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Straube AV, Winkelmann S, Höfling F. Accurate Reduced Models for the pH Oscillations in the Urea-Urease Reaction Confined to Giant Lipid Vesicles. J Phys Chem B 2023; 127:2955-2967. [PMID: 36976257 DOI: 10.1021/acs.jpcb.2c09092] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/29/2023]
Abstract
This theoretical study concerns a pH oscillator based on the urea-urease reaction confined to giant lipid vesicles. Under suitable conditions, differential transport of urea and hydrogen ion across the unilamellar vesicle membrane periodically resets the pH clock that switches the system from acid to basic, resulting in self-sustained oscillations. We analyze the structure of the phase flow and of the limit cycle, which controls the dynamics for giant vesicles and dominates the pronouncedly stochastic oscillations in small vesicles of submicrometer size. To this end, we derive reduced models, which are amenable to analytic treatments that are complemented by numerical solutions, and obtain the period and amplitude of the oscillations as well as the parameter domain, where oscillatory behavior persists. We show that the accuracy of these predictions is highly sensitive to the employed reduction scheme. In particular, we suggest an accurate two-variable model and show its equivalence to a three-variable model that admits an interpretation in terms of a chemical reaction network. The faithful modeling of a single pH oscillator appears crucial for rationalizing experiments and understanding communication of vesicles and synchronization of rhythms.
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Affiliation(s)
| | | | - Felix Höfling
- Zuse Institute Berlin, Takustraße 7, 14195 Berlin, Germany
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
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Abstract
The urea-urease clock reaction is a pH switch from acid to basic that can turn into a pH oscillator if it occurs inside a suitable open reactor. We numerically study the confinement of the reaction to lipid vesicles, which permit the exchange with an external reservoir by differential transport, enabling the recovery of the pH level and yielding a constant supply of urea molecules. For microscopically small vesicles, the discreteness of the number of molecules requires a stochastic treatment of the reaction dynamics. Our analysis shows that intrinsic noise induces a significant statistical variation of the oscillation period, which increases as the vesicles become smaller. The mean period, however, is found to be remarkably robust for vesicle sizes down to approximately 200 nm, but the periodicity of the rhythm is gradually destroyed for smaller vesicles. The observed oscillations are explained as a canard-like limit cycle that differs from the wide class of conventional feedback oscillators.
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Affiliation(s)
| | | | - Christof Schütte
- Zuse Institute Berlin, Takustraße 7, 14195 Berlin, Germany
- Freie Universität Berlin, Department of Mathematics and Computer Science, Arnimallee 6, 14195 Berlin, Germany
| | - Felix Höfling
- Zuse Institute Berlin, Takustraße 7, 14195 Berlin, Germany
- Freie Universität Berlin, Department of Mathematics and Computer Science, Arnimallee 6, 14195 Berlin, Germany
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Stoop RL, Straube AV, Johansen TH, Tierno P. Collective Directional Locking of Colloidal Monolayers on a Periodic Substrate. Phys Rev Lett 2020; 124:058002. [PMID: 32083892 DOI: 10.1103/physrevlett.124.058002] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/03/2019] [Accepted: 01/16/2020] [Indexed: 06/10/2023]
Abstract
We investigate the directional locking effects that arise when a monolayer of paramagnetic colloidal particles is driven across a triangular lattice of magnetic bubbles. We use an external rotating magnetic field to generate a two-dimensional traveling wave ratchet forcing the transport of particles along a direction that intersects two crystallographic axes of the lattice. We find that, while single particles show no preferred direction, collective effects induce transversal current and directional locking at high density via a spontaneous symmetry breaking. The colloidal current may be polarized via an additional bias field that makes one transport direction energetically preferred.
