Self-propelling, coalescing droplets

This work proposes and explores a new propulsion mechanism for sessile droplets which could be of interest for microfluidic applications. This mechanism relies on the Marangoni stresses resulting from the surface tension gradient arising when two droplets of different surface tensions coalesce. We argue that the tendency of the fluid to flow towards regions of higher surface tension is sufficient to displace the droplet. The coalescence of two miscible, partially wetting droplets with different surface tensions is investigated theoretically in this paper and modeled in the lubrication approximation framework. The problem is described by a set of three highly non-linear, coupled partial differential equations which is solved with a commercial finite element code. The analysis reveals two important dimensionless numbers which govern the flow characteristics, one related to the strength of the surface tension gradient and the other to the diffusion time scale. The numerical results confirm the occurrence of the self-propulsion behavior and a parametric study is performed to explore the role of the two dimensionless numbers on the propulsion speed and the total displacement. Unsurprisingly, self-propulsion is enhanced for larger values of the surface tension contrast between the two droplets and smaller values of the diffusion time scale which results in more time for the surface tension gradient to act. ∗ [email protected]; http://www.mech.canterbury.ac.nz/people/sellier.shtml † [email protected] ‡ [email protected]