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Tangde VM, Bhalekar AA. How Flexible Is the Concept of Local Thermodynamic Equilibrium? ENTROPY (BASEL, SWITZERLAND) 2023; 25:e25010145. [PMID: 36673286 PMCID: PMC9858024 DOI: 10.3390/e25010145] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/24/2022] [Revised: 12/26/2022] [Accepted: 12/31/2022] [Indexed: 06/01/2023]
Abstract
It has been demonstrated by using generalized phenomenological irreversible thermodynamic theory (GPITT) that by replacing the conventional composition variables {xk} by the quantum level composition variables {x˜k,j} corresponding to the nonequilibrium population of the quantum states, the resultant description remains well within the local thermodynamic equilibrium (LTE) domain. The next attempt is to replace the quantum level composition variables by their respective macroscopic manifestations as variables. For example, these manifestations are, say, the observance of fluorescence and phosphorescence, existence of physical fluxes, and ability to register various spectra (microwave, IR, UV-VIS, ESR, NMR, etc.). This exercise results in a framework that resembles with the thermodynamics with internal variables (TIV), which too is obtained as a framework within the LTE domain. This TIV-type framework is easily transformed to an extended irreversible thermodynamics (EIT) type framework, which uses physical fluxes as additional variables. The GPITT in EIT version is also obtained well within the LTE domain. Thus, GPITT becomes a complete version of classical irreversible thermodynamics (CIT). It is demonstrated that LTE is much more flexible than what CIT impresses upon. This conclusion is based on the realization that the spatial uniformity for each tiny pocket (cell) of a spatially non-uniform system remains intact while developing GPITT and obviously in its other versions.
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Affiliation(s)
- Vijay M. Tangde
- Department of Chemistry, Rashtrasant Tukadoji Maharaj Nagpur University, Nagpur 440 033, India
| | - Anil A. Bhalekar
- Department of Chemistry, Rashtrasant Tukadoji Maharaj Nagpur University, Nagpur 440 033, India
- 106, Himalaya Prestige, South Ambazari Marg, SBI Colony, Gopal Nagar, Nagpur 440 022, India
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Martínez-Calvo A, Moreno-Boza D, Sevilla A. Non-linear dynamics and self-similarity in the rupture of ultra-thin viscoelastic liquid coatings. SOFT MATTER 2021; 17:4363-4374. [PMID: 33908465 DOI: 10.1039/d0sm02204g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
The influence of viscoelasticity on the dewetting of ultrathin polymer films is unraveled by means of theory and numerical simulations in the inertialess limit. Three viscoelastic models are employed to analyse the dynamics of the film, namely the Oldroyd-B, Giesekus, and FENE-P models. We revisit the linear stability analysis first derived by [Tomar et al., Eur. Phys. J. E., 2006, 20, 185-200] for a Jeffrey's film to conclude that all three models formally share the same dispersion relation. For times close to the rupture singularity, the self-similar regime recently discovered [Moreno-Boza et al., Phys. Rev. Fluids, 2020, 5, 014002], where the dimensionless minimum film thickness scales with the dimensionless time until rupture as hmin = 0.665τ1/3, is asymptotically established independently of the rheological model. The spatial structure of the flow is characterised by a Newtonian core and a thin viscoelastic boundary layer at the free surface, where polymeric stresses become singular as τ → 0. The Deborah number and the solvent-to-total viscosity ratio affect the rupture time but not the length scale of the resulting dewetting pattern and asymptotic flow structure close to rupture, which is thus shown to be universal. Our three-dimensional simulations lead us to conclude that bulk viscoelasticity alone does not explain the experimental observations of dewetting of polymeric films near the glass transition.
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Affiliation(s)
- A Martínez-Calvo
- Grupo de Mecánica de Fluidos, Universidad Carlos III de Madrid, Av. Universidad 30, 28911 Leganés (Madrid), Spain.
| | - D Moreno-Boza
- Grupo de Mecánica de Fluidos, Universidad Carlos III de Madrid, Av. Universidad 30, 28911 Leganés (Madrid), Spain.
| | - A Sevilla
- Grupo de Mecánica de Fluidos, Universidad Carlos III de Madrid, Av. Universidad 30, 28911 Leganés (Madrid), Spain.
