Structure of Marangoni-driven Singularities

This work presents an analytical study of the structure of steady Marangoni-driven singularities in the context of chemical-reaction driven tip-streaming, which identifies the conditions when such singularities are observable. As motivated by experimental observations of the conical symmetry of the problem, one can construct self-similar solutions of the Stokes equations, which are singular at the tip; these solutions, however, provide no information on the thread structure which is responsible for a resolution of the singularity via tip-streaming. The cone-tip singularity is resolved here with the help of asymptotic matching of the cone and thread solutions using slender jet approximation, which gives an explicit asymptotic formula for the thread radius and thus of the emitted droplets size as a function of physical parameters governing the problem. (c) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.3685831]