The problem of capillary-driven flow in a V-shaped surface groove is addressed. A nonlinear diffusion equation for the liquid shape is derived from mass conservation and Poiseuille flow conditions. A similarity transformation for this nonlinear equation is obtained and the resulting ordinary differential equation is solved numerically for appropriate boundary conditions. It is shown that the position of the wetting front is proportional to (Dt)½ where D is a diffusion coefficient proportional to the ratio of the liquid-vapour surface tension to viscosity and the groove depth, and a function of the contact angle and the groove angle. For flow into the groove from a sessile drop source it is shown that the groove angle must be greater than the contact angle. Certain arbitrarily shaped grooves are also addressed.

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(R,θ)-[γh0/µ]t where R is related to the included groove angle β (R ) 90 -β/2), θ is the contact angle, and h0 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 R f θ, and both require R -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(R,θ) term which is shown to be only weakly dependent on the range of R,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.

Heptanol flow in irregularly shaped surface grooves in Pd-coated Cu is shown to be an example of Poiseuille flow with simple Washburn kinetics of the form z 2 ) C(γ/µ)t, where γ is the liquid surface tension, µ is the viscosity, and C is a function of the groove dimensions and the contact angle θ. A shape independent expression is derived for the geometric factor, C(S,w,θ) ) (S cos(θ)w)/4π, where w is the width of the groove at the surface and S is the arc length, or total length of groove surface in a plane perpendicular to the groove axis. This expression is general for any groove shape and reduces to the form derived previously for V-shaped grooves. Along with scanning electron microscopy, three different techniques, stylus profilometry, laser profilometry, and optical interferometry, were used to characterize the groove geometry, especially to determine S and w. While reasonable agreement is obtained between literature values of γ/µ and values obtained from the experimental kinetics, the main conclusion is that measurement of the groove dimensions is the main limitation to experimental verification of the form of C and to the use of the kinetics of groove flow as an absolute measure of the factor γ/µ. However, we show that if C is calibrated for a specific groove with a known liquid, the kinetics of capillary flow in open surface grooves furnishes a simple, easily applied method for measurement of the surface tension-to-viscosity ratio, γ/µ. LA9712247

No abstract