Diffusiophoresis of a Charged Droplet in Asymmetric as Well as Mixed Electrolytes through Numerical and Semianalytic Models

Abstract

A numerical study on the diffusiophoresis of a droplet in an electrolyte medium is carried out by solving the full set of coupled governing equations, which are based on the conservation principle. Diffusiophoresis is considered for monovalent as well as non-z:z electrolytes and mixed electrolytes. The numerical model is supplemented with a semianalytic simplified model based on first-order perturbation analysis, which agrees with the numerical model for a low to moderate range of surface potential. The mobility for a low-viscosity fluid at a thinner Debye length is dominated by the chemiphoresis part, which creates the mobility to become an even function of the surface charge density for a monovalent electrolyte. Such a pattern in mobility does not appear in a non-z:z asymmetric electrolyte. At a thinner Debye length, diffusiophoresis becomes independent of the diffusion field, hence the mobility is independent of the composition of electrolytes in a mixed monovalent electrolyte solution. Our results show that the size-based sorting of droplets is efficient when a mixed electrolyte is considered. We have also addressed the finite ion size effects by considering a modified ion transport equation. One of the key features of the present study is the simplified semianalytical model for the diffusiophoresis of a droplet in a z:z electrolyte as well as in non-z:z and mixed electrolytes, which is shown to be valid up to a moderate range of surface potential for a finite Debye length.