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Affiliation(s)
- Ralph L Stoop
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, 08028 Barcelona, Spain
| | - Arthur V Straube
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, 08028 Barcelona, Spain
- Department of Mathematics and Computer Science, Freie Universität Berlin, 14195 Berlin, Germany
- Group "Dynamics of Complex Materials", Zuse Institute Berlin, 14195 Berlin, Germany
| | - Tom H Johansen
- Department of Physics, University of Oslo, P. O. Box 1048 Blindern, 0316 Oslo, Norway
- Institute for Superconducting and Electronic Materials, University of Wollongong, Northfields Avenue, Wollongong, NSW 2522, Australia
| | - Pietro Tierno
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, 08028 Barcelona, Spain
- Universitat de Barcelona Institute of Complex Systems (UBICS), Universitat de Barcelona, 08028 Barcelona, Spain
- Institut de Nanociència i Nanotecnologia, IN2UB, Universitat de Barcelona, 08028 Barcelona, Spain
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Abstract
The performance of nanoscale magnetic devices is often limited by the presence of thermal fluctuations, whereas in micro- and nanofluidic applications the same fluctuations may be used to spread reactants or drugs. Here, we demonstrate the controlled motion and the enhancement of diffusion of magnetic nanoparticles that are manipulated and driven across a series of Bloch walls within an epitaxially grown ferrite garnet film. We use a rotating magnetic field to generate a traveling wave potential that unidirectionally transports the nanoparticles at a frequency tunable speed. Strikingly, we find an enhancement of diffusion along the propulsion direction and a frequency-dependent diffusion coefficient that can be precisely controlled by varying the system parameters. To explain the reported phenomena, we develop a theoretical approach that shows a fair agreement with the experimental data enabling an exact analytical expression for the enhanced diffusivity above the magnetically modulated periodic landscape. Our technique to control thermal fluctuations of driven magnetic nanoparticles represents a versatile and powerful way to programmably transport magnetic colloidal matter in a fluid, opening the doors to different fluidic applications based on exploiting magnetic domain wall ratchets.
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Affiliation(s)
- Ralph L Stoop
- Departament de Física de la Matèria Condensada , Universitat de Barcelona , Avenida Diagonal 647 , 08028 Barcelona , Spain
| | - Arthur V Straube
- Departament de Física de la Matèria Condensada , Universitat de Barcelona , Avenida Diagonal 647 , 08028 Barcelona , Spain
- Department of Mathematics and Computer Science , Freie Universität Berlin , Arnimalle 6 , 14195 Berlin , Germany
| | - Pietro Tierno
- Departament de Física de la Matèria Condensada , Universitat de Barcelona , Avenida Diagonal 647 , 08028 Barcelona , Spain
- Institut de Nanociència i Nanotecnologia , Universitat de Barcelona , 08028 Barcelona , Spain
- Universitat de Barcelona Institute of Complex Systems (UBICS) , Universitat de Barcelona , 08028 Barcelona , Spain
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Abstract
We present a quantitative analysis of the nonequilibrium assembly of colloidal particles dispersed in a nematic liquid crystal. The driven particles assemble into reconfigurable circular clusters by liquid-crystal-enabled electrokinetic phenomena generated by an AC electric field that provides propulsion along the local director. We identify the coexistence of different aggregation states, including a central, jammed core, where short-range elastic attraction dominates, surrounded by a liquid-like corona where particles retain their mobility but reach a mechanical equilibrium that we rationalize in terms of a balance between centripetal phoretic drive and pairwise repulsion. An analysis of the compressible liquid-like region reveals a linear density profile that can be tuned with the field frequency, and a bond-orientational order that reaches a maximum at intermediate packing densities, where elastic effects are minimized. Since the phoretic propulsion force acts also on assembled particles, we compute the mechanical pressure and show that a hard-disk equation of state can be used to describe the assembly of this driven system.
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Affiliation(s)
- Josep M Pagès
- Departament de Ciència de Materials i Química Física, Universitat de Barcelona, Catalonia, Spain.
