Neither Lippmann nor Young: Enabling Electrowetting Modeling on Structured Dielectric Surfaces

Abstract

Aiming to illuminate mechanisms of wetting transitions on geometrically patterned surfaces induced by the electrowetting phenomenon, we present a novel modeling approach that goes beyond the limitations of the Lippmann equation and is even relieved from the implementation of the Young contact angle boundary condition. We employ the equations of the capillary electrohydrostatics augmented by a disjoining pressure term derived from an effective interface potential accounting for solid/liquid interactions. Proper parametrization of the liquid surface profile enables efficient simulation of multiple and reconfigurable three-phase contact lines (TPL) appearing when entire droplets undergo wetting transitions on patterned surfaces. The liquid/ambient and the liquid/solid interfaces are treated in a unified context tackling the assumption that the liquid profile is wedge-shaped at any three-phase contact line. In this way, electric field singularities are bypassed, allowing for accurate electric field and liquid surface profile computation, especially in the vicinity of TPLs. We found that the invariance of the microscopic contact angle in electrowetting systems is valid only for thick dielectrics, supporting published experiments. By applying our methodology to patterned dielectrics, we computed all admissible droplet equilibrium profiles, including Cassie-Baxter, Wenzel, and mixed wetting states. Mixed wetting states are computed for the first time in electrowetting systems, and their relative stability is presented in a clear and instructive way.

Effect of substrate topography, material wettability and dielectric thickness on reversible electrowetting

“…On the contrary, such a transition is not observed for the thicker dielectric case. The above argument is in line with our previous theoretical [36] as well as experimental work [1,18] claiming that the collapse transition can be avoided and thus the contact angle reversibility is feasible above a critical solid substrate thickness. In Figure 8 we present the normalized contact radius of a droplet equilibrating on a structured substrate with decreased pillar width, ‫,ݓ‬ compared to that of Figure 7; the width of the protrusions here is w = 30 um (see Figure 2b) while the period of the asperities (pitch), ‫,‬ is kept constant.…”

Droplet spreading on rough surfaces: Tackling the contact line boundary condition

“…where p 0 is a reference pressure (constant along the interface) representing the pressure of the ambient phase. The disjoining pressure term, p LS , expresses the excess pressure due to the liquid/solid interactions and is given by the following expression 29,30 :…”

“…We recently presented static equilibrium computations of droplets with multiple contact lines, wetting geometrically patterned solid surfaces [29][30][31] . According to our approach, the liquid/ambient (LA) and the liquid/solid interfaces are treated in a unified context (one equation for both interfaces) by: a) employing the Young-Laplace equation 32 augmented with a disjoining (or Derjaguin) pressure term 33,34 , which accounts for the micro-scale liquid/solid interactions, and b) parameterizing the liquid surface in terms of its arc-length of the effectively onedimensional droplet profile.…”

Impact of Surface Electrostatic Potential on Icephobic Properties of Nanoimprinted Flexible Polymer Foils

“…This could explain the slower decrease of CA, as already reported in refs. [31,32]. Chamakos et al [31] explained that the Young-Lippman equation does not take into account electric fringe fields close to the three-phase contact line.…”

“…[31,32]. Chamakos et al [31] explained that the Young-Lippman equation does not take into account electric fringe fields close to the three-phase contact line. The model is therefore valid only for low voltages and flat dielectrics.…”