Detachment work of prolate spheroidal particles from fluid droplets: role of viscous dissipation

Abstract

The force–displacement curve for removal of an elongated solid particle from the surface of liquid droplets or gas bubbles is calculated and compared to our previous reported results for spherical particles. The surface adsorption energy for prolate particles is known to be larger than that for spheres. We show that in fact the minimum possible work done upon removal of an elongated particle from surface can be less than that for a sphere. This result is obtained when the dissipation of interfacial energy, stored in the fluid film, attaching the particles to the surface during their displacement, is properly accounted for. This dissipation is unavoidable, even if the particles are removed infinitely slowly. Once the particle actually leaves the surface, the formed liquid bridge relaxes thus dissipating any stored interfacial energy as the surface returns to its original undistorted state. The difference between the work of removal of a particle from surface and its adsorption energy is seen to become increasingly larger with smaller particle to droplet size ratios. For example, for a size ratio of 1 : 100, the work of removal is 1.93 times greater than the adsorption energy. However, we also find that for any given size ratio, there is a value of particle aspect ratio for which the work of removal of particles (combined dissipated and adsorbed energy) attains its minimum value.