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Tierno P, Straube AV. Transport and selective chaining of bidisperse particles in a travelling wave potential. Eur Phys J E Soft Matter 2016; 39:54. [PMID: 27194527 DOI: 10.1140/epje/i2016-16054-1] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/26/2016] [Revised: 04/08/2016] [Accepted: 04/13/2016] [Indexed: 06/05/2023]
Abstract
We combine experiments, theory and numerical simulation to investigate the dynamics of a binary suspension of paramagnetic colloidal particles dispersed in water and transported above a stripe-patterned magnetic garnet film. The substrate generates a one-dimensional periodic energy landscape above its surface. The application of an elliptically polarized rotating magnetic field causes the landscape to translate, inducing direct transport of paramagnetic particles placed above the film. The ellipticity of the applied field can be used to control and tune the interparticle interactions, from net repulsive to net attractive. When considering particles of two distinct sizes, we find that, depending on their elevation above the surface of the magnetic substrate, the particles feel effectively different potentials, resulting in different mobilities. We exploit this feature to induce selective chaining for certain values of the applied field parameters. In particular, when driving two types of particles, we force only one type to condense into travelling parallel chains. These chains confine the movement of the other non-chaining particles within narrow colloidal channels. This phenomenon is explained by considering the balance of pairwise magnetic forces between the particles and their individual coupling with the travelling landscape.
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Affiliation(s)
- Pietro Tierno
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, Av. Diagonal 647, 08028, Barcelona, Spain.
- Institut de Nanociència i Nanotecnologia IN2UB, Universitat de Barcelona, Barcelona, Spain.
| | - Arthur V Straube
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, Av. Diagonal 647, 08028, Barcelona, Spain
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Martinez-Pedrero F, Tierno P, Johansen TH, Straube AV. Regulating wave front dynamics from the strongly discrete to the continuum limit in magnetically driven colloidal systems. Sci Rep 2016; 6:19932. [PMID: 26837286 PMCID: PMC4738245 DOI: 10.1038/srep19932] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/08/2015] [Accepted: 12/21/2015] [Indexed: 02/02/2023] Open
Abstract
The emergence of wave fronts in dissipative driven systems is a fascinating phenomenon which can be found in a broad range of physical and biological disciplines. Here we report the direct experimental observation of discrete fronts propagating along chains of paramagnetic colloidal particles, the latter propelled above a traveling wave potential generated by a structured magnetic substrate. We develop a rigorously reduced theoretical framework and describe the dynamics of the system in terms of a generalized one-dimensional dissipative Frenkel-Kontorova model. The front dynamics is explored in a wide range of field parameters close to and far from depinning, where the discrete and continuum limits apply. We show how symmetry breaking and finite size of chains are used to control the direction of front propagation, a universal feature relevant to different systems and important for real applications.
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Affiliation(s)
- Fernando Martinez-Pedrero
- Estructura i Constituents de la Matèria, Universitat de Barcelona, Av. Diagonal 647, 08028, Barcelona, Spain
| | - Pietro Tierno
- Estructura i Constituents de la Matèria, Universitat de Barcelona, Av. Diagonal 647, 08028, Barcelona, Spain
- Institut de Nanociència i Nanotecnologia, Universitat de Barcelona, Barcelona, Spain
| | - Tom H. Johansen
- Department of Physics, The University of Oslo, P.O. Box 1048 Blindern, 0316 Oslo, Norway
- Institute for Superconducting and Electronic Materials, University of Wollongong Innovation Campus, Squires Way, North Wollongong NSW 2500, Australia
| | - Arthur V. Straube
- Department of Physics, Humboldt-Universität zu Berlin, Newtonstr. 15, D-12489 Berlin, Germany
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Juniper MPN, Straube AV, Aarts DGAL, Dullens RPA. Colloidal particles driven across periodic optical-potential-energy landscapes. Phys Rev E 2016; 93:012608. [PMID: 26871123 DOI: 10.1103/physreve.93.012608] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/08/2015] [Indexed: 11/07/2022]
Abstract
We study the motion of colloidal particles driven by a constant force over a periodic optical potential energy landscape. First, the average particle velocity is found as a function of the driving velocity and the wavelength of the optical potential energy landscape. The relationship between average particle velocity and driving velocity is found to be well described by a theoretical model treating the landscape as sinusoidal, but only at small trap spacings. At larger trap spacings, a nonsinusoidal model for the landscape must be used. Subsequently, the critical velocity required for a particle to move across the landscape is determined as a function of the wavelength of the landscape. Finally, the velocity of a particle driven at a velocity far exceeding the critical driving velocity is examined. Both of these results are again well described by the two theoretical routes for small and large trap spacings, respectively. Brownian motion is found to have a significant effect on the critical driving velocity but a negligible effect when the driving velocity is high.
