Investigation of Equilibrium Droplet Shapes on Chemically Striped Patterned Surfaces Using Phase-Field Method

Abstract

We systematically investigate the equilibrium shapes of droplets deposited on a set of chemically striped patterned surfaces by using an Allen–Cahn-type phase-field model. Varying the widths of the stripes d, the volume V, as well as the initial positions of the droplets, we release the droplets on the top of the surfaces and observe the final droplet shapes. It is found that there are either one or two equilibrium shapes for a fixed ratio of d/V 1/3 and each equilibrium shape corresponds to an energy minimum state. The aspect ratio of the droplets ξ shows a periodic oscillation behavior with a decreasing amplitude as d/V 1/3 decreases, similar to the stick–slip–jump movement of a slowly condensing droplet on a chemically striped patterned surface. Additionally, by comparing the movements of slowly evaporating and condensing droplets, we have observed a hysteresis phenomenon, which reveals that the final shapes of droplets also rely on the moving paths. Through modifying the dynamic contact angle boundary condition, the contact line movements of droplets under condensation and evaporation, which are far from equilibrium, are addressed.

Autonomous transport and splitting of a droplet on an open surface

“…wherein using p f (m) as the liquid-gas interface thickness, we can identify 1 2 p f 2 | ∇φ | 2 as the interfacial free-energy density and K 0 = λ 4 p f 2 (φ 2 − 1) 2 [37] is the bulk-energy density. To choose the interface thickness p f we referred to Wu et al [38]. They observed that the numerical results vary drastically for Cahn number Cn = p f d 0 > 0.15.…”

“…If we consider a realistic value (thickness on the nm scale) of the interface then the number of grid cells becomes so large that it requires a supercomputer to simulate. Thus, for numerical modeling of such sharp interfaces, researchers use the maximum feasible value of the interface thickness, which generally ranges from 10 to 100 μm [38]. The mixing energy density λ (N) is related to the interfacial energy of the droplet σ as σ = 2 √ 2 3 λ p f [36].…”

Spreading and rebound dynamics of sub-millimetre urea-water-solution droplets impinging on substrates of varying wettability

“…Approaches that explicitly model non-equilibrium at the contact line by a time-dependent (relaxation) boundary condition at the solid surface [53,64,65], as used e.g. in the computations in [66], are not considered here.…”

Droplet impingement and wetting behavior on a chemically heterogeneous surface in the Beyond–Cassie–Baxter regime

“…Different from wetting on homogeneous surfaces, the droplet morphology will adapt to the alternations of wettability on the chemically heterogeneous surface, and the droplet's final shape strongly depends on the topology of wettability of the surface. Various chemically heterogeneous surfaces such as stripes [8][9][10] , square 11,12 , and triangular patterns 13 have been investigated. Striped surfaces get a lot of attention due to their relatively easy fabrication.…”