Journal ArticleDOI
Long-scale evolution of thin liquid films
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TLDR
In this article, 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.Abstract:
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.read more
Citations
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Hydrodynamics of soft active matter
M. C. Marchetti,Jean-François Joanny,Jean-François Joanny,Sriram Ramaswamy,Sriram Ramaswamy,Tanniemola B. Liverpool,Jacques Prost,Jacques Prost,Madan Rao,R. Aditi Simha,R. Aditi Simha +10 more
TL;DR: This review summarizes theoretical progress in the field of active matter, placing it in the context of recent experiments, and highlights the experimental relevance of various semimicroscopic derivations of the continuum theory for describing bacterial swarms and suspensions, the cytoskeleton of living cells, and vibrated granular material.
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Electrowetting: from basics to applications
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Dynamics and stability of thin liquid films
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Analysis of the effects of Marangoni stresses on the microflow in an evaporating sessile droplet.
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References
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Journal ArticleDOI
Nonlinear evolution equations for thin liquid films with insoluble surfactants
TL;DR: In this article, the authors derived asymptotically from the full Navier-Stokes equations for free films and incorporated the effect of van der Waals attraction, capillary forces and Marangoni forces due to gradients of surface tension.
Journal ArticleDOI
The rewetting of an inclined solid surface by a liquid
N. Silvi,E. B. Dussan +1 more
TL;DR: In this paper, the role played by the contact angle in the rewetting process was investigated by performing a specific set of experiments of the type introduced by Huppert, and it was found that a small static advancing contact angle promoted rewetting, while a large value of the angle does not.
Journal ArticleDOI
A Legendre spectral element method for simulation of unsteady incompressible viscous free-surface flows
L.-W. Ho,Anthony T. Patera +1 more
TL;DR: In this article, a new Legendre spectral element method is presented for the solution of viscous incompressible free-surface flows based on the full viscous stress tensor for natural imposition of traction (surface tension) boundary conditions.
Journal ArticleDOI
Nonlinear saturation of Rayleigh–Taylor instability in thin films
TL;DR: In this article, a general nonlinear saturation of instabiities in flowing films is described using the Rayleigh-Taylor instability as an example, and the combined action of flow shear and surface tension is the essence of the saturation mechanism.
Journal ArticleDOI
Rayleigh–Taylor instability in thin viscous films
S.G. Yiantsios,Brian G. Higgins +1 more
TL;DR: In this article, the behavior of a viscous fluid film bounded by a wall and a heavier overlying immiscible phase is examined in the limit of small Bond number, and an energy stability analysis reveals that one drop per wavelength is the most energetically favorable.