Electrostatic suppression of the "coffee stain effect"

The dynamics of a slender, evaporating, particle-laden droplet under the effect of electric fields are examined. Lubrication theory is used to reduce the governing equations to a coupled system of evolution equations for the interfacial position and the local, depth-averaged particle concentration. The model incorporates the effects of capillarity, viscous stress, Marangoni stress, elecrostatically induced Maxwell stress, van der Waals forces, concentration-dependent rheology, and evaporation. Via a parametric numerical study, the one-dimensional model is shown to recover the expected inhomogeneous ring-like structures in appropriate parameter ranges due to a combination of enhanced evaporation close to the contact line, and resultant capillarity-induced flow. It is then demonstrated that this effect can be significantly suppressed via the use of carefully chosen electric fields. Finally, the three-dimensional behavior of the film and the particle concentration field is briefly examined.