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Xiang JX, Liu Z. Observation of a Large Slip Effect in the Nanoscale Flow of Highly Viscous Supercooled Liquid Metals. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2023; 39:11224-11230. [PMID: 37537154 DOI: 10.1021/acs.langmuir.3c00352] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 08/05/2023]
Abstract
Understanding and controlling the flow of materials confined in channels play important roles in science and engineering. The general no-slip boundary condition will result in it being more challenging to drive the flow as the channel size decreases to the nanoscale, especially for highly viscous liquids. Here, we report the observation of a large boundary slip in the nanoscale flow of highly viscous supercooled liquid metals (with viscosities of ≲108 Pa s), enabled by the hydrophobic treatment of smooth nanochannels. The slip length significantly depends on the pressure, which can be rationalized by the shear-dependent viscosity. Our findings provide not only new insights into the field of nanofluidics but also a practical technique for resolving the challenge in the net formation of highly viscous supercooled liquid metals at the nanoscale.
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Affiliation(s)
- Jun-Xiang Xiang
- Department of Engineering Mechanics, School of Civil Engineering, Wuhan University, Wuhan, Hubei 430072, China
| | - Ze Liu
- Department of Engineering Mechanics, School of Civil Engineering, Wuhan University, Wuhan, Hubei 430072, China
- State Key Laboratory of Water Resources Engineering and Management, Wuhan University, Wuhan, Hubei 430072, China
- The Institute of Technological Science, Wuhan University, Wuhan, Hubei 430072, China
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2
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Sekhar S, Sharma A, Shankar V. Instability and rupture of ultrathin freestanding viscoelastic solid films. Phys Rev E 2022; 106:024803. [PMID: 36109925 DOI: 10.1103/physreve.106.024803] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2022] [Accepted: 08/12/2022] [Indexed: 06/15/2023]
Abstract
We analyze the instability of viscoelastic solid freestanding thin films under the influence of van der Waals forces using linear stability analysis and nonlinear simulations. Linear stability analysis shows that the zero-frequency elastic modulus governs the onset of instability and stabilizes the film beyond a critical value analogous to thin supported viscoelastic solid films. However, for freestanding solid films, the critical shear modulus is found to be independent of surface tension, unlike that of thin supported viscoelastic solid films. It is further shown that freestanding viscoelastic solid films with higher moduli can be destabilized for a given film thickness and Hamaker constant compared to supported solid films. In contrast to thin viscoelastic liquid films where the growth rate is enhanced due to elastic effects but length scale is unaltered, freestanding films with solidlike viscoelasticity show a retarded growth rate and enhanced length scale. The presence of solidlike viscoelasticity has a stabilizing effect and affects all the key aspects of instability such as critical wave number, dominant wave number, and maximum growth rate. We numerically solve the set of coupled nonlinear evolution equations for film thickness and tangential displacement in order to elucidate the dynamics of film rupture. Our simulations show that, consistent with the linear stability predictions, an increase in the elastic modulus delays film rupture. The dynamics exhibits self-similarity in the vicinity of film rupture and the film thins as (t_{r}-t)^{3/4}, where t_{r} is the rupture time and t_{r}-t is the time remaining until film rupture. The scaling exponent 3/4 obtained for a thin freestanding viscoelastic solid film is significantly greater than the scaling exponent (1/3) for a thin freestanding viscous film.
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Affiliation(s)
- Satya Sekhar
- Department of Chemical Engineering, Indian Institute of Technology Kanpur, Uttar Pradesh 208016, India
| | - Ashutosh Sharma
- Department of Chemical Engineering, Indian Institute of Technology Kanpur, Uttar Pradesh 208016, India
| | - V Shankar
- Department of Chemical Engineering, Indian Institute of Technology Kanpur, Uttar Pradesh 208016, India
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Kirk J, Wang Z, Ilg P. Entanglement dynamics at flat surfaces: Investigations using multi-chain molecular dynamics and a single-chain slip-spring model. J Chem Phys 2019; 150:094906. [PMID: 30849883 DOI: 10.1063/1.5045301] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The dynamics of an entangled polymer melt confined in a channel by parallel plates is investigated by Molecular Dynamics (MD) simulations of a detailed, multi-chain model. A primitive path analysis predicts that the density of entanglements remains approximately constant throughout the gap and drops to lower values only in the immediate vicinity of the surface. Based on these observations, we propose a coarse-grained, single-chain slip-spring model with a uniform density of slip-spring anchors and slip-links. The slip-spring model is compared to the Kremer-Grest MD bead-spring model via equilibrium correlation functions of chain orientations. Reasonably good agreement between the single-chain model and the detailed multi-chain model is obtained for chain relaxation dynamics, both away from the surface and for chains whose center of mass positions are at a distance from the surface that is less than the bulk chain radius of gyration, without introducing any additional model parameters. Our results suggest that there is no considerable drop in topological interactions for chains in the vicinity of a single flat surface. We infer from the slip-spring model that the experimental plateau modulus of a confined polymer melt may be different to a corresponding unconfined system even if there is no drop in topological interactions for the confined case.
