Nikolaos T. Chamakos

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

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 Youngs 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 methods 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.

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

The complicated dynamics of the contact line of a moving droplet on a solid substrate often hamper the efficient modeling of microfluidic systems. In particular, the selection of the effective boundary conditions, specifying the contact line motion, is a controversial issue since the microscopic physics that gives rise to this displacement is still unknown. Here, a sharp interface, continuum-level, novel modeling approach, accounting for liquid/solid micro-scale interactions assembled in a disjoining pressure term, is presented. By following a unified conception (the model applies both to the liquid/solid and the liquid/ambient interfaces), the friction forces at the contact line, as well as the dynamic contact angle are derived implicitly as a result of the disjoining pressure and viscous effects interplay in the vicinity of the substrate’s intrinsic roughness. Previous hydrodynamic model limitations, of imposing the contact line boundary condition to an unknown number and reconfigurable contact lines, when modeling the spreading dynamics on textured substrates, are now overcome. The validity of our approach is tested against experimental data of a droplet impacting on a horizontal solid surface. The study of the early spreading stage on hierarchically structured and chemically patterned solid substrates reveal an inertial regime where the contact radius grows according to a universal power law, perfectly agreeing with recently published experimental findings.

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

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.

Thermocapillary Droplet Actuation: Effect of Solid Structure and Wettability

We examine the thermocapillary-driven flow of a droplet on a nonuniformly heated patterned surface. Using a sharp-interface scheme, capable of efficiently modeling the flow over complex surfaces, we perform 2D and 3D finite element simulations for a wide range of substrate wettabilities, i.e., from hydrophilic to superhydrophobic surfaces. Our results demonstrate that the contact angle hysteresis, due to the presence of the solid structures, is responsible for the appearance of a critical thermal gradient beyond which droplet migration is possible; the latter has been reported by experimental observations. The migration velocity as well as the direction of motion strongly depend on the combined action of the net mechanical force along the contact line and the thermocapillary induced flow at the liquid-air interface. We also show that through proper control and design of the substrate wettability, contact angle hysteresis, and induced flow field it is possible to manipulate the droplet dynamics: in particular, controlling its motion along a predefined track or entrapping by a wetting defect a droplet based on its size, as well as providing appropriate conditions for enhanced mixing inside the droplet.

How to Achieve Reversible Electrowetting on Superhydrophobic Surfaces

Collapse (Cassie to Wenzel) wetting transitions impede the electrostatically induced reversible modification of wettability on superhydrophobic surfaces, unless a strong external actuation (e.g., substrate heating) is applied. Here we show that collapse transitions can be prevented (the droplet remains suspended on the solid roughness protrusions) when the electrostatic force, responsible for the wetting modification, is smoothly distributed along the droplet surface. The above argument is initially established theoretically and then verified experimentally.

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

Abstract Recent experiments by Kavousanakis et al., Langmuir, 2018 [1], showed that reversible electrowetting on superhydrophobic surfaces can be achieved by using a thick solid dielectric layer (e.g. tens of micrometers). It has also been shown, through equilibrium (static) computations, that when the dielectric layer is thick enough the electrostatic pressure is smoothly distributed along the droplet surface, thus the irreversible Cassie to Wenzel wetting transitions can be prevented. In the present work we perform more realistic, dynamic simulations of the electrostatically-induced spreading on superhydrophobic surfaces. To this end, we employ an efficient numerical scheme which enables us to fully take into account the topography of the solid substrate. We investigate in detail the role of the various characteristics of the substrate (i.e. the dielectric thickness, geometry and material wettability) and present relevant flow maps for the resulting wetting states. Through our dynamic simulations, we identify the conditions under which it is possible to achieve reversible electrowetting. We have found that not only the collapse (Cassie-Baxter to Wenzel) transitions but also the contact angle hysteresis of the substrate significantly affects the reversibility.