Capillarity Effects on Viscous Gravity Spreadings of Wetting Liquids

Abstract

Highly viscous silicone oils within a wide range of volumes were left to spread on smooth horizontal substrates to investigate the effects of capillarity on viscous gravity spreadings under the condition of complete wetting. The study was centered on the intermediate asymptotic behavior, where the details of the initial liquid distribution are irrelevant. We detected small but appreciable departures from the well-known solution without surface tension forces (viscous gravity self similar solution, or base solution). Two stages are clearly identified in the spreadings. During the first, which is usually rather brief, capillarity does not play an appreciable role on the dynamics of the spreading, i.e., the base solution is a very good approximation. The head of the current displays a wheel-like profile progressively decreasing in size; when the size becomes on the order of the capillary length, this stage ends. The wheel-like configuration cannot be associated either with the rheological behavior of the fluid used or with the initial conditions. To observe this first stage without the influences due to peculiarities of the initial conditions, a proper release of the spreading is needed. The second stage is characterized by a spreading rate below the base solution; the slowing is associated with a change of the current head shape, which takes the form of a wedge as a consequence of capillarity. The rate of advance of the front may still be well approximated by the same power law as given by the base solution, but with a smaller prefactor. In this work we measure the parameters that characterize the flow during both stages; besides, for the second stage, we develop a heuristic calculation which shows that the wedge-like shape of the current head gives place to a higher viscous dissipation rate, thus explaining the observed slowing of the spreading.