Coalescence of Polymer Droplets Moving on a Surface with Stiffness Gradient

Abstract

Here, we study the coalescence of two droplets that are moving in the same direction on a soft surface; the motion of the droplets is caused by a gradient in the surface stiffness. As reference, stationary coalescence of the same droplets is also studied on the corresponding uniform surfaces for different stiffness values. To describe the coalescence phenomenon on a surface with stiffness gradient, a relevant range of velocity ratios of the leading and the trailing droplet was considered to elucidate the effect of this parameter on coalescence. Moreover, to analyze the dynamics of the process, the temporal growth of the bridge height $(h)$ was investigated, which follows a power law $(h \sim t^{\alpha})$, before eventually attaining a constant value. The obtained values of $\alpha$ show a transition from a higher to a lower value as a function of time, pointing to the presence of two distinct power-law growth regimes, where the transition signifies the crossover from the capillarity-dominated regime to the viscoelasticty-dominated regime of coalescence. In addition, varying attractive strengths for droplet--droplet and intra-droplet interactions were considered. The results indicate that both the dynamics and the degree of the coalescence strongly depend on these interaction parameters. Thus, we anticipate that our results will shed more light on the durotaxis-driven coalescence of polymeric droplets for various relevant system parameters, which will have practical implications for applications ranging from microfluidics to ink-jet printing, where substrate properties may vary. In addition, results may add to the fundamental understanding of the interactions among multicellular aggregates moving on biological surfaces.