Analytical and numerical study of equilibrium characteristics of a droplet with charged condensation nucleus in the external electric field

Abstract

The equilibrium parameters of small dielectric droplet with charged condensation nucleus in the external uniform electric field are studied. Two typical cases are considered: (i) the droplet with charged nucleus suspended by external uniform electric field in the gravitational field and (ii) the droplet moves steadily under the action of external electric field with allowance for the resistance of surrounding vapor-gas medium. It is taken into account that the charged condensation nucleus can be displaced from the mass center of the droplet to new equilibrium position inside the droplet under the action of external electric field and response field. The scheme of the numerical solution of a nonlinear system of differential equations for the droplet equilibrium pro- file and electric potentials inside the droplet and in the vapor-gas medium at the arbitrary values of droplet size, strength of external field, and the charge of condensation nucleus is formulated and realized. Dependences of an equilibrium profile and the thermodynamic characteristics of a droplet such as the chemical potential of con- densate and formation work on the droplet size, mass, and charge of condensation nucleus, the strength of exter- nal field and ratio of permittivities of droplet and the vapor-gas medium are plotted. Results of numerical cal- culations are supplemented by the analytical relations for equilibrium droplet characteristics in the first orders of the perturbation theory for a weak external field.