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Affiliation(s)
- Michael P N Juniper
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, OX1 3QZ Oxford, United Kingdom
| | - Arthur V Straube
- Department of Physics, Humboldt-Universität zu Berlin, Newtonstraße 15, 12489 Berlin, Germany
| | - Dirk G A L Aarts
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, OX1 3QZ Oxford, United Kingdom
| | - Roel P A Dullens
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, OX1 3QZ Oxford, United Kingdom
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Martinez-Pedrero F, Massana-Cid H, Ziegler T, Johansen TH, Straube AV, Tierno P. Bidirectional particle transport and size selective sorting of Brownian particles in a flashing spatially periodic energy landscape. Phys Chem Chem Phys 2016; 18:26353-26357. [DOI: 10.1039/c6cp05599k] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Abstract
Precise bidirectional transport and size fractionation of microscopic colloidal particles is demonstratedviasquare-wave modulation of a magnetic landscape.
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Affiliation(s)
| | - Helena Massana-Cid
- Departament de Física de la Matèria Condensada
- Universitat de Barcelona
- Barcelona
- Spain
| | - Till Ziegler
- Department of Physics
- Humboldt-Universität zu Berlin
- 12489 Berlin
- Germany
| | - Tom H. Johansen
- Department of Physics
- The University of Oslo
- 0316 Oslo
- Norway
- Institute for Superconducting and Electronic Materials
| | - Arthur V. Straube
- Departament de Física de la Matèria Condensada
- Universitat de Barcelona
- Barcelona
- Spain
- Department of Mathematics and Computer Science
| | - Pietro Tierno
- Departament de Física de la Matèria Condensada
- Universitat de Barcelona
- Barcelona
- Spain
- Institut de Nanociència i Nanotecnologia
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10
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Martinez-Pedrero F, Straube AV, Johansen TH, Tierno P. Functional colloidal micro-sieves assembled and guided above a channel-free magnetic striped film. Lab Chip 2015; 15:1765-1771. [PMID: 25685897 DOI: 10.1039/c5lc00067j] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Colloidal inclusions in lab-on-a-chip devices can be used to perform analytic operations in a non-invasive fashion. We demonstrate here a novel approach to realize fast and reversible micro-sieving operations by manipulating and transporting colloidal chains via mobile domain walls in a magnetic structured substrate. We show that this technique allows one to precisely move and sieve non-magnetic particles, to tweeze microscopic cargos or to mechanically compress highly dense colloidal monolayers.
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Affiliation(s)
- Fernando Martinez-Pedrero
- Departament de Estructura i Constituents de la Matèria, Universitat de Barcelona, Av. Diagonal 647, 08028 Barcelona, Spain.
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Straube AV, Tierno P. Tunable interactions between paramagnetic colloidal particles driven in a modulated ratchet potential. Soft Matter 2014; 10:3915-3925. [PMID: 24664122 DOI: 10.1039/c4sm00132j] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
We study experimentally and theoretically the interactions between paramagnetic particles dispersed in water and driven above the surface of a stripe patterned magnetic garnet film. An external rotating magnetic field modulates the stray field of the garnet film and generates a translating potential landscape which induces directed particle motion. By varying the ellipticity of the rotating field, we tune the inter-particle interactions from net repulsive to net attractive. For attractive interactions, we show that pairs of particles can approach each other and form stable doublets which afterwards travel along the modulated landscape at a constant mean speed. We measure the strength of the attractive force between the moving particles and propose an analytically tractable model that explains the observations and is in quantitative agreement with experiment.
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Affiliation(s)
- Arthur V Straube
- Department of Physics, Humboldt University of Berlin, Newtonstr. 15, D-12489 Berlin, Germany.
