Effective Viscosity of a Near-Critical Binary Fluid Mixture with Colloidal Particles Dispersed Dilutely under Weak Shear

We consider a spherical liquid droplet immersed in a near-critical binary fluid mixture whose components interact with the droplet slightly unequally. Assuming uniform viscosity of the mixture, we use the Gaussian free-energy functional to calculate the pressure and velocity fields occurring when a weak linear shear flow is imposed far from the droplet. These fields in the limit of infinite droplet viscosity give those for a rigid sphere. Using these fi elds, we calculate the effective viscosity emerging when identical droplets or rigid spheres are dilutely dispersed in the mixture.