An extension of Miller scaling to scale sorptivity by contact angle

This study sheds light on the limitations of using [(cos θ) ^1/2] to scale sorptivity by contact angle while reaffirming its scaling by geometrical Miller scaling factor (λ^1/2). The sorptivity for uniform and nonuniform (wavy) capillary tubes was determined by a mathematical model that includes the effect of inertia and dynamic contact angle. Given that real porous media are preferably represented by a bundle of nonuniform rather than uniform capillary tubes, the relationship between sorptivity and contact angle was examined for different combinations of contact angles and capillary tube degrees of waviness. A general relationship of S = f [cos θ)^β] (with β ≤ 1/2) was found. The deviation of β from 1/2 (associated with uniform capillary tubes) increased with contact angle and capillary waviness increase. Zero sorptivity was obtained even for wettable capillaries, θ < 90°, a phenomenon that has been generally associated with hydrophobic capillaries (θ ≥ 90°). Contact angle and nonuniform pore structure had a synergistic effect on sorptivity. Capillary nonuniformity per se diminished sorptivity but its synergy with contact angle markedly magnified this reduction. Thus, following the sorptivity impact on finger width, it is rational to assume that larger-than-zero contact angles are involved in the formation of narrow fingers with an abrupt change between the inner wet and surrounding dry areas. Key Points Narrower fingers will develop at higher contact angels and/or wavier pores shape Sorptivity dependence on contact angle vary with pore geometry characteristics