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Affiliation(s)
- Jack Kirk
- School of Mathematical, Physical and Computational Sciences, University of Reading, Reading RG6 6AX, United Kingdom
| | - Zuowei Wang
- School of Mathematical, Physical and Computational Sciences, University of Reading, Reading RG6 6AX, United Kingdom
| | - Patrick Ilg
- School of Mathematical, Physical and Computational Sciences, University of Reading, Reading RG6 6AX, United Kingdom
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McGraw JD, Klos M, Bridet A, Hähl H, Paulus M, Castillo JM, Horsch M, Jacobs K. Influence of bidisperse self-assembled monolayer structure on the slip boundary condition of thin polymer films. J Chem Phys 2017; 146:203326. [DOI: 10.1063/1.4978676] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Joshua D. McGraw
- Soft Matter Physics Group, Experimental Physics, Saarland University, 66041 Saarbrücken, Germany
- Département de Physique, Ecole Normale Supérieure/PSL Research University, CNRS, 24 Rue Lhomond, 75005 Paris, France
| | - Mischa Klos
- Soft Matter Physics Group, Experimental Physics, Saarland University, 66041 Saarbrücken, Germany
| | - Antoine Bridet
- Soft Matter Physics Group, Experimental Physics, Saarland University, 66041 Saarbrücken, Germany
| | - Hendrik Hähl
- Soft Matter Physics Group, Experimental Physics, Saarland University, 66041 Saarbrücken, Germany
| | - Michael Paulus
- Fakultät Physik/DELTA, TU Dortmund, 44221 Dortmund, Germany
| | - Juan Manuel Castillo
- Laboratory of Engineering Thermodynamics, University of Kaiserslautern, Erwin-Schrödinger-Strasse 44, 67663 Kaiserslautern, Germany
| | - Martin Horsch
- Laboratory of Engineering Thermodynamics, University of Kaiserslautern, Erwin-Schrödinger-Strasse 44, 67663 Kaiserslautern, Germany
| | - Karin Jacobs
- Soft Matter Physics Group, Experimental Physics, Saarland University, 66041 Saarbrücken, Germany
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5
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Gutfreund P, Maccarini M, Dennison AJC, Wolff M. The Search for Nanobubbles by Using Specular and Off-Specular Neutron Reflectometry. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2016; 32:9091-9096. [PMID: 27516185 DOI: 10.1021/acs.langmuir.6b02087] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We apply specular and off-specular neutron reflection at the hydrophobic silicon/water interface to check for evidence of nanoscopic air bubbles whose presence is claimed after an ad hoc procedure of solvent exchange. Nanobubbles and/or a depletion layer at the hydrophobic/water interface have long been discussed and generated a plethora of controversial scientific results. By combining neutron reflectometry (NR), off-specular reflectometry (OSS), and grazing incidence small angle neutron scattering (GISANS), we studied the interface between hydrophobized silicon and heavy water before and after saturation with nitrogen gas. Our specular reflectometry results can be interpreted by assuming a submolecular sized depletion layer and the off-specular measurements show no change with nitrogen super saturated water. This picture is consistent with the assumption that, following the solvent exchange, no additional nanobubbles are introduced at significant concentrations (if present at all). Furthermore, we discuss the results in terms of the maximum surface coverage of nanobubbles that could be present on the hydrophobic surface compatibly with the sensitivity limit of these techniques.
