Modeling of Droplet Evaporation on Superhydrophobic Surfaces

Abstract

When a drop of water is placed on a rough surface, there are two possible extreme regimes of wetting: the one called Cassie-Baxter (CB) with air pockets trapped underneath the droplet and the one called the Wenzel (W) state characterized by the homogeneous wetting of the surface. A way to investigate the transition between these two states is by means of evaporation experiments, in which the droplet starts in a CB state and, as its volume decreases, penetrates the surface's grooves, reaching a W state. Here we present a theoretical model based on the global interfacial energies for CB and W states that allows us to predict the thermodynamic wetting state of the droplet for a given volume and surface texture. We first analyze the influence of the surface geometric parameters on the droplet's final wetting state with constant volume and show that it depends strongly on the surface texture. We then vary the volume of the droplet, keeping the geometric surface parameters fixed to mimic evaporation and show that the drop experiences a transition from the CB to the W state when its volume reduces, as observed in experiments. To investigate the dependency of the wetting state on the initial state of the droplet, we implement a cellular Potts model in three dimensions. Simulations show very good agreement with theory when the initial state is W, but it disagrees when the droplet is initialized in a CB state, in accordance with previous observations which show that the CB state is metastable in many cases. Both simulations and the theoretical model can be modified to study other types of surfaces.

Wettability of Reentrant Surfaces: A Global Energy Approach

“…behavior of θ C and B and iii) the surface of type 3 is able to sustain a high value of the contact angle for smaller values of volumes for this particular geometry of the surface we chose. Features i) and ii) have already been reported for pillared surfaces experimentally, 38 in simulations 12,29 and more recently for the reentrant surfaces. 27,28 The staircase behavior in our case is due to the fact that the energy is minimized subject to the constraint that the contact line is pinned.…”

“…(3) When θ Y > 90 • , the CB state is the thermodynamic stable state for small values of a and high values of h and there is a transition to the W state when a increases and h decreases, as the dashed line indicates in Fig.(3)-c,d. 29 When θ Y decreases, the CB region also decreases gradually and disappears for θ Y = 90 • . Below this value, there is no transition: the only stable thermodynamic state is the Wenzel state.…”

“…In this section we develop a model that takes into account the energy cost of creating interfaces between different phases when a droplet of a given volume V 0 is placed on a surface of three types, as schematized in Fig.(1). The model and the method used to minimize the global energy were developed in a previous work 29 to study the case where a droplet is placed on a surface of type 1, Fig.(1a). Here we extend the method for the reentrant and We consider a three dimensional spherical droplet with geometric parameters as defined in Fig.(2).…”

“…22 Also some simulations were developed to measure the energy barrier between the super-repellent and wetting states 23,24 and to test the robustness of the superomniphobic behavior, 25,26 as well as experiments to better understand its properties. 27,28 Inspired by Kim's experiment, 21 in this work we extend a theoretical model developed for pillared surfaces in the reference 29 to the surfaces with a simple and double reentrance, as schematized in Fig.(1). The theoretical continuous model takes into account all the interfacial energies associated to the energy of a liquid droplet deposited on top of the surfaces.…”

Effect of Structure Hierarchy for Superhydrophobic Polymer Surfaces Studied by Droplet Evaporation

“…In this article we study how droplets behave over time when left to evaporate from different surfaces. This approach has been widely used for the investigation of the droplet evaporation rates [ 17 , 18 ] and for analyzing superhydrophobic and patterned surfaces [ 19 , 20 , 21 ], and several modeling techniques have been proposed to describe this process [ 19 , 22 , 23 , 24 ]. Erbil published a review on the topic in 2012 [ 25 ].…”