Electrical demulsification of oil-in-water emulsion

Application of a weak external electric field destroys stable oil-in-water emulsions by accelerating the coalescence of oil droplets. The acceleration is induced by the reduction of repulsive double layer force due to electric field-induced migration of ions adsorbed on the surface of oil droplets. The potential energy for the front surfaces of the approaching two droplets is given by U = ε l κ ζ 2   e − κ w 8 ( h + 1 ) [ 4 ( h + 1 ) + 3 h ( a 1 − a 2 ) E 0   cos   η / ζ ] 2 h + 1 + ( h − 1 )   e − κ w − [ 3 h ( a 1 + a 2 ) E 0   cos   η / ζ ] 2 h + 1 − ( h − 1 )   e − κ w − A H 12 π w 2 where h = zseζ(s+,0 + s−,0)/[kT(s+,0 − s−,0)], zs is the valence of surface ions, e the unit charge, s+,0 and s−,0 the number densities of positive and negative surface ions, kT the thermal energy at temperature T, ɛl the dielectric constant of water, κ the Debye reciprocal length, ζ the zeta potential, w the separation distance between the front surfaces of approaching two droplets with radii a1 and a2, E0 the intensity of the external electric field, η the angle between the axis of approach and the external field, and AH is the Hamaker constant of the droplets, respectively. The above equation indicates that two oil droplets are coalesced into one droplet by applying the external electric field of E 0 ≥ 2 [ z s e ζ ( s + , 0 + s − , 0 ) + k T ( s + , 0 − s − , 0 ) ] 3 z s e ( s + , 0 + s − , 0 ) a where a is the radius of the larger droplet.