Droplet dynamics on chemically heterogeneous substrates

Abstract

Slow droplet motion on chemically heterogeneous substrates is considered analytically and numerically. We adopt the long-wave approximation which yields a single partial differential equation for the droplet height in time and space. A matched asymptotic analysis in the limit of nearly circular contact lines and vanishingly small slip lengths yields a reduced model consisting of a set of ordinary differential equations for the evolution of the Fourier harmonics of the contact line. The analytical predictions are found, within the domain of their validity, to be in good agreement with the solutions to the governing partial differential equation. The limitations of the reduced model when the contact line undergoes stronger deformations are partially lifted by proposing a hybrid scheme which couples the results of the asymptotic analysis with the boundary integral method. This approach improves the agreement with the governing partial differential equation, but at a computational cost which is significantly lower compared to that required for the full problem.

Steering droplets on substrates using moving steps in wettability

“…to the shape of the contact line. In a very recent example of the same research line, Savva et al 32 extended Glasner's method by describing the gas-liquid interface with the so-called thin-film approximation for Stokes flow for highly wettable substrates.…”

Droplets on substrates with oscillating wettability

“…Early theoretical studies used perturbation methods to analytically estimate the influence of small local wettability gradients on droplets with simple circular or cylindrical shapes 15,16 . Later, experimental and numerical work investigated more complex shapes which occur, for example, when a droplet crosses a static step in wettability 17,18 , flows over two neighboring stripes of increased wettability 19 , over a checker-board pattern 20,21 , or random spatial fluctuations in wettability 21 . From the perspective of the droplet these patterns also become time-varying if the droplets starts to move, for example, on an inclined substrate 22 .…”

Droplet motion on chemically heterogeneous substrates with mass transfer. I. Two-dimensional dynamics

“…Although the outcomes of a 2D model cannot be straightforwardly scrutinized by experiments, the combined analytical and computational work we have undertaken made looking into the complex bifurcation structure of the dynamics possible; gaining further insights into how hysteresis-like effects and transients to periodic motion occur by following the topological changes that take place as the nature and stability of droplet equilibria evolve with changing the droplet area. Importantly, the outcomes of this work are to be combined with the recent developments presented by Savva et al on 3D droplet motion over chemically heterogeneous surfaces [63], to offer a novel extension to the fully 3D geometry, which is the subject of the second part of the present study [47].…”