Coalescence of sessile droplets on hydrophobic surfaces under magnetic fields

Digital microfluidics deals with the behavior of sessile droplets on an open surface and is advantageous over emulsion microfluidics due to the absence of confinement, which in turn enables droplets to act as independent virtual reactors that are often utilized in point-of-care diagnostics applications. Here, we employ a phase field method-based solver to investigate the dynamic behavior between a pair of sessile droplets on hydrophobic surfaces under the presence of a permanent magnetic field. The results suggest that a non-uniform magnetic field is capable of forcing a pair of droplets towards each other, which eventually leads to a jumping off phenomenon of the merged droplet after coalescence on a superhydrophobic surface (i.e., θ_c = 150°). Also, interestingly, there exists a critical magnetic Bond number Bo_cr, beyond which the droplets do not experience any coalescence phenomenon. Moreover, the merging event between droplets appears different on less superhydrophobic surfaces (θ_c ≤ 120°). Additionally, the viscosity of droplets plays a critical role in determining the upward flight of droplets, where the merged droplet experiences increased vertical migration at higher viscosity ratios.