Structure Factor in the Presence of Shear - an RPA Calculation

We consider the structure factor of a system of colloidal particles immersed in a host liquid. Each particle is assumed to be affected by forces due to other particles, a drag force proportional to the velocity of the particle relative to the local velocity of the fluid and a fluctuating random noise. The effect of the particles on the velocity field of the host liquid is neglected. The problem is treated within the RPA approximation which is a widely used tool in many body theory. The validity of the RPA result is discussed.