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Barra V, Afkhami S, Kondic L. Thin viscoelastic dewetting films of Jeffreys type subjected to gravity and substrate interactions. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2019; 42:12. [PMID: 30687884 DOI: 10.1140/epje/i2019-11774-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/04/2018] [Accepted: 01/04/2019] [Indexed: 06/09/2023]
Abstract
This work presents a study of the interfacial dynamics of thin viscoelastic films subjected to the gravitational force and substrate interactions induced by the disjoining pressure, in two spatial dimensions. The governing equation is derived as a long-wave approximation of the Navier-Stokes equations for incompressible viscoelastic liquids under the effect of gravity, with the Jeffreys model for viscoelastic stresses. For the particular cases of horizontal or inverted planes, the linear stability analysis is performed to investigate the influence of the physical parameters involved on the growth rate and length scales of instabilities. Numerical simulations of the nonlinear regime of the dewetting process are presented for the particular case of an inverted plane. Both gravity and the disjoining pressure are found to affect not only the length scale of instabilities, but also the final configuration of dewetting, by favoring the formation of satellite droplets, that are suppressed by the slippage with the solid substrate.
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Affiliation(s)
- Valeria Barra
- Department of Mathematical Sciences, New Jersey Institute of Technology, 07102, Newark, NJ, USA
| | - Shahriar Afkhami
- Department of Mathematical Sciences, New Jersey Institute of Technology, 07102, Newark, NJ, USA.
| | - Lou Kondic
- Department of Mathematical Sciences, New Jersey Institute of Technology, 07102, Newark, NJ, USA
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Benzaquen M, Fowler P, Jubin L, Salez T, Dalnoki-Veress K, Raphaël E. Approach to universal self-similar attractor for the levelling of thin liquid films. SOFT MATTER 2014; 10:8608-8614. [PMID: 25180467 DOI: 10.1039/c4sm01483a] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
We compare the capillary levelling of a random surface perturbation on a thin polystyrene film with a theoretical study on the two-dimensional capillary-driven thin film equation. Using atomic force microscopy, we follow the time evolution of samples prepared with different initial perturbations of the free surface. In particular, we show that the surface profiles present long term self-similarity, and furthermore, that they converge to a universal self-similar attractor that only depends on the volume of the perturbation, consistent with the theory. Finally, we look at the convergence time for the different samples and find very good agreement with the analytical predictions.
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Affiliation(s)
- Michael Benzaquen
- Laboratoire de Physico-Chimie Théorique, UMR CNRS 7083 Gulliver, ESPCI ParisTech, PSL Research University, France.
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5
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Probing Properties of Polymers in Thin Films Via Dewetting. GLASS TRANSITION, DYNAMICS AND HETEROGENEITY OF POLYMER THIN FILMS 2012. [DOI: 10.1007/12_2012_174] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/12/2023]
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6
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Léonforte F, Servantie J, Pastorino C, Müller M. Molecular transport and flow past hard and soft surfaces: computer simulation of model systems. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2011; 23:184105. [PMID: 21508476 DOI: 10.1088/0953-8984/23/18/184105] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
The equilibrium and flow of polymer films and drops past a surface are characterized by the interface and surface tensions, viscosity, slip length and hydrodynamic boundary position. These parameters of the continuum description are extracted from molecular simulations of coarse-grained models. Hard, corrugated substrates are modelled by a Lennard-Jones solid while polymer brushes are studied as prototypes of soft, deformable surfaces. Four observations are discussed. (i) If the surface becomes strongly attractive or is coated with a brush, the Navier boundary condition fails to describe the effect of the surface independently of the strength and type of the flow. This failure stems from the formation of a boundary layer with an effective, higher viscosity. (ii) In the case of brush-coated surfaces, flow induces a cyclic, tumbling motion of the tethered chain molecules. Their collective motion gives rise to an inversion of the flow in the vicinity of the grafting surfaces and leads to strong, non-Gaussian fluctuations of the molecular orientations. The flow past a polymer brush cannot be described by Brinkman's equation. (iii) The hydrodynamic boundary condition is an important parameter for predicting the motion of polymer droplets on a surface under the influence of an external force. Their steady-state velocity is dictated by a balance between the power that is provided by the external force and the dissipation. If there is slippage at the liquid-solid interface, the friction at the solid-liquid interface and the viscous dissipation of the flow inside the drop will be the dominant dissipation mechanisms; dissipation at the three-phase contact line appears to be less important on a hard surface. (iv) On a soft, deformable substrate like a polymer brush, we observe a lifting-up of the three-phase contact line. Controlling the grafting density and the incompatibility between the brush and the polymer liquid we can independently tune the softness of the surface and the contact angle and thereby identify the parameters for maximizing the deformation at the three-phase contact.
