Springer Online Journal Archives 1860-2000
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.
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