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We consider the solutions of Riemann problems for polymer flooding models. In a suitable Lagrangian coordinate the systems take a triangular form, where the equation for thermodynamics is decoupled from the hydrodynamics, leading to the study of scalar conservation laws with discontinuous flux functions. We prove three equivalent admissibility conditions for shocks for scalar conservation laws with discontinuous flux. Furthermore, we show that a variation of minimum path of  proposed in  is the vanishing viscosity limit of a partially viscous model with viscosity only in the hydro-dynamics.