Spatially inhomogeneous shear flow occurs in entangled polymer solutions, both as steady state shear banding and transiently after a large step strain or during startup to a steady uniform shear rate. Theoretically, steady state shear banding is a hallmark of models with a nonmonotonic constitutive relation between total shear stress and applied shear rate, but transient banding is sometimes seen in fluids that do not shear band at steady state. We model this behavior using the diffusive Rolie-Poly model in a Newtonian solvent, whose steady state constitutive behavior can be monotonic or nonmonotonic depending on the degree of convective constraint release. We study monotonic steady state constitutive behavior. Linear stability analysis of the startup to a sufficiently high shear rate shows that spatial fluctuations are unstable at early times. There is a strong correlation between this instability and the negative slope of the (time dependent) constitutive curve. If the time integral of the most unstable eigenvalue is sufficiently large, then the system exhibits transient shear bands that later vanish in steady state. We show how perturbations, due to fluctuations or the inhomogeneous stresses, can trigger this instability. This transient behavior is similar to recent observations in entangled polymer solutions.
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