Viscous coalescence of unequally sized spherical and cylindrical doublets
A coalescence model is developed for pairs of unequally sized particles, assuming surface tension driven flow opposed by viscosity. The flow field is extensional, biaxial for spheres and planar for cylinders. The balance of surface energy and viscous dissipation results in a system of two ordinary differential equations for each of the two doublet shapes studied. The solution of the differential equations provides growth of neck radius (or width) as well as surface and cross-sectional area evolution. For an infinitely large size ratio, the model describes the coalescence of a sphere or a cylinder with a semi-infinite wall of the same material. The model is compared to some numerical simulations and experimental measurements available in the literature. The comparison to experiments includes PDMS spheres, macromolecule-rich droplets, spherical bitumen particles, and a smectic circular island with a meniscus.