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Affiliation(s)
| | - Marco Maccarini
- Institut Laue-Langevin , 38000 Grenoble, France
- TIMC-IMAG, Université Joseph Fourier , 38706 Grenoble, France
| | - Andrew J C Dennison
- Institut Laue-Langevin , 38000 Grenoble, France
- Department of Chemistry, Technical University Berlin , 10623 Berlin, Germany
- Department of Physics and Astronomy, University of Sheffield , S102TN Sheffield, United Kingdom
| | - Max Wolff
- Materials Physics, Department of Physics and Astronomy, Uppsala University , 75121 Uppsala, Sweden
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Abstract
Classical hydrodynamic models predict that infinite work is required to move a three-phase contact line, defined here as the line where a liquid/vapor interface intersects a solid surface. Assuming a slip boundary condition, in which the liquid slides against the solid, such an unphysical prediction is avoided. In this article, we present the results of experiments in which a contact line moves and where slip is a dominating and controllable factor. Spherical cap-shaped polystyrene microdroplets, with nonequilibrium contact angle, are placed on solid self-assembled monolayer coatings from which they dewet. The relaxation is monitored using in situ atomic force microscopy. We find that slip has a strong influence on the droplet evolutions, both on the transient nonspherical shapes and contact line dynamics. The observations are in agreement with scaling analysis and boundary element numerical integration of the governing Stokes equations, including a Navier slip boundary condition.
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Sabzevari SM, McGraw JD, Jacobs K, Wood–Adams P. Sacrificial mica substrates influence the slip boundary condition of dewetting polymer films. POLYMER 2015. [DOI: 10.1016/j.polymer.2015.08.038] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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Ilton M, Bäumchen O, Dalnoki-Veress K. Onset of Area-Dependent Dissipation in Droplet Spreading. PHYSICAL REVIEW LETTERS 2015; 115:046103. [PMID: 26252697 DOI: 10.1103/physrevlett.115.046103] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/16/2015] [Indexed: 06/04/2023]
Abstract
We probe the viscous relaxation of structured liquid droplets in the partial wetting regime using a diblock copolymer system. The relaxation time of the droplets is measured after a step change in temperature as a function of three tunable parameters: droplet size, equilibrium contact angle, and the viscosity of the fluid. Contrary to what is typically observed, the late-stage relaxation time does not scale with the radius of the droplet-rather, relaxation scales with the radius squared. Thus, the energy dissipation depends on the contact area of the droplet, rather than the contact line.
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Affiliation(s)
- Mark Ilton
- Department of Physics and Astronomy and the Brockhouse Institute for Materials Research, McMaster University, Hamilton, Ontario L8S 4M1, Canada
| | - Oliver Bäumchen
- Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen, Germany
| | - Kari Dalnoki-Veress
- Department of Physics and Astronomy and the Brockhouse Institute for Materials Research, McMaster University, Hamilton, Ontario L8S 4M1, Canada
- Laboratoire de Physico-Chimie Théorique, UMR CNRS 7083 Gulliver, ESPCI ParisTech, PSL Research University, Paris, France
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Sang L, Mudalige A, Sigdel AK, Giordano AJ, Marder SR, Berry JJ, Pemberton JE. PM-IRRAS Determination of Molecular Orientation of Phosphonic Acid Self-Assembled Monolayers on Indium Zinc Oxide. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2015; 31:5603-5613. [PMID: 25924006 DOI: 10.1021/acs.langmuir.5b00129] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Self-assembled monolayers (SAMs) of phosphonic acids (PAs) on transparent conductive oxide (TCO) surfaces can facilitate improvement in TCO/organic semiconductor interface properties. When ordered PA SAMs are formed on oxide substrates, interface dipole and electronic structure are affected by the functional group properties, orientation, and binding modes of the modifiers. Choosing octylphosphonic acid (OPA), F13-octylphosphonic acid (F13OPA), pentafluorophenyl phosphonic acid (F5PPA), benzyl phosphonic acid (BnPA), and pentafluorobenzyl phosphonic acid (F5BnPA) as a representative group of modifiers, we report polarization modulation-infrared reflection-absorption spectroscopy (PM-IRRAS) of binding and molecular orientation on indium-doped zinc oxide (IZO) substrates. Considerable variability in molecular orientation and binding type is observed with changes in PA functional group. OPA exhibits partially disordered alkyl chains but on average the chain axis is tilted ∼57° from the surface normal. F13OPA tilts 26° with mostly tridentate binding. The F5PPA ring is tilted 23° from the surface normal with a mixture of bidentate and tridentate binding; the BnPA ring tilts 31° from normal with a mixture of bidentate and tridentate binding, and the F5BnPA ring tilts 58° from normal with a majority of bidentate with some tridenate binding. These trends are consistent with what has been observed previously for the effects of fluorination on orientation of phosphonic acid modifiers. These results from PM-IRRAS are correlated with recent results on similar systems from near-edge X-ray absorption fine structure (NEXAFS) and density functional theory (DFT) calculations. Overall, these results indicate that both surface binding geometry and intermolecular interactions play important roles in dictating the orientation of PA modifiers on TCO surfaces. This work also establishes PM-IRRAS as a routine method for SAM orientation determination on complex oxide substrates.
