Spreading of rotating liquid annular ring with hysteresis effects

Abstract The spreading of a liquid, subjected to centrifugal forces or an air jet, leads toa lowering of the liquid height at the center. If the system is partially wetting,experiments show a break up of the liquid and the appearance of a dry patch atthe center. In this article, the spreading of a droplet or a liquid film, featuring adry patch at the center, is investigated. Via a generalized Tanner’s law, we allowfor a contact–angle hysteresis in partially–wetting system. By means of the lubrication approximation, an analytical quasi–steady solution can be derived in thelimit of small capillary numbers. We find a power–law regime for the spreading,in which at least one of the contact lines follows a power law in time, almost independent of both static contact angles. The influence of the static contact anglesremains restricted to the beginning of the spreading and to transition periods.Four different types of spreading can be identified, namely spreading (i) with avery thin central liquid layer, (ii) as annular ring with central dry patch, (iii) intoa static equilibrium, and (iv) with closing of the central dry patch. In a flow map,these types of spreading are mapped as function of both static contact angles.Moreover, the dependency from gravitational and centrifugal forces is investigated and included in the flow map. For a perfectly–wetting system, a disjoiningpressure correction in combination with Tanner’s law prohibits negative liquidheights at the center. Hereby, the magnitudes of the Hamaker constants have anegligible influence and arbitrary–small values can be used, since the dynamicsof the contact line remains controlled by Tanner’s law.