Dynamic Capillary Pressure in Porous Media

We analyse an imbibition process where a water/oil interface moves in a porous, hydrophilic structure with a macroscopic velocity V . Our microscopic description is based on the classical interpretation of the Hoffmann-Tanner law, where the local contact line velocity V L is proportional to the cube of the dynamic contact angle θ, and the dissipation (per unit length of line) scales like γθ 2 V L (where γ is the water/oil interfacial tension). The result is a dynamic capillary pressure Δ p d ∼ γ/ r t ( Ca ) 2/3 τ 5/3 , where τ is a tortuosity factor (>1) and r t a throat size. The data of Weitz et al. give Δ p d ∼ Ca 0.5±0.1 and could be interpreted in this way.