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Sibley DN, Llombart P, Noya EG, Archer AJ, MacDowell LG. How ice grows from premelting films and water droplets. Nat Commun 2021; 12:239. [PMID: 33431836 PMCID: PMC7801427 DOI: 10.1038/s41467-020-20318-6] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/09/2020] [Accepted: 11/14/2020] [Indexed: 11/08/2022] Open
Abstract
Close to the triple point, the surface of ice is covered by a thin liquid layer (so-called quasi-liquid layer) which crucially impacts growth and melting rates. Experimental probes cannot observe the growth processes below this layer, and classical models of growth by vapor deposition do not account for the formation of premelting films. Here, we develop a mesoscopic model of liquid-film mediated ice growth, and identify the various resulting growth regimes. At low saturation, freezing proceeds by terrace spreading, but the motion of the buried solid is conveyed through the liquid to the outer liquid-vapor interface. At higher saturations water droplets condense, a large crater forms below, and freezing proceeds undetectably beneath the droplet. Our approach is a general framework that naturally models freezing close to three phase coexistence and provides a first principle theory of ice growth and melting which may prove useful in the geosciences.
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Affiliation(s)
- David N Sibley
- Department of Mathematical Sciences, Loughborough University, Loughborough, LE11 3TU, UK
| | - Pablo Llombart
- Instituto de Química Física Rocasolano, CSIC, Calle Serrano 119, Madrid, 28006, Spain
- Departamento de Química Física (Unidad de I+D+i Asociada al CSIC), Facultad de Ciencias Químicas, Universidad Complutense de Madrid, Madrid, 28040, Spain
| | - Eva G Noya
- Instituto de Química Física Rocasolano, CSIC, Calle Serrano 119, Madrid, 28006, Spain
| | - Andrew J Archer
- Department of Mathematical Sciences, Loughborough University, Loughborough, LE11 3TU, UK
| | - Luis G MacDowell
- Departamento de Química Física (Unidad de I+D+i Asociada al CSIC), Facultad de Ciencias Químicas, Universidad Complutense de Madrid, Madrid, 28040, Spain.
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Honisch C, Lin TS, Heuer A, Thiele U, Gurevich SV. Instabilities of Layers of Deposited Molecules on Chemically Stripe Patterned Substrates: Ridges versus Drops. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2015; 31:10618-10631. [PMID: 26339749 DOI: 10.1021/acs.langmuir.5b02407] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
A mesoscopic continuum model is employed to analyze the transport mechanisms and structure formation during the redistribution stage of deposition experiments where organic molecules are deposited on a solid substrate with periodic stripe-like wettability patterns. Transversally invariant ridges located on the more wettable stripes are identified as very important transient states and their linear stability is analyzed accompanied by direct numerical simulations of the fully nonlinear evolution equation for two-dimensional substrates. It is found that there exist two different instability modes that lead to different nonlinear evolutions that result (i) at large ridge volume in the formation of bulges that spill from the more wettable stripes onto the less wettable bare substrate and (ii) at small ridge volume in the formation of small droplets located on the more wettable stripes. In addition, the influence of different transport mechanisms during redistribution is investigated focusing on the cases of convective transport with no-slip at the substrate, transport via diffusion in the film bulk and via diffusion at the film surface. In particular, it is shown that the transport process does neither influence the linear stability thresholds nor the sequence of morphologies observed in the time simulation, but only the ratio of the time scales of the different process phases.
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Affiliation(s)
- Christoph Honisch
- Institute for Theoretical Physics, University of Münster , Wilhelm-Klemm-Str. 9, 48149 Münster, Germany
| | - Te-Sheng Lin
- Department of Applied Mathematics, National Chiao Tung University, Hsinchu , 30010 Taiwan
| | - Andreas Heuer
- Institute for Physical Chemistry, University of Münster , Correnstrasse 28/30, 48149 Münster, Germany
- Center of Nonlinear Science (CeNoS), University of Münster , Corrensstrasse 2, 48149 Münster, Germany
- Center for Multiscale Theory and Computation(CMTC), University of Münster , Corrensstrasse 40, 48149 Münster, Germany
| | - Uwe Thiele
- Institute for Theoretical Physics, University of Münster , Wilhelm-Klemm-Str. 9, 48149 Münster, Germany
- Center of Nonlinear Science (CeNoS), University of Münster , Corrensstrasse 2, 48149 Münster, Germany
- Center for Multiscale Theory and Computation(CMTC), University of Münster , Corrensstrasse 40, 48149 Münster, Germany
| | - Svetlana V Gurevich
- Institute for Theoretical Physics, University of Münster , Wilhelm-Klemm-Str. 9, 48149 Münster, Germany
- Center of Nonlinear Science (CeNoS), University of Münster , Corrensstrasse 2, 48149 Münster, Germany
- Center for Multiscale Theory and Computation(CMTC), University of Münster , Corrensstrasse 40, 48149 Münster, Germany
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Yochelis A, Ebrahim S, Millis B, Cui R, Kachar B, Naoz M, Gov NS. Self-organization of waves and pulse trains by molecular motors in cellular protrusions. Sci Rep 2015; 5:13521. [PMID: 26335545 PMCID: PMC4558574 DOI: 10.1038/srep13521] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/26/2015] [Accepted: 07/29/2015] [Indexed: 11/13/2022] Open
Abstract
Actin-based cellular protrusions are an ubiquitous feature of cells, performing a variety of critical functions ranging from cell-cell communication to cell motility. The formation and maintenance of these protrusions relies on the transport of proteins via myosin motors, to the protrusion tip. While tip-directed motion leads to accumulation of motors (and their molecular cargo) at the protrusion tip, it is observed that motors also form rearward moving, periodic and isolated aggregates. The origins and mechanisms of these aggregates, and whether they are important for the recycling of motors, remain open puzzles. Motivated by novel myosin-XV experiments, a mass conserving reaction-diffusion-advection model is proposed. The model incorporates a non-linear cooperative interaction between motors, which converts them between an active and an inactive state. Specifically, the type of aggregate formed (traveling waves or pulse-trains) is linked to the kinetics of motors at the protrusion tip which is introduced by a boundary condition. These pattern selection mechanisms are found not only to qualitatively agree with empirical observations but open new vistas to the transport phenomena by molecular motors in general.
