The Flow of Liquids in Surface Grooves

We have obtained detailed capillary kinetic data for flow of a series of alcohols with various surface tension to viscosity ratios, γ/μ, spreading in open V-shaped grooves cut in Cu with three different groove angles. The location of the three-phase contact line, z, with time always follows the formula z 2 = K(α,θ)[γh 0/μ]t where α is related to the included groove angle β (α = 90 − β/2), θ is the contact angle, and h 0 is the groove depth. Two theoretical models which assume Poiseuille flow and static advancing contact angles were tested against the experimental data. One is a detailed hydrodynamic model with the basic driving force resulting from the pressure drop across a curved interface. The second depends on the total interfacial energy change, independent of the shape of the liquid interface. Both agree with the experimental data. In agreement with experiment, both models predict that the rate approaches zero as α → θ, and both require α − θ > 0. Both, including a physically unrealistic approximation by a cylindrical capillary, correctly scale the experimental data. Both predict numerical values in general agreement with experiment and with each other. Differentiation between the models is possible only in the K(α,θ) term which is shown to be only weakly dependent on the range of α,θ values studied. In the threshold region where the transition occurs between filled and empty regions of the groove, the liquid height decreases linearly with distance, within experimental limitations, and forms an angle which roughly scales as the contact angle for a significant fraction of the threshold region. On the basis of the present detailed experimental data for both kinetics and threshold profile, the differences between experiment and theory and between the theoretical models are insufficient to allow a clear choice between the models.