Molecular Continua for Polymeric Liquids in Large-Amplitude Oscillatory Shear Flow
Giacomin, A. Jeffrey
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In this paper, we connect a molecular description of the rheology of a polymeric liquid to a continuum description, and then test this connection for large-amplitude oscillatory shear flow (LAOS). Specifically, for the continuum description we use the 6-constant Oldroyd framework, and for the molecular, we use the simplest relevant molecular model, the suspension of rigid dumbbells. By relevant, we mean predicting at least higher harmonics in the shear stress response in LAOS. We call this connection a molecular continuum, and we examine two ways of arriving at this connection. The first goes through the retarded motion expansion, and the second, expands each of a set of specific material functions (complex, steady shear, and steady uniaxial extensional viscosities). Both ways involve comparing the coefficients of expansions to then solve for the six constants of the continuum framework in terms of the two constants of the rigid dumbbell suspension. The purpose of a molecular continuum is that many well-known results for rigid dumbbell suspensions in other flow fields can then also be easily obtained, without having to first find the orientation distribution function. In this paper, we focus on the recent result for the rigid dumbbell suspension in LAOS. We compare the accuracies of the retarded motion molecular continuum (RMMC) with the material function molecular continuum (MFMC). We find the RMMC to be the most accurate for LAOS.