Transporting Particles with Vortex Rings

Due to their long-lived nature, vortex rings are highly promising for the non-contact transportation of colloidal microparticles. However, because of the high complexity of the structures, their description using rigorous, closed-form mathematical expressions is challenging, particularly in the presence of strongly inhomogeneous colloidal suspensions. In this work, we comprehensively study this phenomenon, placing special emphasis on a quantitative description of the ability of vortex rings to move the particles suspended in a liquid over distances significantly exceeding the ring's dimensions. Moreover, within the study, we present straightforward analytical approximations extracted by using the fitting of the experimental and numerical simulation observations that reveal the dynamics of vortex rings transporting the microparticles. It includes both the dependence of the concentration on the distance traveled by the vortex ring and coefficients describing the evolution of vortex ring shape in time, which were not presented in the literature before. It turns out that despite the fact that 2D modeling is a simplification of the full 3D problem solution and is unable to capture some of the minor effects of real behavior, it has demonstrated a good consistency with the results obtained via experiments regarding the process of particles transportation.