Volume 48, Number 4, July-August 2014
|Page(s)||969 - 1009|
|Published online||30 June 2014|
A mixed formulation of a sharp interface model of stokes flow with moving contact lines∗
Department of Mathematics and Center for Computation and
Technology, Louisiana State University, Baton Rouge, LA
Received: 17 December 2012
Revised: 10 July 2013
Two-phase fluid flows on substrates (i.e. wetting phenomena) are important in many industrial processes, such as micro-fluidics and coating flows. These flows include additional physical effects that occur near moving (three-phase) contact lines. We present a new 2-D variational (saddle-point) formulation of a Stokesian fluid with surface tension that interacts with a rigid substrate. The model is derived by an Onsager type principle using shape differential calculus (at the sharp-interface, front-tracking level) and allows for moving contact lines and contact angle hysteresis and pinning through a variational inequality. Moreover, the formulation can be extended to include non-linear contact line motion models. We prove the well-posedness of the time semi-discrete system and fully discrete method using appropriate choices of finite element spaces. A formal energy law is derived for the semi-discrete and fully discrete formulations and preliminary error estimates are also given. Simulation results are presented for a droplet in multiple configurations to illustrate the method.
Mathematics Subject Classification: 65N30 / 65M12 / 76D45 / 76M30
Key words: Mixed method / Stokes equations / surface tension / contact line motion / contact line pinning / variational inequality / well-posedness
© EDP Sciences, SMAI, 2014
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.