  A model is developed for describing the transport of charged colloidal
particles in an evaporating sessile droplet on the electrified metal substrate
in the presence of a solvent flow. The model takes into account the electric
charge of colloidal particles and small ions produced by electrolytic
dissociation of the active groups on the colloidal particles and solvent
molecules. We employ a system of self-consistent Poisson and Nernst--Planck
equations for electric potential and average concentrations of colloidal
particles and ions with the appropriate boundary conditions. The fluid
dynamics, temperature distribution and evaporation process are described with
the Navier--Stokes equations, equations of heat conduction and vapor diffusion
in air, respectively. The developed model is used to carry out a
first-principles numerical simulation of charged silica colloidal particle
transport in an evaporating aqueous droplet. We find that electric double
layers can be destroyed by a sufficiently strong fluid flow.
