The onset of particle segregation in plane Couette flows of concentrated suspensions

We analyze particle segregation in suspensions of rigid particles immersed in Newtonian liquids flowing in plane Couette devices by considering the stability of the system to two-dimensional perturbations in the plane of shear. We obtain the dispersion relation analytically for small wave numbers, finding that when the velocity of the walls is kept constant, the system is always stable and the particle concentration remains uniform. On the other hand, when we keep constant the shear applied at one wall, we predict that a disorder–order transition will occur, provided that σ>1, where σ is the non-dimensional parameter, σ=(μ0′Ê0)/(μ0D̂0). Here μ0 and μ0′ are the effective viscosities of the suspension, μ, and its derivative, dμ/dφ, evaluated at the mean particle volume fraction φ0, while D̂0 and Ê0 are two transport coefficients appearing in the constitutive relation for the material flux. Substituting experimental correlations for D̂0 and Ê0 into this condition, we conclude that for no values of φ0 will particles cluster along the plane of shear.