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12
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Straube AV, Dullens RPA, Schimansky-Geier L, Louis AA. Zigzag transitions and nonequilibrium pattern formation in colloidal chains. J Chem Phys 2013; 139:134908. [DOI: 10.1063/1.4823501] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023] Open
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13
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Thomas P, Straube AV, Timmer J, Fleck C, Grima R. Signatures of nonlinearity in single cell noise-induced oscillations. J Theor Biol 2013; 335:222-34. [DOI: 10.1016/j.jtbi.2013.06.021] [Citation(s) in RCA: 41] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/10/2013] [Revised: 05/20/2013] [Accepted: 06/18/2013] [Indexed: 01/10/2023]
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Piet DL, Straube AV, Snezhko A, Aranson IS. Model of dynamic self-assembly in ferromagnetic suspensions at liquid interfaces. Phys Rev E Stat Nonlin Soft Matter Phys 2013; 88:033024. [PMID: 24125361 DOI: 10.1103/physreve.88.033024] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2013] [Indexed: 06/02/2023]
Abstract
Ferromagnetic microparticles suspended at the interface between immiscible liquids and energized by an external alternating magnetic field show a rich variety of self-assembled structures, from linear snakes to radial asters. In order to obtain insight into the fundamental physical mechanisms and the overall balance of forces governing self-assembly, we develop a modeling approach based on analytical solutions of the time-averaged Navier-Stokes equations. These analytical expressions for the self-consistent hydrodynamic flows are then employed to modify effective interactions between the particles, which in turn are formulated in terms of the time-averaged quantities. Our method allows effective computational verification of the mechanisms of self-assembly and leads to a testable prediction, e.g., on the transitions between various patterns versus viscosity of the solvent.
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Affiliation(s)
- D L Piet
- Department of Engineering Science and Applied Mathematics, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208, USA and Materials Science Division, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439, USA
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Piet DL, Straube AV, Snezhko A, Aranson IS. Viscosity control of the dynamic self-assembly in ferromagnetic suspensions. Phys Rev Lett 2013; 110:198001. [PMID: 23705741 DOI: 10.1103/physrevlett.110.198001] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/14/2012] [Indexed: 06/02/2023]
Abstract
Recent studies of dynamic self-assembly in ferromagnetic colloids suspended in liquid-air or liquid-liquid interfaces revealed a rich variety of dynamic structures ranging from linear snakes to axisymmetric asters, which exhibit novel morphology of the magnetic ordering accompanied by large-scale hydrodynamic flows. Based on controlled experiments and first principles theory, we argue that the transition from snakes to asters is governed by the viscosity of the suspending liquid where less viscous liquids favor snakes and more viscous, asters. By obtaining analytic solutions of the time-averaged Navier-Stokes equations, we gain insight into the role of mean hydrodynamic flows and an overall balance of forces governing the self-assembly. Our results illustrate that the viscosity can be used to control the outcome of the dynamic self-assembly in magnetic colloidal suspensions.
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Affiliation(s)
- D L Piet
- Department of Engineering Science and Applied Mathematics, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208, USA
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Martens S, Straube AV, Schmid G, Schimansky-Geier L, Hänggi P. Hydrodynamically enforced entropic trapping of Brownian particles. Phys Rev Lett 2013; 110:010601. [PMID: 23383770 DOI: 10.1103/physrevlett.110.010601] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/25/2012] [Indexed: 06/01/2023]
Abstract
We study the transport of Brownian particles through a corrugated channel caused by a force field containing curl-free (scalar potential) and divergence-free (vector potential) parts. We develop a generalized Fick-Jacobs approach leading to an effective one-dimensional description involving the potential of mean force. As an application, the interplay of a pressure-driven flow and an oppositely oriented constant bias is considered. We show that for certain parameters, the particle diffusion is significantly suppressed via the property of hydrodynamically enforced entropic particle trapping.
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Affiliation(s)
- S Martens
- Department of Physics, Humboldt-Universität zu Berlin, Newtonstraße 15, 12489 Berlin, Germany.