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Affiliation(s)
- F Léonforte
- Institut für Theoretische Physik, Georg-August-Universität, 37077 Göttingen, Germany
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7
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Münch A, Wagner B. Impact of slippage on the morphology and stability of a dewetting rim. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2011; 23:184101. [PMID: 21508486 DOI: 10.1088/0953-8984/23/18/184101] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
In this study lubrication theory is used to describe the stability and morphology of the rim that forms as a thin polymer film dewets from a hydrophobized silicon wafer. Thin film equations are derived from the governing hydrodynamic equations for the polymer to enable the systematic mathematical and numerical analysis of the properties of the solutions for different regimes of slippage and for a range of timescales. Dewetting rates and the cross sectional profiles of the evolving rims are derived for these models and compared to experimental results. Experiments also show that the rim is typically unstable in the spanwise direction and develops thicker and thinner parts that may grow into 'fingers'. Linear stability analysis as well as nonlinear numerical solutions are presented to investigate shape and growth rate of the rim instability. It is demonstrated that the difference in morphology and the rate at which the instability develops can be directly attributed to the magnitude of slippage. Finally, a derivation is given for the dominant wavelength of the bulges along the unstable rim.
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Affiliation(s)
- Andreas Münch
- Mathematical Institute, University of Oxford, Oxford, UK
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Patra A, Bandyopadhyay D, Tomar G, Sharma A, Biswas G. Instability and dewetting of ultrathin solid viscoelastic films on homogeneous and heterogeneous substrates. J Chem Phys 2011; 134:064705. [DOI: 10.1063/1.3554748] [Citation(s) in RCA: 13] [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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9
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Bäumchen O, Jacobs K. Slip effects in polymer thin films. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2010; 22:033102. [PMID: 21386275 DOI: 10.1088/0953-8984/22/3/033102] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
Probing the fluid dynamics of thin films is an excellent tool for studying the solid/liquid boundary condition. There is no need for external stimulation or pumping of the liquid, due to the fact that the dewetting process, an internal mechanism, acts as a driving force for liquid flow. Viscous dissipation, within the liquid, and slippage balance interfacial forces. Thus, friction at the solid/liquid interface plays a key role towards the flow dynamics of the liquid. Probing the temporal and spatial evolution of growing holes or retracting straight fronts gives, in combination with theoretical models, information on the liquid flow field and, especially, the boundary condition at the interface. We review the basic models and experimental results obtained during the last several years with exclusive regard to polymers as ideal model liquids for fluid flow. Moreover, concepts that aim to explain slippage on the molecular scale are summarized and discussed.
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Affiliation(s)
- O Bäumchen
- Department of Experimental Physics, Saarland University, D-66041 Saarbrücken, Germany
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10
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Halpern D, Fujioka H, Grotberg JB. The effect of viscoelasticity on the stability of a pulmonary airway liquid layer. PHYSICS OF FLUIDS (WOODBURY, N.Y. : 1994) 2010; 22:11901. [PMID: 20157445 PMCID: PMC2821416 DOI: 10.1063/1.3294573] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/08/2009] [Accepted: 12/07/2009] [Indexed: 05/02/2023]
Abstract
The lungs consist of a network of bifurcating airways that are lined with a thin liquid film. This film is a bilayer consisting of a mucus layer on top of a periciliary fluid layer. Mucus is a non-Newtonian fluid possessing viscoelastic characteristics. Surface tension induces flows within the layer, which may cause the lung's airways to close due to liquid plug formation if the liquid film is sufficiently thick. The stability of the liquid layer is also influenced by the viscoelastic nature of the liquid, which is modeled using the Oldroyd-B constitutive equation or as a Jeffreys fluid. To examine the role of mucus alone, a single layer of a viscoelastic fluid is considered. A system of nonlinear evolution equations is derived using lubrication theory for the film thickness and the film flow rate. A uniform film is initially perturbed and a normal mode analysis is carried out that shows that the growth rate g for a viscoelastic layer is larger than for a Newtonian fluid with the same viscosity. Closure occurs if the minimum core radius, R(min)(t), reaches zero within one breath. Solutions of the nonlinear evolution equations reveal that R(min) normally decreases to zero faster with increasing relaxation time parameter, the Weissenberg number We. For small values of the dimensionless film thickness parameter epsilon, the closure time, t(c), increases slightly with We, while for moderate values of epsilon, ranging from 14% to 18% of the tube radius, t(c) decreases rapidly with We provided the solvent viscosity is sufficiently small. Viscoelasticity was found to have little effect for epsilon>0.18, indicating the strong influence of surface tension. The film thickness parameter epsilon and the Weissenberg number We also have a significant effect on the maximum shear stress on tube wall, max(tau(w)), and thus, potentially, an impact on cell damage. Max(tau(w)) increases with epsilon for fixed We, and it decreases with increasing We for small We provided the solvent viscosity parameter is sufficiently small. For large epsilon approximately 0.2, there is no significant difference between the Newtonian flow case and the large We cases.
