  In light of recent advancements in the constitutive modelling of bidisperse
and polydisperse entangled linear polymers, we present a new multi fluid
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 lognormal 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 (kT
per entanglement) scaled by the contrast between chains (e.g. polydispersity
index minus one) exceed the entropic forces for mixing (kT per chain). For
bi-disperse blends, we show that the non-linear dynamics of SID strongly
resemble what has previously been shown for SID in entangled polymer solutions.
