The effects of bead inertia on the Rouse model

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Abstract
The Rouse model for dilute polymer solutions undergoing homogeneous flows has been generalized to include the inertia of the beads in the equations of motion. To obtain the correct ‘‘diffusion equation’’ for the probability density distribution function in phase space, we generalize the diffusion equation derived by Murphy and Aguirre [J. Chem. Phys. 57, 2098 (1972)] from Hamilton’s equations of motion for an arbitrary number of interacting Brownian particles at equilibrium. Material functions are found, and the noninertial case is seen to be obtained as the zero mass limit in all steps of the development. In particular, the steady-state shear results are unaffected by the inclusion of inertia. It is also shown how two assumptions, ‘‘equilibration in momentum space,’’ and the neglect of acceleration, made independently by Curtiss, Bird, and Hassager in their phase-space kinetic theory, are actually the result of assuming zero mass.