s)
- Roberto Verdel
- Physics Department, Universidad Autonoma Metropolitana-Iztapalapa, 09340 Mexico City, Mexico
| | - Leonardo Dagdug
- Physics Department, Universidad Autonoma Metropolitana-Iztapalapa, 09340 Mexico City, Mexico
| | - Alexander M Berezhkovskii
- Mathematical and Statistical Computing Laboratory, Division for Computational Bioscience, Center for Information Technology, National Institutes of Health, Bethesda, Maryland 20892, USA
| | - Sergey M Bezrukov
- Program in Physical Biology, Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, Maryland 20892, USA
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18
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Khalilian H, Fazli H. Obstruction enhances the diffusivity of self-propelled rod-like particles. J Chem Phys 2016; 145:164909. [DOI: 10.1063/1.4966188] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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19
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Sandoval M, Jimenez A. Two-dimensional motion of Brownian swimmers in linear flows. J Biol Phys 2015; 42:199-212. [PMID: 26428909 DOI: 10.1007/s10867-015-9401-4] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2015] [Accepted: 09/07/2015] [Indexed: 11/28/2022] Open
Abstract
The motion of viruses and bacteria and even synthetic microswimmers can be affected by thermal fluctuations and by external flows. In this work, we study the effect of linear external flows and thermal fluctuations on the diffusion of those swimmers modeled as spherical active (self-propelled) particles moving in two dimensions. General formulae for their mean-square displacement under a general linear flow are presented. We also provide, at short and long times, explicit expressions for the mean-square displacement of a swimmer immersed in three canonical flows, namely, solid-body rotation, shear and extensional flows. These expressions can now be used to estimate the effect of external flows on the displacement of Brownian microswimmers. Finally, our theoretical results are validated by using Brownian dynamics simulations.
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Affiliation(s)
- Mario Sandoval
- Department of Physics, Universidad Autonoma Metropolitana-Iztapalapa, Mexico, Distrito Federal, 09340, Mexico.
| | - Alonso Jimenez
- Department of Physics, Universidad Autonoma Metropolitana-Iztapalapa, Mexico, Distrito Federal, 09340, Mexico
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