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11
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Ziebert F, Raphaël E. Dewetting dynamics of stressed viscoelastic thin polymer films. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:031605. [PMID: 19391952 DOI: 10.1103/physreve.79.031605] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/04/2008] [Indexed: 05/27/2023]
Abstract
Ultrathin polymer films that are produced, e.g., by spin coating are believed to be stressed since polymers are "frozen in" into out-of-equilibrium configurations during this process. In the framework of a viscoelastic thin-film model, we study the effects of lateral residual stresses on the dewetting dynamics of the film. The temporal evolution of the height profiles and the velocity profiles inside the film as well as the dissipation mechanisms are investigated in detail. Both the shape of the profiles and the importance of frictional dissipation vs viscous dissipation inside the film are found to change in the course of dewetting. The interplay of the nonstationary profiles, the relaxing initial stress, and the changes in the dominance of the two dissipation mechanisms caused by nonlinear friction with the substrate is responsible for the rich behavior of the system. In particular, our analysis sheds a different light on the occurrence of the unexpected maximum in the rim width obtained recently in experiments on polystyrene-polydimethylsiloxane systems.
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Affiliation(s)
- Falko Ziebert
- Laboratoire de Physico-Chimie Théorique-UMR CNRS Gulliver 7083, ESPCI, 10 rue Vauquelin, F-75231 Paris, France
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12
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Rauscher M, Blossey R, Münch A, Wagner B. Spinodal dewetting of thin films with large interfacial slip: implications from the dispersion relation. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2008; 24:12290-12294. [PMID: 18844382 DOI: 10.1021/la802260b] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
We compare the dispersion relations for spinodally dewetting thin liquid films for increasing magnitude of interfacial slip length in the lubrication limit. While the shape of the dispersion relation, in particular the position of the maximum, are equal for no-slip up to moderate-slip lengths, the position of the maximum shifts to much larger wavelengths for large slip lengths. Here, we discuss the implications of this fact for recently developed methods to assess the disjoining pressure in spinodally unstable thin films by measuring the shape of the roughness power spectrum. For polystyrene (PS) films on octadecyltrichlorosilane (OTS) covered Si wafers (with slip length b approximately 1 microm), we predict a 20% shift of the position of the maximum of the power spectrum which should be detectable in experiments.
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Affiliation(s)
- Markus Rauscher
- Max-Planck-Institut for Metallforschung, Heisenbergstrasse 3, 70569 Stuttgart, Germany.
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Fetzer R, Münch A, Wagner B, Rauscher M, Jacobs K. Quantifying hydrodynamic slip: a comprehensive analysis of dewetting profiles. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2007; 23:10559-66. [PMID: 17803324 DOI: 10.1021/la7010698] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/17/2023]
Abstract
To characterize nontrivial boundary conditions of a liquid flowing past a solid, the slip length is commonly used as a measure. From the profile of a retracting liquid front (e.g., measured with atomic force microscopy), the slip length can be extracted with the help of a Stokes model for a thin liquid film dewetting from a solid substrate. Specifically, we use a lubrication model derived from the Stokes model for strong slippage and linearize the film profile around the flat, unperturbed film. For small slip lengths, we expand the linearized full Stokes model for small slopes up to third order. Using the respective model, we obtain, in addition to the slip length, the capillary number, from which we can estimate the viscosity of the fluid film. We compare numerical and experimental results, test the consistency and the validity of the models/approximations, and give an easy-to-follow guide of how they can be used to analyze experiments.
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Affiliation(s)
- R Fetzer
- Department of Experimental Physics, Saarland University, D-66123 Saarbrücken, Germany.
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15
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Boudaoud A. Non-Newtonian thin films with normal stresses: dynamics and spreading. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2007; 22:107-9. [PMID: 17377751 DOI: 10.1140/epje/e2007-00026-9] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/06/2006] [Indexed: 05/14/2023]
Abstract
The dynamics of a thin film on a horizontal solid substrate is investigated in the case of non-Newtonian fluids exhibiting normal stress differences, the rheology of which is strongly non-linear. Two coupled equations of evolution for the thickness of the film and the shear rate are proposed within the lubrication approximation. This framework is applied to the motion of an advancing contact line. The apparent dynamic contact angle is found to depend logarithmically on a lengthscale determined solely by the rheological properties of the fluid and the velocity of the contact line.
