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Capillary hyperdisperson of wetting liquids in fractal porous media (1993)

Toledo, Pedro G. ; Ted Davis, H. ; Scriven, L. E.

Springer

Transport in porous media 10 (1993), S. 81-94

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ISSN: 1573-1634

Keywords: Capillary dispersion ; hyperdispersion ; fractals ; low saturation ; diffusion equation

Source: Springer Online Journal Archives 1860-2000

Topics: Geosciences , Technology

Notes: Abstract Recent displacement experiments show ‘anomalously’ rapid spreading of water during imbibition into a prewet porous medium. We explain this phenomenon, calledhyperdispersion, as viscous flow along fractal pore walls in thin films of thicknessh governed by disjoining forces and capillarity. At high capillary pressure, total wetting phase saturation is the sum of thin-film and pendular stucture inventories:S w =S tf +S ps . In many cases, disjoining pressure ∏ is inversely proportional to a powerm of film thicknessh, i.e. ∏ ∞h −m , so thatS tf ∞P c −1/m. The contribution of fractal pendular structures to wetting phase saturation often obeys a power lawS ps ∞P c (3−D), whereD is the Hausdorff or fractal dimension of pore wall roughness. Hence, if wetting phase inventory is primarily pendular structures, and if thin films control the hydraulic resistance of wetting phase, the capillary dispersion coefficient obeysD c ∞S w v , where v=[3−m(4−D) ]/m(3−D). The spreading ishyperdispersive, i.e.D c (S w ) rises as wetting phase saturation approaches zero, ifm〉3/(4−D),hypodispersive, i.e.D c (S 2) falls as wetting phase saturation tends to zero, ifm〈3/(4−D), anddiffusion-like ifm=3/(4−D). Asymptotic analysis of the ‘capillary diffusion’ equation is presented.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF00617512

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Coating flow theory by finite element and asymptotic analysis of the navier-stokes systemThis invited paper is an extended and refereed version of one presented at the Fourth International Symposium on Finite Elements in Flow Problems held in Tokyo, Japan, 26-29 July 1982. (1984)

Kistler, S. F. ; Scriven, L. E.

Chichester : Wiley-Blackwell

International Journal for Numerical Methods in Fluids 4 (1984), S. 207-229

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ISSN: 0271-2091

Keywords: Coating Flows ; Viscous Flows ; Free Surfaces ; Free Boundaries ; Boundary ; Parameterization Moving Spine Method ; Engineering ; Engineering General

Source: Wiley InterScience Backfile Collection 1832-2000

Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics

Notes: Coating flows are laminar free surface flows, preferably steady and two-dimensional, by which a liquid film is deposited on a substrate. Their theory rests on mass and momentum accounting for which Galerkin's weighted residual method, finite element basis functions, isoparametric mappings, and a new free surface parametrization prove particularly well-suited, especially in coping with the highly deformed free boundaries, irregular flow domains, and the singular nature of static and dynamic contact lines where fluid interfaces intersect solid surfaces. Typically, short forming zones of rapidly rearranging two-dimensional flow merge with simpler asymptotic regimes of developing or developed flow upstream and downstream. The two-dimensional computational domain can be shrunk in size by imposing boundary conditions from asymptotic analysis of those regimes or by matching to one-dimensional finite element solutions of asymptotic equations.The theory is laid out with special attention to conditions at free surfaces, contact lines, and open inflow and outflow boundaries. Efficient computation of predictions is described with emphasis on a grand Newton iteration that converges rapidly and brings other benefits. Sample results for curtain coating and roll coating flows of Newtonian liquids illustrate the power and effectiveness of the theory.

Additional Material: 20 Ill.