Hyperdispersive flow of liquid thin films in fractal porous media

✍ Scribed by Pedro G. Toledo; H.Ted Davis; L.E. Scriven

• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 752 KB
• Volume: 104
• Category: Article
• ISSN: 0927-7757
• DOI: 10.1016/0927-7757(95)03208-u

✦ Synopsis

Recent displacement experiments show "anomalously" rapid spreading of water during imbibition into a prewet porous medium. We explain this phenomenon, called hyperdispersion, as viscous flow along fractal pore walls in thin films of thickness h governed by disjoining forces and capillarity. At high capillary pressure Pc, the total wetting phase saturation Sw is the sum of wetting phases in thin films Stf and in pendular structures Sps. In many cases, the disjoining pressure H is inversely proportional to a power m of the film thickness h, i.e. H~h-", so that StfoCPc TM. The contribution of fractal pendular structures to wetting phase saturation often obeys a power law Sps ~ p~3-o~, where D is the Hausdorff or fractal dimension of the pore wall roughness. Hence, if wetting phase inventory is primarily pendular structures, and if thin films control the hydraulic resistance of wetting phase, then the capillary dispersion coefficient obeys Dc~S~,, where v = [-3-m(4--D)]/m(3--D). The spreading is hyperdispersive, i.e. Dc(Sw) rises as wetting phase saturation approaches zero, if m > 3/(4 -D), hypodispersive, i.e. Dc(Sw) falls as wetting phase saturation tends to zero, if m < 3/(4-D), and diffusion-like if m = 3/(4-D). Asymptotic analysis of the "capillary diffusion" equation indicates hyperdispersive behavior for -2 < v < 0. In addition, we also predict the values of Dc by Monte Carlo simulation in porous media which are idealized as networks of pore segments.