The droplet race: Optimization of a wettability gradient surface

Abstract

Droplet behavior influenced by wettability distribution is a pertinent field of research with applications in lab-on-a-chip and heat transfer devices among others. Some have proposed patterned surfaces with controlled variation of wettability to orient the direction of the droplet motion or to increase its velocity. These patterns are arrived upon with experience and knowledge of this phenomenon. In this research paper, the authors used a mathematical approach to the physical problem by using a gradient based optimizer for maximizing droplet velocity. Given some initial conditions, the optimizer marches toward the optimum wettability distribution profile. The droplet motion is modeled in two dimensions (i.e., on the xy-plane), on a plate having a wettability distribution in one dimension (i.e., along the x axis). The single component pseudopotential model allows for the quantification of the wettability distribution as a distribution of a pseudodensity of the solid nodes of the flat plate. Starting with several monotonous analytical profiles, a quadratic convex profile allows us to reach the maximum mean velocity for the threshold droplet displacement. Different sets of initial profiles, length of the plate (L), and diameter of the droplet (D) are tested. For smaller L/D ratio, the optimal wettability distributions exhibit non-trivial features: profiles can be non-monotonous, and wettability gradient could be locally null. With the increase in the L/D ratio, these specificities tend to be less prominent and optimal profiles converge to the quadratic convex one. The main innovation and significance of the paper is that mathematical optimization algorithms have been used conjointly with a multiphase lattice Boltzmann model solver to address for the first time the droplet race defined as: “what is the best wettability profile in order for a droplet to reach a desired location as quickly as possible?”