Radial spreading of a viscous drop between parallel-plane surfaces

The radial spreading dynamics of a thin film of viscous Newtonian fluid squeezed between parallel plane walls at gap spacings much smaller than the capillary length is examined both experimentally and theoretically. Using a squeezing flow model, analogous to the classical solution derived by Stefan [K. Akad. Wiss. (Mathem-Naturwiss. Kl) 69, 713 (1874)], the effects of surface tension and viscosity on dynamic spreading of squeezed droplets are analyzed. The interaction between squeezing and surface tension is parameterized by a single dimensionless variable, $F$⁠, which is the ratio of the constant external squeezing force, supplied by gravity acting on the top wall, to surface tension acting on a spreading droplets circumference. An analytical solution relating the gap height and time elapsed is derived in the limit of small Reynolds and negligible capillary numbers. Also, asymptotic solutions are derived for the change in gap height as a function of time, in the limit of either vanishingly small surface tension or external force. Experiments are performed using three fluids with different viscosity and surface tension for gap spacings $O(10–100μm)$⁠. There is excellent agreement between theory and the experimental results for the dynamic change in gap spacing.