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Affiliation(s)
- A Yochelis
- Department of Solar Energy and Environmental Physics, Swiss Institute for Dryland Environmental and Energy Research, Blaustein Institutes for Desert Research (BIDR), Ben-Gurion University of the Negev, Sede Boqer Campus, Midreshet Ben-Gurion 84990, Israel
| | - S Ebrahim
- Laboratory of Cell Structure and Dynamics, NIDCD, National Institutes of Health, 50 South Drive, Bethesda, MD 20892-8027, USA
| | - B Millis
- Laboratory of Cell Structure and Dynamics, NIDCD, National Institutes of Health, 50 South Drive, Bethesda, MD 20892-8027, USA
| | - R Cui
- Laboratory of Cell Structure and Dynamics, NIDCD, National Institutes of Health, 50 South Drive, Bethesda, MD 20892-8027, USA
| | - B Kachar
- Laboratory of Cell Structure and Dynamics, NIDCD, National Institutes of Health, 50 South Drive, Bethesda, MD 20892-8027, USA
| | - M Naoz
- Department of Chemical Physics, Weizmann Institute of Science, P.O.B. 26, Rehovot, Israel 76100
| | - N S Gov
- Department of Chemical Physics, Weizmann Institute of Science, P.O.B. 26, Rehovot, Israel 76100
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Asgari M, Moosavi A. Coarsening dynamics of nanodroplets on topographically structured substrates. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2013; 25:045012. [PMID: 23288482 DOI: 10.1088/0953-8984/25/4/045012] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
Employing a biharmonic boundary integral method with linear elements, coarsening dynamics of nanodroplets on topographical step heterogeneity is investigated. It is shown that the step height and droplet configuration have an influential effect on the dynamics. Increasing the step height slows down the process while locating the droplets close to the step boosts the coarsening rate. Considering a slip boundary condition enhances the dynamics and reveals a transition in the droplet migration direction. Our results reveal that increasing the surface wettability weakens the dynamics. Various types of the disjoining pressure over the step are also considered and their effects on the coarsening are investigated.
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Affiliation(s)
- M Asgari
- Center of Excellence in Energy Conversion (CEEC), School of Mechanical Engineering, Sharif University of Technology, Azadi Avenue, PO Box 11365-9567 Tehran, Iran
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Moosavi A, Rauscher M, Dietrich S. Dynamics of nanodroplets on topographically structured substrates. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2009; 21:464120. [PMID: 21715884 DOI: 10.1088/0953-8984/21/46/464120] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
Mesoscopic hydrodynamic equations are solved to investigate the dynamics of nanodroplets positioned near a topographic step of the supporting substrate. Our results show that the dynamics depends on the characteristic length scales of the system given by the height of the step and the size of the nanodroplets as well as on the constituting substances of both the nanodroplets and the substrate. The lateral motion of nanodroplets far from the step can be described well in terms of a power law of the distance from the step. In general the direction of motion depends on the details of the effective laterally varying intermolecular forces. But for nanodroplets positioned far from the step it is solely given by the sign of the Hamaker constant of the system. Moreover, our study reveals that the steps always act as a barrier for transporting liquid droplets from one side of the step to the other.
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Affiliation(s)
- A Moosavi
- Department of Mechanical Engineering, Sharif University of Technology, Azadi Avenue, PO Box 11365-9567 Tehran, Iran
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Moosavi A, Rauscher M, Dietrich S. Size dependent motion of nanodroplets on chemical steps. J Chem Phys 2008; 129:044706. [DOI: 10.1063/1.2955860] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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