No Access Submitted: 19 January 2009 Accepted: 14 August 2009 Published Online: 09 September 2009
Physics of Fluids 21, 092102 (2009); https://doi.org/10.1063/1.3223628
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  • Nikos Savva
  • Serafim Kalliadasis
Contact line motion over a topographical substrate is considered using the spreading of a two-dimensional droplet as a model system. The spreading dynamics is modeled under the assumption of small contact angles where the long-wave expansion in the Stokes-flow regime can be employed to derive a single equation for the evolution of the droplet thickness. The contact line singularity is removed through the Navier slip condition, while the contact angle at the contact points is assumed to remain always equal to its static value. Through a singular perturbation approach, the flow in the vicinity of the contact line is matched asymptotically with the flow in the bulk of the droplet to yield a set of two coupled integrodifferential equations for the location of the two droplet fronts. Our matching procedure is verified through direct comparisons with numerical solutions to the full problem. Analysis of the equations obtained by asymptotic matching reveals a number of intriguing features that are not present when the substrate is flat. In particular, we demonstrate the existence of multiple equilibrium states which allows for a hysteresislike effect on the apparent contact line. Further, we demonstrate a stick-slip-type behavior of the contact line as it moves along the local variations of the substrate shape and the interesting possibility of a relatively brief recession of one of the contact lines.
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