In light of recent advancements in the constitutive modeling of bidisperse and polydisperse entangled linear polymers, we present a new "multifluid" generalization of the classic two-fluid approximation for flows of inhomogeneous polymer blends. As an application of the model, we consider predictions for the linear and nonlinear dynamics of shear induced demixing (SID) instabilities in blends with bidisperse and log-normal molecular weight distributions. We find that even in the absence of any chemical contrast between component chains, an imposed flow can induce a demixing instability provided there is sufficient contrast in the size of the two chains. The lower bound polydispersity for SID coincides with the point where elastic forces (k(B)T per entanglement) scaled by the contrast between chains (e.g., polydispersity index minus one) exceed the entropic forces for mixing (k(B)T per chain). For bidisperse blends, we show that the nonlinear dynamics of SID strongly resemble what has previously been shown for SID in entangled polymer solutions. (C) 2020 The Society of Rheology.