Fundamentals Of Topographic Substrate Leveling

Stillwagon, L. E.; Larson, Ronald G.

doi:10.1117/12.968332

Cited by 17 publications

(24 citation statements)

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“…Numerical solutions of Eq. (2.40) showed a good agreement with experimental data (Stillwagon and Larson, 1988). At short times there is film deplanarization due to the emergence of capillary humps, but these relax at longer times.…”

Section: Constant Surface Tension and Gravity Onlysupporting

confidence: 83%

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Long-scale evolution of thin liquid films

1997

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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 f...

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Section: Constant Surface Tension and Gravity Onlysupporting

confidence: 83%

“…The problem of leveling of a film under the action of capillary force on a corrugated substrate at zϭl(x) was considered by Stillwagon and Larson (1988). Using the approach described above, they derived the evolution equation, which for the case of zero gravity reads…”

Section: Constant Surface Tension and Gravity Onlymentioning

confidence: 99%

Long-scale evolution of thin liquid films

1997

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“…The interaction between viscous free-surface flows and topography has received considerable attention owing to its importance in a wide range of industrial and environmental contexts. These include the down-slope migration of lava flows, which develop when liquid magma erupts from a volcano (Sparks et al 1976;Cashman et al 2006), ice flows over Greenland and Antarctica (Rignot et al 2011) and thin 'coating' flows in engine bearings, printing, painting and other manufacturing processes (Huppert 1982a;Stillwagon & Larson 1988;Kistler & Schweizer 1997;Baxter et al 2009).…”

Section: Introductionmentioning

confidence: 99%

Interaction of viscous free-surface flows with topography

2019

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The interaction of gravitationally driven, free-surface flows of viscous fluid with topographic features is investigated theoretically. The motion is studied in the regime where the depth of the flow is much smaller than the streamwise extent of the topography. A lubrication model of the motion is developed, integrated numerically and analysed asymptotically. For small mounds, it is shown that the flow surmounts the obstacles, but for larger mounds the flow is deflected around it and can form dry zones in its wake into which fluid does not flow, as well as forming deeper ponded regions upstream. Which of these phenomena prevails is shown to depend upon the amplitude of the mound height and the thickness of the oncoming flow relative to the streamwise length scale over which the topography varies. By using numerical and asymptotic results, we demonstrate that relatively wide mounds lead to the development of deep ponds of material upstream, which may lead to flow overtopping if the mound is not sufficiently high. These insights can be used to inform the design of barriers that defend built infrastructures from lava flows, and it is shown how this model can also provide an upper bound on the force exerted by the flow on them.

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“…Applying boundary conditions (8), (9) and (10) to the velocity profile (17) results in the following tridiagonal linear system of algebraic equations for the interfacial velocities:…”

Section: Depth-averaged Form (Daf)mentioning

confidence: 99%

“…It has motivated numerous investigations, experimental and theoretical, over the past 30 years or so as to the affect of surface topography on thin film flow, directed primarily at understanding the gravity-driven flow of single layer films open to the atmosphere and about which much of the basic physics involved is now well understood. The topography explored include local, trench/peak and step-up/-down features, and the same repeated periodically; experimental data has remained scarce, [6][7][8][9], while modelling and prediction have relied heavily on lubrication theory, [10][11][12][13][14], with the odd attempt made to address the problem more generally by solving the Navier-Stokes equations, [15][16][17], or Stokes flow, [18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Steady bilayer channel and free-surface isothermal film flow over topography

Abdalla

Veremieiev

Gaskell

2018

Chemical Engineering Science

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Fundamentals Of Topographic Substrate Leveling

Cited by 17 publications

References 0 publications

Long-scale evolution of thin liquid films

Long-scale evolution of thin liquid films

Interaction of viscous free-surface flows with topography

Steady bilayer channel and free-surface isothermal film flow over topography

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