Capillary Flow in Irregular Surface Grooves

1-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.