To coalesce or not to coalesce: Droplets and surface tension gradients

Abstract

We numerically study the coalescence dynamics of two sessile droplets with radii $R_0$. The droplets are placed on top of a rigid substrate with a contact angle of $\theta_{eq.} = \pi/9$. Having a highly wettable substrate ($\theta_{eq} \ll \pi/2$) theory predicts that the bridge height ($h_0$) scales according to $h_0(t) \sim t^{2/3}.$ This behavior can be altered with e.g. surface tension gradients ($\partial_x\gamma \neq 0$). These gradients appear for example with heat transfer, surfactants or having different but miscible liquids. Instead of coalescence, these gradients can lead to a stable two droplet state. In this work, we focus on two aspects of this problem. The first one is the concrete choice of the surface tension, therefore making it spatially correlated. The second one is the reduction of scale towards a regime in which the disjoining pressure becomes important. We find that coalescence can be suppressed, given that there is a sharp gradient in surface tension. If this gradient is smeared, we find an intermediate agreement with the $2/3$ power-law. In the limit of large smearing width, we observe an asymmetric coalescence.