Statics and dynamics of liquid barrels in wedge geometries

Abstract

We present a theoretical study of the statics and dynamics of a partially wetting liquid droplet, of equilibrium contact angle θ e , confined in a solid wedge geometry of opening angle β. We focus on a mostly non-wetting regime, given by the condition θ e − β > 90 • , where the droplet forms a liquid barrel -a closed shape of positive mean curvature. Using a quasi-equilibrium assumption for the shape of the liquid-gas interface, we compute the surface energy landscapes experienced by the liquid upon translations along the symmetry plane of the wedge. Close to equilibrium, our model is in good agreement with numerical calculations of the surface energy minimisation subject to a constrained position of the centre of mass of the liquid. Beyond the statics, we put forward a Lagrangian description for the droplet dynamics. We focus on the the over-damped limit, where the driving capillary force is balanced by the frictional forces arising from the bulk hydrodynamics, the corner flow near the contact lines and the contact line friction. Our results provide a theoretical framework to describe the motion of partially wetting liquids in confinement, and can be used to gain further understanding on the relative importance of dissipative processes that span from microscopic to macroscopic length scales. †

Slippery when wet: mobility regimes of confined drops in electrowetting

“…In particular, the single friction force of ref. 22 does not capture the succession of fast and slow relaxation processes as shown in Fig. 2 and 3.…”

“…the oil-water interfacial area) and A sl is the drop-substrate interfacial area. The dependence F(x) can be found by constrained numerical minimization, or modeled by analytical approximation, as discussed by Ruiz-Gutiérrez et al 22 For a given contact angle, F has a minimum at a position x e , where the droplet shape is a truncated sphere with contact angle y e . Upon displacing the drop inward or outward from x e , the surface energy increases, as shown in Fig.…”

“…Close to equilibrium and for small wedge angles, the restoring force can be modelled as ÀdF/dx E Àk(x À x e ), where k B gb 2 . To model the opposing dissipation forces, Ruiz-Gutiérrez et al 22 considered the friction caused by the flow within the bulk of the droplet, the flow within the vicinity of the contact line, and the motion of the contact line itself. This leads to a friction force Àndx/dt, with a friction coefficient n B mV 1/3 .…”

“…However, unlike the experiments in ref. 22, there is clearly no single and universal curve that describes both inward and outward relaxation. In particular, the single friction force of ref.…”

Spreading Dynamics of Droplet Impact on a Wedge-Patterned Biphilic Surface

“…They made a surface with a wettable gradient along the radial direction by chemical coating, and studied the spreading characteristics that occur when a droplet impacts an edge of different wettability. Recently the statics and dynamics of liquid barrels in wedge geometries have been studied theoretically and experimentally [15,16].…”