In this work, we will be concerned with a kinetic model for diluted solutions of polymeric liquid and its viscoelastic fluid limit when the elastic character of the fluid is small. Differential relationships between stress and velocity are derived by the use of Chapman-Enskog expansions. These viscoelastic fluid models are derived in the case of unsteady, nonhomogeneous and nonpotential flows. Furthermore, the limiting model recovers both the linear (as Oldroyd-B models) and the nonlinear (as FENE models) elastic character of the fluid.

Joint work with P. Degond and and M. Picasso.

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