Flow Patterns in the Vicinity of Triple Line Dynamics Arising from a Local Surface Tension Model

Abstract

Abstract. We model and simulate numerically a droplet impact onto a solid substrate. The triple line dynamics modelling is implicit (as opposed to classical explicit mobility relations), it is based on the Shikhmurzaev equations. These equations include generalized Navier slip type boundary conditions with extra local surface tension gradient terms. Numerical results when spreading and recoiling are presented. A particular attention is paid to flow patterns near the contact line.

Numerical Modeling of Electrowetting by a Shape Inverse Approach

“…We do not consider a polynomial reconstruction of the underlying smooth surface then evaluate its curvature, since it leads to inaccurate results and unexpected behavior. Following [9,14], we consider a local least-square approximation then we evaluate the curvature. In the present algorithm, we consider a second order local Bezier approximation, see [14].…”

“…Following [9,14], we consider a local least-square approximation then we evaluate the curvature. In the present algorithm, we consider a second order local Bezier approximation, see [14]. As the numerical tests presented below show, this method filters noise reasonably.…”

“…In summary, with the present model, we do not manage to simulate properly the locking phenomena, but we observe an overestimate of the Lippman predictions, and this overestimate becomes more important when using a higher control points density. Computed shape compared to plane capacitor approximation shape for u0 = 800 V Curvature.. We use the algorithm described in previous section, see also [14]. For all computations we performed, the droplet shapes obtained had a constant curvature everywhere but in a vicinity of the triple point.…”