Morphological evolution of microscopic dewetting droplets with slip

Abstract

We investigate the dewetting of a droplet on a smooth horizontal solid surface for different slip lengths and equilibrium contact angles. Specifically, we solve for the axisymmetric Stokes flow using the boundary element method with (i) the Navier-slip boundary condition at the solid/liquid boundary and (ii) a time-independent equilibrium contact angle at the contact line. When decreasing the rescaled slip length $\tilde{b}$ with respect to the initial central height of the droplet, the typical non-sphericity of a droplet first increases, reaches a maximum at a characteristic rescaled slip length $\tilde{b}_{m}\approx O(0.1{-}1)$ and then decreases. Regarding different equilibrium contact angles, two universal rescalings are proposed to describe the behaviour of the non-sphericity for rescaled slip lengths larger or smaller than $\tilde{b}_{m}$. Around $\tilde{b}_{m}$, the early time evolution of the profiles at the rim can be described by similarity solutions. The results are explained in terms of the structure of the flow field governed by different dissipation channels: elongational flows for $\tilde{b}\gg \tilde{b}_{m}$, friction at the substrate for $\tilde{b}\approx \tilde{b}_{m}$ and shear flows for $\tilde{b}\ll \tilde{b}_{m}$. Following the changes between these dominant dissipation mechanisms, our study indicates a crossover to the quasistatic regime when $\tilde{b}$ is many orders of magnitude smaller than $\tilde{b}_{m}$.

Steering droplets on substrates using moving steps in wettability

“…First, in two articles McGraw et al implemented the boundary element method to gain insights into the internal flow fields of axisymmetric droplets. 29,30 They combined theory and experiment to study how droplets relax towards their new equilibrium shape on a substrate after an instantaneous change in the spatially uniform wettability. Second, Glasner 31 implemented the boundary element method to study the dynamics of droplets placed on substrates with static but non-uniform wettability profiles.…”

Film deposition and dynamics of a self-propelled wetting droplet on a conical fibre

“…Thus there is sufficient time for the droplet to relax to a quasi-static shape when the apparent contact lines move. For the large slip length regime, elongational flow has been proposed to appear and dominate the viscous dissipation (Münch et al 2005), which has been observed for dewetting droplets (McGraw et al 2016;Chan et al 2017). The large slip regime in our model, assuming Poiseuille flow as the dominating flow structure, is considered as the intermediate slip regime in the analysis of Münch et al (2005).…”

“…2016; Chan et al. 2017). The large slip regime in our model, assuming Poiseuille flow as the dominating flow structure, is considered as the intermediate slip regime in the analysis of Münch et al.…”

“…Interestingly, slip lengths have been reported to be as large as a few micrometres for fluids such as polymer melts (Bäumchen, Fetzer & Jacobs 2009) and for superhydrophobic surfaces (Rothstein 2010). When the droplet size is decreased to a few micrometres or below, effects due to the fluid slip on solid surface may become significant, as demonstrated in dynamical fluidic systems (Lauga, Brenner & Stone 2007;Bocquet & Charlaix 2009) such as the dewetting of microdroplets (McGraw et al 2016;Chan et al 2017) and of liquid films (Fetzer et al 2005). However, the influence of slip on the droplet dynamics and film deposition is not known for the directional droplet motion on a cone.…”

Electrostatic control of dewetting dynamics

“…1 shows that initially there exists a short transient while the rectangular film dewets into a thin liquid rivulet 25 . Following this a capillary rim is formed at short timescales and after coalescence of these rims a spherical cap droplet is formed at long timescales 4,26 . Due to the short length scale of the y-direction the dewetting and appearance of capillary rims is more prominent in the x-direction.…”