The influence of electrostatic forces on the deposition of particles from a volatile carrier liquid

Electrostatic forces are known to influence the pattern deposition of colloidal particles on a solid substrate. Several experimental studies suggest a direct connection between the morphology of the deposits and the electrical potential on the particles in the carrier liquid and on the substrate. The path by which electrostatic forces may influence the deposition was attributed to the adsorption of particles to the substrate and the coagulation of particles in the liquid. Here, we use theory to test this assertion. We employ the interaction--force boundary layer theorem and the Smoluchowski theorem to determine the rate of adsorption and coagulation, respectively, from the free energy in the system. The expressions for coagulation and adsorption are added to a dynamic advection-diffusion equation, which governs the transport of particles in the liquid. We thus present a continuum formulation for the influence of electrostatic forces on the adsorption and coagulation of particles in a volatile liquid drop. It appears that one should expect to find larger aggregates of particles near the edge of the drop when coagulation takes place. In addition, fast particle adhesion to the solid substrate will smear the morphology of the deposits. Sufficiently fast adhesion will lead to the formation of dome or disk shaped deposits.