Pressure-driven fully developed flow of a viscoelastic fluid in narrow channels: the role of different microscopic features in an elastic dumbbell model

Abstract Viscoelastic fluid flows are widely described by elastic dumbbell models such as Oldroyd-B and FENE-P. However, these constitutive equations can yield significantly different predictions, which may contradict experimental observations. In this work, we analyze the fully developed flow of a viscoelastic fluid in a straight channel and present a theory based on the lubrication approximation for calculating the elastic stresses and flow rate for four elastic dumbbell models, including various microstructurally inspired terms. We compare the predictions of different models and elucidate the impact of (i) the finite extensibility, (ii) conformation-dependent friction coefficient, and (iii) conformation-dependent non-affine deformation on the polymer stresses, velocity, and flow rate. We demonstrate that including all three microstructurally inspired terms in a constitutive equation can significantly affect the response of a viscoelastic fluid even in a fully developed flow, thus highlighting their potential necessity for accurate modeling of viscoelastic channel flows with mixed kinematics.