Enabling efficient energy barrier computations of wetting transitions on geometrically patterned surfaces

Abstract

Proper roughness design is important in realizing surfaces with fully tunable wetting properties. Engineering surface roughness boils down to an energy barrier optimization problem, in which the geometric features of roughness serve as the optimization parameters. Computations of energy barriers, separating admissible equilibrium wetting states on patterned surfaces, have been demonstrated utilizing fine-scale simulators (e.g., lattice-Boltzmann for mesoscale and molecular dynamics for microscale simulations), however with substantial computational requirements. Here, by solving an augmented Young–Laplace equation with a disjoining pressure term, we demonstrate accurate and efficient computations of equilibrium shapes of entire millimeter sized droplets on patterned surfaces. In particular, by adopting a natural parameterization of the Young–Laplace equation along the liquid/air and liquid/solid interfaces, the tedious implementation of the Young's contact angle boundary condition at multiple three phase contact lines is bypassed. We, thus, enable the computation of wetting transition energy barriers, separating the well-known Cassie–Baxter and Wenzel states, as well as intermediate states, but with negligible computational cost. We demonstrate the method's efficiency by computing the equilibrium of droplets on stripe-patterned surfaces, and compare the results with mesoscopic lattice Boltzmann simulations. Our computationally efficient continuum-level analysis can be readily applied to patterned surfaces with increased and unstructured geometric complexity, and straightforwardly coupled with shape optimizers towards the design of surfaces with desirable wetting behavior.

Connection of Intrinsic Wettability and Surface Topography with the Apparent Wetting Behavior and Adhesion Properties

“…This quantity can be computed from the solution of the Eikonal equation, 16,34 practically for any kind of solid surface geometry, structured or unstructured. Finally, the parameter l 0 regulates the minimum distance between the liquid and the solid phase, δ min .…”

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.…”

“…Here, we take δ as the Euclidean distance from the solid. This quantity is obtained from the solution of the Eikonal equation45 which expresses the signed distance from a boundary (even arbitrarily shaped), as proposed in our previous work29,30 . The solution of the Eikonal equation is discussed in Appendix A.…”

Three-gradient regular solution model for simple liquids wetting complex surface topologies

“…Macroscopic approaches such as solving the Young–Laplace equation [26–27], minimizing the availability [28], or using geometry and energy [12] to find the droplet shape, do not take molecular details into account, and often require the contact angle as input parameter. Furthermore, air entrapment and coalescence [29] cannot be obtained by solving the Young–Laplace equation, and surfaces with re-entrant curvatures give impossible solutions [29].…”