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Affiliation(s)
- A Boudaoud
- Laboratoire de Physique Statistique de l'ENS, UMR8550 du CNRS, 24 rue Lhomond, 75231, Paris Cedex 05, France.
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Vilmin T, Raphaël E. Dewetting of thin polymer films. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2006; 21:161-74. [PMID: 17146593 DOI: 10.1140/epje/i2006-10057-5] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/04/2006] [Accepted: 11/09/2006] [Indexed: 05/12/2023]
Abstract
We study the dewetting of thin polymer films deposited on slippery substrate. Recent experiments on these systems have revealed many unexpected features. We develop here a model that takes into account the rheological properties of polymer melts, focussing on two dewetting geometries (the receding of a straight edge, and the opening of a hole). We show that the friction law associated with the slippage between the film and the substrate has a direct influence on the dewetting dynamic. In addition, we demonstrate that residual stresses, which can be stored in the films due to their viscoelasticity, are a source of destabilization for polymer films, and accelerate the dewetting process.
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Affiliation(s)
- T Vilmin
- Laboratoire de Physico-Chimie Théorique, UMR CNRS 7083, ESPCI, 10 rue Vauquelin, 75231, Paris Cedex 05, France.
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17
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Münch A, Wagner B, Rauscher M, Blossey R. A thin-film model for corotational Jeffreys fluids under strong slip. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2006; 20:365-8. [PMID: 16902756 DOI: 10.1140/epje/i2006-10031-3] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/19/2006] [Accepted: 08/07/2006] [Indexed: 05/11/2023]
Abstract
We derive a thin-film model for viscoelastic liquids under strong slip which obey the stress tensor dynamics of corotational Jeffreys fluids.
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Affiliation(s)
- A Münch
- Institute of Mathematics, Humboldt University of Berlin, D-10099, Berlin, Germany
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18
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Blossey R, Münch A, Rauscher M, Wagner B. Slip vs. viscoelasticity in dewetting thin films. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2006; 20:267-71. [PMID: 16794776 DOI: 10.1140/epje/i2006-10018-0] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/30/2006] [Accepted: 06/06/2006] [Indexed: 05/10/2023]
Abstract
Ultrathin polymer films on non-wettable substrates display dynamic features which have been attributed to either viscoelastic or slip effects. Here we show that in the weak- and strong-slip regime, effects of viscoelastic relaxation are either absent or essentially indistinguishable from slip effects. Strong slip modifies the fastest unstable mode in a rupturing thin film, which questions the standard approach to reconstruct the effective interface potential from dewetting experiments.
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Affiliation(s)
- R Blossey
- Biological Nanosystems, Interdisciplinary Research Institute, c/o IEMN Avenue Poincaré, BP 60069, F-59652, Villeneuve d'Ascq, France.
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Tomar G, Shankar V, Shukla SK, Sharma A, Biswas G. Instability and dynamics of thin viscoelastic liquid films. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2006; 20:185-200. [PMID: 16786198 DOI: 10.1140/epje/i2006-10011-7] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/18/2006] [Accepted: 05/19/2006] [Indexed: 05/10/2023]
Abstract
The instability, rupture, and subsequent growth of holes in a thin Jeffreys-type viscoelastic film under the influence of long-range van der Waals force are investigated using both linear stability analysis and nonlinear numerical solutions. The linear stability analysis of full governing equations valid for arbitrary wave numbers shows that although fluid rheology does not influence the dominant length scale of the instability, it significantly affects the growth rate. It is shown that neglect of inertia and solvent dynamics results in a nonphysical singularity in the growth rate beyond a critical value of relaxation time. We further carry out numerical simulations of a set of long-wave, nonlinear differential equations (also derived in Rauscher et al., Eur. Phys. J. E 17, 373 (2005)) governing the evolution of the free surface. The nonlinear simulations, in their domain of validity, confirm the results of the linear analysis. Interestingly, results from nonlinear simulations further show that both for Newtonian and viscoelastic liquids, the shape and the dewetting dynamics of a hole are identical when examined in terms of a rescaled time which depends on rheological parameters. Thus, viscoelasticity of Jeffreys type merely accelerates the growth rate, without however affecting the important morphological characteristics.
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Affiliation(s)
- G Tomar
- Department of Mechanical Engineering, Indian Institute of Technology, Kanpur 208016, India.
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20
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Gabriele S, Damman P, Sclavons S, Desprez S, Coppée S, Reiter G, Hamieh M, Akhrass SA, Vilmin T, Raphaël E. Viscoelastic dewetting of constrained polymer thin films. ACTA ACUST UNITED AC 2006. [DOI: 10.1002/polb.20919] [Citation(s) in RCA: 41] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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