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Thomas P, Grima R, Straube AV. Rigorous elimination of fast stochastic variables from the linear noise approximation using projection operators. Phys Rev E Stat Nonlin Soft Matter Phys 2012; 86:041110. [PMID: 23214532 DOI: 10.1103/physreve.86.041110] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/30/2012] [Indexed: 06/01/2023]
Abstract
The linear noise approximation (LNA) offers a simple means by which one can study intrinsic noise in monostable biochemical networks. Using simple physical arguments, we have recently introduced the slow-scale LNA (ssLNA), which is a reduced version of the LNA under conditions of timescale separation. In this paper we present the first rigorous derivation of the ssLNA using the projection operator technique and show that the ssLNA follows uniquely from the standard LNA under the same conditions of timescale separation as those required for the deterministic quasi-steady-state approximation. We also show that the large molecule number limit of several common stochastic model reduction techniques under timescale separation conditions constitutes a special case of the ssLNA.
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Affiliation(s)
- Philipp Thomas
- Department of Physics, Humboldt University of Berlin, Newtonstr. 15, D-12489 Berlin, Germany.
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Thomas P, Straube AV, Grima R. Communication: limitations of the stochastic quasi-steady-state approximation in open biochemical reaction networks. J Chem Phys 2012; 135:181103. [PMID: 22088045 DOI: 10.1063/1.3661156] [Citation(s) in RCA: 48] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
It is commonly believed that, whenever timescale separation holds, the predictions of reduced chemical master equations obtained using the stochastic quasi-steady-state approximation are in very good agreement with the predictions of the full master equations. We use the linear noise approximation to obtain a simple formula for the relative error between the predictions of the two master equations for the Michaelis-Menten reaction with substrate input. The reduced approach is predicted to overestimate the variance of the substrate concentration fluctuations by as much as 30%. The theoretical results are validated by stochastic simulations using experimental parameter values for enzymes involved in proteolysis, gluconeogenesis, and fermentation.
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Affiliation(s)
- Philipp Thomas
- Department of Physics, Humboldt University of Berlin, Newtonstr. 15, D-12489 Berlin, Germany
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19
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Grima R, Thomas P, Straube AV. How accurate are the nonlinear chemical Fokker-Planck and chemical Langevin equations? J Chem Phys 2011; 135:084103. [DOI: 10.1063/1.3625958] [Citation(s) in RCA: 93] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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20
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Straube AV. Small-scale particle advection, manipulation and mixing: beyond the hydrodynamic scale. J Phys Condens Matter 2011; 23:184122. [PMID: 21508483 DOI: 10.1088/0953-8984/23/18/184122] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
In this paper we discuss the problems of particle advection, manipulation and mixing at small scales. We start by considering reaction-advection-diffusion systems with the focus on mixing. We show how mixing advection affects the processes of reaction-diffusion and discuss mixing-induced instabilities. Further, we consider the problem of particle manipulation and discuss collective effects in systems comprising solid and compressible particles. We particularly discuss mechanisms of particle entrapment, the role of compressibility in the dynamics of bubbly liquids and nonequilibrium colloidal explosion. Finally, we address two issues related to the problem of wetting. First, we study the role of contact line motion for a sessile droplet (or a bubble) on an oscillating substrate. Second, we discuss an instability of a thin film leading to the formation of a fractal structure of droplets.
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Affiliation(s)
- Arthur V Straube
- Department of Physics, Humboldt University of Berlin, Berlin, Germany.
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21
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Thomas P, Straube AV, Grima R. Stochastic theory of large-scale enzyme-reaction networks: Finite copy number corrections to rate equation models. J Chem Phys 2010; 133:195101. [DOI: 10.1063/1.3505552] [Citation(s) in RCA: 35] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Shklyaev S, Straube AV, Pikovsky A. Superexponential droplet fractalization as a hierarchical formation of dissipative compactons. Phys Rev E Stat Nonlin Soft Matter Phys 2010; 82:020601. [PMID: 20866766 DOI: 10.1103/physreve.82.020601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/27/2010] [Indexed: 05/29/2023]
Abstract
We study the dynamics of a thin film over a substrate heated from below in a framework of a strongly nonlinear one-dimensional Cahn-Hilliard equation. The evolution leads to a fractalization into smaller and smaller scales. We demonstrate that a primitive element in the appearing hierarchical structure is a dissipative compacton. Both direct simulations and the analysis of a self-similar solution show that the compactons appear at superexponentially decreasing scales, which means vanishing dimension of the fractal.
