Statistical‐Mechanical Theory on the Probability Distribution Function for the Net Charge of an Electrolyte Droplet

Droplets of electrolyte solutions in an insulating medium are ubiquitous in nature. The net charges of these droplets are normally nonzero, and they fluctuate. However, a theory on the probability distribution function for the net charge of droplets is lacking, so far. Thus, a statistical‐mechanical theory of a charged droplet is developed including the effect of the electrostatic energy of charging as well as the random distribution of ions. Then, the probability distribution function for the net charge of an electrolyte droplet is calculated assuming that it is generated from a macroscopic solution with the different cation and anion concentrations. Using the Gaussian approximation and Stirling's formula, the analytic results for the average and variance of the net charge of a droplet are obtained.