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Affiliation(s)
- Lingzi Sang
- †Department of Chemistry and Biochemistry University of Arizona, 1306 E. University Boulevard, Tucson, Arizona 85721, United States
| | - Anoma Mudalige
- †Department of Chemistry and Biochemistry University of Arizona, 1306 E. University Boulevard, Tucson, Arizona 85721, United States
| | - Ajaya K Sigdel
- ‡Department of Physics and Astronomy, University of Denver, Denver, Colorado 80208, United States
- §National Renewable Energy Laboratory, Golden, Colorado 80401, United States
| | - Anthony J Giordano
- ∥School of Chemistry and Biochemistry and Center for Organic Photonics and Electronics, Georgia Institute of Technology, Atlanta, Georgia 30332, United States
| | - Seth R Marder
- ∥School of Chemistry and Biochemistry and Center for Organic Photonics and Electronics, Georgia Institute of Technology, Atlanta, Georgia 30332, United States
| | - Joseph J Berry
- §National Renewable Energy Laboratory, Golden, Colorado 80401, United States
| | - Jeanne E Pemberton
- †Department of Chemistry and Biochemistry University of Arizona, 1306 E. University Boulevard, Tucson, Arizona 85721, United States
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Lessel M, Bäumchen O, Klos M, Hähl H, Fetzer R, Paulus M, Seemann R, Jacobs K. Self‐assembled silane monolayers: an efficient step‐by‐step recipe for high‐quality, low energy surfaces. SURF INTERFACE ANAL 2015. [DOI: 10.1002/sia.5729] [Citation(s) in RCA: 85] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Affiliation(s)
- M. Lessel
- Saarland UniversityExperimental Physics Saarbrücken D‐66041 Germany
| | - O. Bäumchen
- Saarland UniversityExperimental Physics Saarbrücken D‐66041 Germany
| | - M. Klos
- Saarland UniversityExperimental Physics Saarbrücken D‐66041 Germany
| | - H. Hähl
- Saarland UniversityExperimental Physics Saarbrücken D‐66041 Germany
| | - R. Fetzer
- Saarland UniversityExperimental Physics Saarbrücken D‐66041 Germany
| | - M. Paulus
- TU DortmundFakultät Physik / DELTA Dortmund D‐44221 Germany
| | - R. Seemann
- Saarland UniversityExperimental Physics Saarbrücken D‐66041 Germany
| | - K. Jacobs
- Saarland UniversityExperimental Physics Saarbrücken D‐66041 Germany
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Castillo JM, Klos M, Jacobs K, Horsch M, Hasse H. Characterization of alkylsilane self-assembled monolayers by molecular simulation. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2015; 31:2630-2638. [PMID: 25668124 DOI: 10.1021/la504178g] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Self-assembled monolayers (SAM) of dodecyltrichlorosilane (DTS) and octadecyltrichlorosilane (OTS) on silica are studied by molecular dynamics simulations at 298 K and 1 bar. The coverage (number of alkylsilane molecules per surface area) is systematically varied. The results yield insight into the properties of the alkylsilane SAMs, which complement experimental studies from the literature. Relationships are reported between thickness, tilt angle, and coverage of alkylsilane SAMs, which also hold for alkylsilanes other than DTS and OTS. They are interpreted based on the information on molecular ordering in the SAMs taken form the simulation data. System size and simulation time are much larger than in most former simulation works on the topic. This reduces the influence of the initial configuration as well as the periodic boundary conditions and hence minimizes the risk of artificial ordering. At the same time, more reliable statistics for the calculated properties can be provided. The evaluation of experimental data in the field is often based on strongly simplified models. The present simulation results suggest that some of these lead to errors, concerning the interpretation of experimental results, which could be avoided by introducing more realistic models.
