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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Wetting and Spreading
TL;DR: In this article, the surface forces that lead to wetting are considered, and the equilibrium surface coverage of a substrate in contact with a drop of liquid is examined, while the hydrodynamics of both wetting and dewetting is influenced by the presence of the three-phase contact line separating "wet" regions from those that are either dry or covered by a microscopic film.
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Electrowetting: from basics to applications
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Dynamics and stability of thin liquid films
Richard V. Craster,Omar Matar +1 more
TL;DR: The dynamics and stability of thin liquid films have fascinated scientists over many decades: the observations of regular wave patterns in film flows along a windowpane or along guttering, the patterning of dewetting droplets, and the fingering of viscous flows down a slope are all examples that are familiar in daily life.
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Analysis of the effects of Marangoni stresses on the microflow in an evaporating sessile droplet.
Hua Hu,Ronald G. Larson +1 more
TL;DR: It is found that surfactant contamination, at a surface concentration as small as 300 molecules/microm(2), can almost entirely suppress the Marangoni flow in the evaporating droplet.
References
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Journal ArticleDOI
On the Theory of Lubrication and Its Application to Mr. Beauchamp Tower's Experiments, Including an Experimental Determination of the Viscosity of Olive Oil
TL;DR: In this paper, the authors considered the boundary or surface actions of fluids and proposed a theoretical treatment of the physical actions of oils and other viscous fluids to diminish friction and wear between solid surfaces.