Digital Microfluidics: Magnetic Transportation and Coalescence of Sessile Droplets on Hydrophobic Surfaces

Magnetic digital microfluidics is advantageous over other existing droplet manipulation methods, which exploits magnetic forces for actuation and offers the flexibility of implementation in resource-limited point-of-care applications. This article discusses the dynamic behavior of a pair of sessile droplets on a hydrophobic surface under the presence of a permanent magnetic field. A phase field method-based solver is employed in a two-dimensional computational domain to numerically capture the dynamic evolution of the droplet interfaces, which again simultaneously solves the magnetic and flow fields. On a superhydrophobic surface (i.e., θ_c = 150°), the nonuniform magnetic field forces the pair of sessile droplets to move toward each other, which eventually leads to a jumping off phenomenon of the merged droplet from the solid surface after coalescence. Also, there exists a critical magnetic Bond number Bo_m^cr, beyond which no coalescence event between droplets is observed. Moreover, on a less hydrophobic surface (θ_c ≤ 120°), the droplets still coalesce under a magnetic field, although the merged droplet does not experience any upward flight after coalescence. Also, the merging phenomenon at lower contact angle values (i.e., θ_c = 90°) appears significantly different than at higher contact angle values (i.e., θ_c = 120°). Additionally, if the pair of sessile droplets is dispersed to a different surrounding medium, the viscosity ratio plays a significant role in the upward flight of the merged droplet, where the coalesced droplet exhibits increased vertical migration at higher viscosity ratios.