Dilatational viscosity of dilute particle-laden fluid interface at different contact angles

We consider a solid spherical particle adsorbed at a flat interface between two immiscible fluids and having arbitrary contact angle at the triple contact line. We derive analytically the flow field corresponding to dilatational surface flow in the case of large ratio of dynamic shear viscosities of two fluids. Considering a dilute assembly of such particles we calculate numerically the dependence upon the contact angle of the effective surface dilatational viscosity particle-laden fluid interface. The effective surface dilatational viscosity is proportional to the size and surface concentration of particles and monotonically increases with the increase in protrusion of particles into the fluid with larger shear viscosity.