Effective surface dilatational viscosity of highly concentrated particle-laden interfaces

The effective surface dilatational viscosity is calculated of a flat interface separating two immiscible fluids laden with half-immersed monodisperse rigid spherical non-Brownian particles in the limit of high particle concentration. The derivation is based upon the facts that (i) highly-concentrated particle arrays in a plane form hexagonal structure, and (ii) the dominant contribution to the viscous dissipation rate arises in the thin gaps between neighboring particles.