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Affiliation(s)
- Juan Manuel Castillo
- Laboratory of Engineering Thermodynamics, Department of Mechanical and Process Engineering, University of Kaiserslautern , Erwin-Schrödinger-Str. 44, 67663 Kaiserslautern, Germany
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Effects of Self-Assembled Monolayers with Different Chemical Groups on Ovarian Cancer Cell Line BehaviorIn Vitro. J CHEM-NY 2015. [DOI: 10.1155/2015/784626] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
In addition to serving as a physical support, the extracellular matrix (ECM) actively influences cell behavior. However, the definitive effects of different chemical structures present in the ECM on cell behavior remain obscure. The current study aimed to investigate the effects of different chemical structures present in the ECM on cellular physiology using the ovarian cancer cell line SKOV-3 as a model. Self-assembled monolayers (SAMs) with different chemical modifications, including methyl (-CH3), hydroxyl (-OH), amino (-NH2), carboxyl (-COOH), and mercapto (-SH) groups, were used as microenvironmental models to explore the effects of different structures on SKOV-3 cells. The cell morphology, cell adhesion, cytotoxicity, and functional alterations in cancer cells cultured on different SAMs were analyzed. The results showed that SKOV-3 cells cultured on -NH2surfaces exhibited the largest contact area, whereas those on -CH3surfaces exhibited the smallest contact area and mostly rounded morphologies. Additionally, -NH2and -COOH promoted cell proliferation and adhesion, whereas CH3inhibited adhesion, leading to G1 arrest during the cell cycle and resulting in cell apoptosis. This study may provide useful information for reconstruction of the ECM and for controlling cell behavior in related areas of study.
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Ohk CW, Koo M, Lee BJ, Lee SE, Jang HS, Park YC. Slip behavior in polymethylmethacrylate films in dependence of self-assembled monolayer wettability. POLYMER 2014. [DOI: 10.1016/j.polymer.2014.10.053] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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McGraw JD, Bäumchen O, Klos M, Haefner S, Lessel M, Backes S, Jacobs K. Nanofluidics of thin polymer films: linking the slip boundary condition at solid-liquid interfaces to macroscopic pattern formation and microscopic interfacial properties. Adv Colloid Interface Sci 2014; 210:13-20. [PMID: 24780402 DOI: 10.1016/j.cis.2014.03.010] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2013] [Revised: 03/28/2014] [Accepted: 03/28/2014] [Indexed: 10/25/2022]
Abstract
If a thin liquid film is not stable, different rupture mechanisms can be observed causing characteristic film morphologies: spinodal dewetting and dewetting by nucleation of holes. This rupturing entails liquid flow and opens new possibilities to study microscopic phenomena. Here we use this process of dewetting to gain insight on the slip boundary condition at the solid-liquid interface. Having established hydrodynamic models that allow for the determination of the slip length in a dewetting experiment based on nucleation, we move on to the quantification and molecular description of slip effects in various systems. For the late stage of the dewetting process involving the Rayleigh-Plateau instability, several distinct droplet patterns can be observed. We describe the importance of slip in determining what pattern may be found. In order to control the slip length, we use polymeric liquids on different hydrophobic coatings of silicon wafers. We find that subtle changes in the coating can lead to large changes in the slip length. Thus, we gain insight into the question of how the structure of the substrate affects the slip length.
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Bäumchen O, Marquant L, Blossey R, Münch A, Wagner B, Jacobs K. Influence of slip on the Rayleigh-Plateau rim instability in dewetting viscous films. PHYSICAL REVIEW LETTERS 2014; 113:014501. [PMID: 25032928 DOI: 10.1103/physrevlett.113.014501] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/11/2013] [Indexed: 06/03/2023]
Abstract
A dewetting viscous film develops a characteristic fluid rim at its receding edge due to mass conservation. In the course of the dewetting process, the rim becomes unstable via an instability of Rayleigh-Plateau type. An important difference exists between this classic instability of a liquid column and the rim instability in a thin film as the growth of the rim is continuously fueled by the receding film. We explain how the development and macroscopic morphology of the rim instability are controlled by the slip of the film on the substrate. A single thin-film model captures quantitatively the characteristics of the complete evolution of the rim observed in the experiments.
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Affiliation(s)
- Oliver Bäumchen
- Saarland University, Department of Experimental Physics, Campus, D-66123 Saarbrücken, Germany
| | - Ludovic Marquant
- Saarland University, Department of Experimental Physics, Campus, D-66123 Saarbrücken, Germany
| | - Ralf Blossey
- Interdisciplinary Research Institute (IRI), CNRS USR 3078, 59658 Villeneuve d'Ascq, France
| | - Andreas Münch
- Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom
| | - Barbara Wagner
- Technical University of Berlin, Institute for Mathematics, D-10623 Berlin, Germany
| | - Karin Jacobs
- Saarland University, Department of Experimental Physics, Campus, D-66123 Saarbrücken, Germany
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