Control of droplet evaporation on smooth chemical patterns

Abstract

We investigate the evaporation of a two-dimensional droplet on a solid surface. The solid is flat but with smooth chemical variations that lead to a space-dependent local contact angle. We perform a detailed bifurcation analysis of the equilibrium properties of the droplet as its size is changed, observing the emergence of a hierarchy of bifurcations that strongly depends on the particular underlying chemical pattern. Symmetric and periodic patterns lead to a sequence of pitchfork and saddle-node bifurcations that make stable solutions to become saddle nodes. Under dynamic conditions, this change in stability suggests that any perturbation in the system can make the droplet to shift laterally while relaxing to the nearest stable point, as is confirmed by numerical computations of the Cahn-Hilliard and Navier-Stokes system of equations. We also consider patterns with an amplitude gradient that creates a set of disconnected stable branches in the solution space, leading to a continuous change of the droplet's location upon evaporation.

On the lifetimes of two-dimensional droplets on smooth wetting patterns

“…As the droplet slowly evaporates the shape and location of the droplet can be modelled by studying the stability of the equilibrium solutions. This approach has recently been used to describe droplets evaporating on chemical patterns [39] and droplet with mass transfer moving on chemical patterns [40]. This section reviews the work presented in these references to study the static stability of a droplet with known volume on a smooth patterned surface.…”

“…2w) is a integer multiple of the pattern wavelength. It has been shown that only the droplets which align with a maximum or minimum of the patterning can be stable [39,40]. In addition, the stability of those solutions depend on the droplet's volume and solutions that are centred on a maximum or minimum of the patterning can be stable, partially stable (saddle node) or fully unstable.…”

“…Indeed, for small volumes or small ε all droplets aligned with a maximum or minimum of the patterning are stable to symmetric perturbations. As ε increases, solutions undergo a pitchfork bifurcation to lose their stability to symmetric perturbations [39].…”

“…The theory behind droplets atop smooth surface has been described in [37]. In addition, it has recently been shown that a droplet evaporating on a slippery surface that has a smooth macroscopic pattern follows a reproducible sequence of events that are characterised by bifurcations on the droplet's shape and position, and it has been referred to as snap evaporation, see [38] for topographical patterns and [39] for chemical patterns. In contrast to the stick-jump mode reported in [29], during snap evaporation, the droplet's contact line is never fully stationary but it moves very slowly except when a shape bifurcation occurs that forces the droplet to shift laterally and/or have a reduction of its base radius.…”

“…A key assumption of this approach is a quasi-static evolution so that the state of the droplet is given by its equilibrium properties. Such approach has been used to quantify droplets evaporating on either smooth topographies [38] or chemical patterns [39], as well as for droplets with mass transfer moving on chemical patterns [40]. However, while all these works have focussed on the control of droplet motion on smooth patterns, little is known on the effect of patterning on the lifetime of evaporating droplets.…”