A simplified model for the impact of dielectric polarization of a charged droplet on its diffusiophoresis

This study aims to quantify the impact of the dielectric permittivity of a droplet on its diffusiophoresis in different types of electrolytes. The dielectric droplet polarizes by the diffusion field along with the local electric field created by the interactions of the double layer with the imposed ionic concentration gradient, which generates an induced surface charge density anti-symmetrically distributed on the droplet surface. This induced surface charge influences both electrophoresis and chemiphoresis parts. Based on a low imposed concentration gradient, a simplified model is derived through a first-order perturbation technique. Dielectric polarization of the droplet attenuates the spinning force at the interface. This creates the mobility of a droplet of higher dielectric permittivity in the presence of a stronger diffusion field significantly higher than that of a perfectly dielectric droplet, and its value depends on the polarity of the droplet surface charge. In the absence of the diffusion field, the mobility of a conducting droplet remains a positive immaterial of the polarity of its surface charge density. We find that the impact of the dielectric polarization becomes significant as the surface charge density increases and attenuates with the increase in droplet viscosity. For a dielectric droplet at a thinner Debye length, a step-jump in mobility occurs at a higher value of the surface charge density. Such a type of step-jump in mobility does not appear for the conducting droplet due to the absence of the Maxwell stress at the interface.