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Affiliation(s)
- Sergey Shklyaev
- Department of Chemical Engineering, California Institute of Technology, Pasadena, 91125, USA
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Shklyaev S, Straube AV. Formation and evolution of bubbly screens in confined oscillating bubbly liquids. Phys Rev E Stat Nonlin Soft Matter Phys 2010; 81:016321. [PMID: 20365474 DOI: 10.1103/physreve.81.016321] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/21/2009] [Revised: 10/15/2009] [Indexed: 05/29/2023]
Abstract
We consider the dynamics of dilute monodisperse bubbly liquid confined by two plane solid walls and subject to small-amplitude high-frequency oscillations normal to the walls. The initial state corresponds to the uniform distribution of bubbles and motionless liquid. The period of external driving is assumed much smaller than typical relaxation times for a single bubble but larger than the period of volume eigenoscillations. The time-averaged description accounting for the two-way coupling between the liquid and the bubbles is applied. We show that the model predicts accumulation of bubbles in thin sheets parallel to the walls. These singular structures, which are formally characterized by infinitely thin width and infinitely high concentration, are referred to as bubbly screens. The formation of a bubbly screen is described analytically in terms of a self-similar solution, which is in agreement with numerical simulations. We study the evolution of bubbly screens and detect a one-dimensional stationary state, which is shown to be unconditionally unstable.
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Affiliation(s)
- Sergey Shklyaev
- Department of Theoretical Physics, Perm State University, Perm, Russia
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Abstract
We describe how local mixing transforms a convectively unstable active field in an open flow into absolutely unstable. Presenting the mixing region as one with a locally enhanced effective diffusion allows us to find the linear transition point to an unstable global mode analytically. We derive the critical exponent that characterizes weakly nonlinear regimes beyond the instability threshold and compare it with numerical simulations of a full two-dimensional flow problem.
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Affiliation(s)
- Arthur V Straube
- Department of Physics, University of Potsdam, Am Neuen Palais 10, PF 601553, D-14415, Potsdam, Germany
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Straube AV, Abel M, Pikovsky A. Temporal chaos versus spatial mixing in reaction-advection-diffusion systems. Phys Rev Lett 2004; 93:174501. [PMID: 15525082 DOI: 10.1103/physrevlett.93.174501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/28/2004] [Indexed: 05/24/2023]
Abstract
We develop a theory describing the transition to a spatially homogeneous regime in a mixing flow with a chaotic in time reaction. The transverse Lyapunov exponent governing the stability of the homogeneous state can be represented as a combination of Lyapunov exponents for spatial mixing and temporal chaos. This representation, being exact for time-independent flows and equal Pe clet numbers of different components, is demonstrated to work accurately for time-dependent flows and different Pe clet numbers.
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Affiliation(s)
- Arthur V Straube
- Department of Physics, University of Potsdam, Am Neuen Palais 10, PF 601553, D-14415, Potsdam, Germany
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Zaks MA, Straube AV. Steady stokes flow with long-range correlations, fractal fourier spectrum, and anomalous transport. Phys Rev Lett 2002; 89:244101. [PMID: 12484945 DOI: 10.1103/physrevlett.89.244101] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/30/2002] [Indexed: 05/24/2023]
Abstract
We consider viscous two-dimensional steady flows of incompressible fluids past doubly periodic arrays of solid obstacles. In a class of such flows, the autocorrelations for the Lagrangian observables decay in accordance with the power law, and the Fourier spectrum is neither discrete nor absolutely continuous. We demonstrate that spreading of the droplet of tracers in such flows is anomalously fast. Since the flow is equivalent to the integrable Hamiltonian system with 1 degree of freedom, this provides an example of integrable dynamics with long-range correlations, fractal power spectrum, and anomalous transport properties.
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Affiliation(s)
- Michael A Zaks
- Institute of Physics, Humboldt University of Berlin, Germany
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