Instability and dynamics of thin viscoelastic liquid films (original) (raw)
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Long-scale evolution of thin liquid films
Reviews of Modern Physics, 1997
Macroscopic thin liquid films are entities that are important in biophysics, physics, and engineering, as well as in natural settings. They can be composed of common liquids such as water or oil, rheologically complex materials such as polymers solutions or melts, or complex mixtures of phases or components. When the films are subjected to the action of various mechanical, thermal, or structural factors, they display interesting dynamic phenomena such as wave propagation, wave steepening, and development of chaotic responses. Such films can display rupture phenomena creating holes, spreading of fronts, and the development of fingers. In this review a unified mathematical theory is presented that takes advantage of the disparity of the length scales and is based on the asymptotic procedure of reduction of the full set of governing equations and boundary conditions to a simplified, highly nonlinear, evolution equation or to a set of equations. As a result of this long-wave theory, a mathematical system is obtained that does not have the mathematical complexity of the original free-boundary problem but does preserve many of the important features of its physics. The basics of the long-wave theory are explained. If, in addition, the Reynolds number of the flow is not too large, the analogy with Reynolds's theory of lubrication can be drawn. A general nonlinear evolution equation or equations are then derived and various particular cases are considered. Each case contains a discussion of the linear stability properties of the base-state solutions and of the nonlinear spatiotemporal evolution of the interface (and other scalar variables, such as temperature or solute concentration). The cases reducing to a single highly nonlinear evolution equation are first examined. These include: (a) films with constant interfacial shear stress and constant surface tension, (b) films with constant surface tension and gravity only, (c) films with van der Waals (long-range molecular) forces and constant surface tension only, (d) films with thermocapillarity, surface tension, and body force only, (e) films with temperature-dependent physical properties, (f) evaporating/condensing films, (g) films on a thick substrate, (h) films on a horizontal cylinder, and (i) films on a rotating disc. The dynamics of the films with a spatial dependence of the base-state solution are then studied. These include the examples of nonuniform temperature or heat flux at liquid-solid boundaries. Problems which reduce to a set of nonlinear evolution equations are considered next. Those include (a) the dynamics of free liquid films, (b) bounded films with interfacial viscosity, and (c) dynamics of soluble and insoluble surfactants in bounded and free films. The spreading of drops on a solid surface and moving contact lines, including effects of heat and mass transport and van der Waals attractions, are then addressed. Several related topics such as falling films and sheets and Hele-Shaw flows are also briefly discussed. The results discussed give motivation for the development of careful experiments which can be used to test the theories and exhibit new phenomena.
The Journal of chemical physics, 1999
Various stages of evolution of the surface instability and pattern formation are investigated for unstable thin ͑Ͻ100 nm͒ fluid films subjected to the long-range van der Waals repulsion and a shorter range attraction. The complete three-dimensional morphology is resolved based on numerical solutions of the nonlinear 2D thin film equation. In the first phase of evolution, initial random nonhomogeneities are quickly reorganized into a small amplitude undulating structure consisting of long ''hills'' and ''valleys.'' Different types of patterns are formed thereafter, depending on the initial mean thickness vis-à-vis location of the minimum in the intermolecular force curve. Dewetting of relatively thick films occurs by circular isolated holes which grow and coalesce to form a large-scale structure with intervening pools and ridges of the liquid, which eventually decay into increasingly circular droplets. In thinner films, the shallow depressions merge and the long ridges of the bicontinuous structure mature, fragment, and directly transform into increasingly circular droplets, which continue to grow by ripening and merger. The characteristics of a pattern, its pathway of evolution, and the morphology at the onset of dewetting thus depend crucially on the form of the intermolecular potential in an extended neighborhood of the initial thickness. The linear and 1D nonlinear analyses used hitherto fail completely in prediction of morphological patterns, but can predict their length scales rather well.
Marangoni instability in a viscoelastic binary film with cross-diffusive effect
Journal of Fluid Mechanics
Oftentimes, during theoretical modelling, although the dynamics of a viscoelastic fluid is studied considering it to be pure, such fluids are usually the blends of polymeric solute in a Newtonian solvent. Stratification of these solutes can take place in the presence of a temperature gradient via the Soret effect. In this study, we investigate the classical Marangoni instability problem for a thin viscoelastic film considering this binary aspect of the fluid. The system, comprising of a thin-film confined between its deformable free surface and a flat solid substrate, is subjected to heating from below. A linear stability analysis carried around the quiescent base state reveals that both long-wave deformational and shortwave disturbances can emerge in this system. Apart from the monotonic instability, the competition between the thermo-and solutocapillary forces in presence of the Soret effect can give rise to two different oscillatory instabilities as aptly demonstrated in this analysis. The characteristics of each instability mode are discussed, and a complete stability picture is perceived in terms of the phase diagram, identifying the parameter space within which a particular instability mode can get dominant. Finally, an approximate model is developed under the framework of long-wave analysis that can qualitatively reflect the stability behaviour without numerically solving the eigenvalue problem.
