Theoretical study of wall effects on the rheology of dilute polymer solutions

The recently developed generalized bracket formulation of transport phenomena (a Helmholtz free energy‐based approach) is used to predict the rheological behavior of high molecular weight, dilute polymer solutions near planar, smooth, noninteracting solid surfaces. A boundary‐value problem (passage to a stochastic differential equation) is set up in order to estimate the entropy reduction caused by the presence of the solid barrier. Under flow, in addition to diffusional effects, such an entropy reduction results in different conformations of the macromolecules next to the wall, which in turn causes a different than the bulk rheological behavior. The resulting continuum equations account for wall effects under arbitrary flow conditions provided the confining flow boundary is smooth. For the steady‐state simple shear flow, two limiting cases, corresponding to a uniform and a nonuniform (fully developed) concentration profile, have been examined. In both cases, calculated apparent slip velocities are found to depend almost linearly on the wall shear stress, corresponding, however, to different proportionality (slip) coefficients. Moreover, both the chain conformation and the first normal stress are found to change appreciably near the wall in a fashion moderately dependent on the applied shear stress. Assuming fully developed concentration profiles, the corresponding depletion layer is found to decrease with increasing shear stress in agreement with the molecular simulation results of Duering and Rabin.