Deformation of advancing gas-liquid interfaces in capillary tubes

Deformation of an advancing gas-liquid meniscus is considered in two cases: prewetted and dry capillary tubes. The shape, slope, and curvature of the gas-liquid interface are determined assuming small Weber and Bond numbers, i.e., in the case of negligible inertia and gravity terms. For the prewetted capillary case, the dynamic contact angle rate-dependency is found to depend on both the capillary number and the ratio of the macroscopic prewetting film thickness to the capillary radius. Results are found intermediate between rate-dependency relations available in the literature. In the case of dry capillaries, the relative magnitudes of the viscous, capillary, and disjoining pressure effects are determined. The actual location of the three-phase contact line is analyzed in relation to the spreading coefficient. Results for the dynamic contact angle rate-dependency are found to agree well with published experimental data. In both cases, prewetted and dry capillaries, results are compared with Tanner's relationship and previous theoretical investigations.