Abstract

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, 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 PI is inversely proportional to a power m of film thickness h, i.e. PI is-proportional-to h(-m), so that S(tf) is-proportional-to P(c)-1/m. The contribution of fractal pendular structures to wetting phase saturation often obeys a power law S(ps) is-proportional-to P(c)-(3-D), where D 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 obeys D(c) is-proportional-to S(w)v, where v = [3-m(4-D)]/m(3-D). The spreading is hyperdispersive, i.e. D(c)(S(w)) rises as wetting phase saturation approaches zero, if m > 3/(4 - D), hypodispersive, i.e. D(c)(S2) 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 is presented.