On the shape of a droplet in a wedge: new insight from electrowetting

Abstract

The equilibrium morphology of liquid drops exposed to geometric constraints can be rather complex. Even for simple geometries, analytical solutions are scarce. Here, we investigate the equilibrium shape and position of liquid drops confined in the wedge between two solid surfaces at an angle α. Using electrowetting, we control the contact angle and thereby manipulate the shape and the equilibrium position of aqueous drops in ambient oil. In the absence of contact angle hysteresis and buoyancy, we find that the equilibrium shape is given by a truncated sphere, at a position that is determined by the drop volume and the contact angle. At this position, the net normal force between drop and the surfaces vanishes. The effect of buoyancy gives rise to substantial deviations from this equilibrium configuration which we discuss here as well. We eventually show how the geometric constraint and electrowetting can be used to position droplets inside a wedge in a controlled way, without mechanical actuation.

Contact angle hysteresis and oil film lubrication in electrowetting with two immiscible liquids

“…d=2 μm is the thickness and =3.1 the dielectric constant of parylene C. Noticeably, the CAH (θadvθrec) on the untreated substrate increases from about 2° at 0 V to about 7° at 30 V (compare Fig. 1a and c), as also mentioned qualitatively in a previous report 13 . Accordingly, cos cos cos rec adv ∆ θ θ θ = − increases with increasing η for both DC-EW and AC-EW in oil on the untreated substrate ( Fig.…”

Energy Invariance in Capillary Systems

“…In such a case, the requirement of a constant equilibrium contact angle over a solid surface imposes the constraint that, close to the contact line, the boundaries are solids of revolution about an axis passing through the centre of the sphere. It is straightforward to apply this criterion to find the force-free equilibrium states of capillary bridges between flat and curved walls [10][11][12][13][14][15], but also those of droplets in contact with suspended solid particles, such as Pickering emulsions [16] and liquid marbles [17,18].…”

Mechanics and stability of vesicles and droplets in confined spaces

“…For instance, two particles with the same surface tension but different size and adhesion can be separated by properly designing a pore that ensures a very distinct CPP. This strategy can further be optimized by altering the wetting properties of pores with techniques such as electrowetting [26]. In the context of deformability-based particle separation [12,13,25], we note that our predictions are for normalized pressure Δ P * = Δ Ps /2 γ , implying that pore opening s and surface tension must also be accounted for to distinguish between two particles with different mechanical properties.…”

“…However, when more complex pore or vesicle shapes are considered, solutions must be derived numerically as discussed by Leong et al [24] in the context of vesicle properties and Zhang et al [25] in the context of pore shapes. Besides deformability, the physical interactions between a pore and a particle, particularly their mutual adhesion, are also known to be an important factor in the permeation problem [26], but surprisingly studies on this topic are scarce in the literature. Indeed, while the physics of adhesion between a vesicle and a substrate is widely known, it was not until the work of Fournier and Galatola [27] that it was applied to the permeation of a vesicle through axisymmetric pores of varying cross sections (both cylindrical and conical).…”