Chemical Physics, 2011
Instability and dewetting engendered by the van der Waals force in soft thin (<100 nm) linear viscoelastic solid (e.g., elastomeric gel) films on uniform and patterned surfaces are explored. Linear stability analysis shows that, although the elasticity of the film controls the onset of instability and the corresponding critical wavelength, the dominant length-scale remains invariant with the elastic modulus of the film. The unstable modes are found to be long-wave, for which a nonlinear long-wave analysis and simulations are performed to uncover the dynamics and morphology of dewetting. The stored elastic energy slows down the temporal growth of instability significantly. The simulations also show that a thermodynamically stable film with zero-frequency elasticity can be made unstable in the presence of physico-chemical defects on the substrate and can follow an entirely different pathway with far fewer holes as compared to the viscous films. Further, the elastic restoring force can retard the growth of a depression adjacent to the hole-rim and thus suppress the formation of satellite holes bordering the primary holes. These findings are in contrast to the dewetting of viscoelastic liquid films where nonzero frequency elasticity accelerates the film rupture and promotes the secondary instabilities. Thus, the zero-frequency elasticity can play a major role in imposing a better-defined long-range order to the dewetted structures by arresting the secondary instabilities.
A general unified theory of field (van der Waals, electric, etc.)-induced surface instabilities in thin viscoelastic films that accounts for a destabilizing field and stabilizing effects of elastic strain and surface energy is presented. The present theory seamlessly covers the instability and its different regimes in films ranging from elastic to viscous, from adhesive (confined) to wetting (free surface), and from short-to long-wave instabilities. The critical conditions for the onset of instability are found to be strongly dependent on elastic properties such as the shear modulus of the film, but the dominant wavelength is strikingly independent of the film rheology. Different regimes based on a nondimensional parameter (γ/μh) are uncovered, where γ is the surface energy, μ is the elastic shear modulus, and h is the film thickness. A short-wave, elasticlike response with wavelength λ ≈ 2.96h is obtained for γ/μh < 0.1, whereas long waves that depend nonlinearly on the field strength and surface energy are obtained for γ/μh > 1. Owing to their small critical thickness, wetting films destabilized by intermolecular forces always display long-wave instability regardless of their viscoelasticity. Furthermore, our numerical simulations based on energy minimization for unstable wetting elastic films show the formation of islands for ultrathin films and a morphological phase transition to holes embedded in the film for relatively thicker films. Unlike viscous films, however, unstable elastic films do not display a unique dominant wavelength but a bimodal distribution of wavelengths.
Instability and rupture of ultrathin freestanding viscoelastic solid films
Physical Review E
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.
Electrohydrodynamic instability of a confined viscoelastic liquid film
Journal of Non-newtonian Fluid Mechanics, 2007
We study the surface instability of a confined viscoelastic liquid film under the influence of an applied electric field using the Maxwell and Jeffreys models for the liquid. It was shown recently for a Maxwell fluid in the absence of inertia that the growth rate of the electrohydrodynamic instability diverges above a critical value of Deborah number [L. Wu, S.Y. Chou, Electrohydrodynamic instability of a thin film of viscoelastic polymer underneath a lithographically manufactured mask, J. Non-Newtonian Fluid Mech. 125 ] and the problem of pattern length selection becomes ill-defined. We show here that inclusion of fluid inertia removes the singularity and leads to finite but large growth rates for all values of Deborah number. The dominant wavelength of instability is thus identified. Our results show that the limit of small inertia is not the same as the limit of zero inertia for the correct description of the dynamics and wavelength of instability in a polymer melt. In the absence of inertia, we show that the presence of a very small amount of solvent viscosity (in the Jeffreys model) also removes the non-physical singularity in the growth rate for arbitrary Deborah numbers. Our linear stability analysis offers a plausible explanation for the highly regular length scales of the electric field induced patterns obtained in experiments for polymer melts. Further, the dominant length scale of the instability is found to be independent of bulk rheological properties such as the relaxation time and solvent viscosity.
Pattern formation in unstable thin liquid films
Physical Review Letters, 1998
The problem of spontaneous evolution of morphological patterns in thin (,100 nm) unstable liquid films on homogeneous solid substrates is resolved based on a 3D nonlinear equation of motion. Initially, a small amplitude bicontinuous structure emerges, which either grows and fragments into a collection of microdroplets (for relatively thinner films), or leads directly to isolated circular holes (for thicker films) which dewet the surface. The characteristics of a pattern, and its pathway of evolution, thus depend crucially on the form of the intermolecular potential in an extended neighborhood of the initial thickness. The linear and 2D nonlinear analyses used hitherto fail completely in prediction of morphological patterns, but can predict their length scales rather well. [S0031-9007(98)07349-9] PACS numbers: 68.15. + e, 47.20.Ma, 47.54. + r, The problem of stability and spontaneous pattern formation in thin (,100 nm) fluid films is central to a host of technological applications (e.g., coatings) and to a diversity of physical and biological thin film phenomena (e.g., wetting, adhesion, colloids, membrane morphology).
Study of instability of Rivlin-Ericksen viscoelastic fluid film
INTERNATIONAL SCIENTIFIC AND PRACTICAL CONFERENCE “TECHNOLOGY IN AGRICULTURE, ENERGY AND ECOLOGY” (TAEE2022)
The instability of the interface shaped by a Rivlin-Ericksen viscoelastic fluid and a Newtonian viscous liquid is examined through the normal mode procedure. The formulated mathematical equations are solved by the potential function hypothesis of viscous/viscoelastic fluids. The polynomial equation of degree two is achieved to discuss the stability/instability of the interface. The Rivlin-Ericksen fluid-viscous fluid interface is found to be more stable than the viscous-viscous fluid interface.