A hierarchical model for surface effects on chain conformation and rheology of polymer solutions. II. Application to a neutral surface

In this part, the general formulation described in Part I is applied to the modeling of the behavior of a dilute polymer solution near a purely repuls ive, planar solid surface, i.e., near a noninteracting wall. The static equ ilibrium problem is considered first. The model equations here reduce to a minimization problem for the Helmholtz free energy of the system, which res ults into the well known equilibrium condition that the chemical potentials of all chain conformations in the interfacial area should be equal to each other. The numerical results show that the loss of polymer conformational entropy in the interfacial region gives rise to a strong polymer depletion which extends up to a distance about three times the equilibrium root-mean- square polymer end-to-end distance. Next, the problem of a polymer solution flowing past the wall is investigated. Here, the full model equations need to be considered; these are solved numerically with a spectral collocation technique. The numerical results show that the flow field enhances polymer depletion phenomena near the wall relative to those observed under equilib rium (static) conditions: By increasing the shear stress, the polymer conce ntration in the interfacial area decreases, in full agreement with availabl e experimental data. Moreover, the flow field is found to affect significan tly the chain conformations near the wall: The applied shear stress is seen to extend the chains along a primary direction, xi, and to depress them in the transverse direction, eta. The depletion of the interfacial region in polymer molecules is further seen to lead to the formation of a boundary la yer close to the wall, where the macroscopic fluid velocity increases rapid ly from its zero value exactly at the wall to its asymptotic bulk profile, resulting into an apparent macroscopic slip at the wall. The theoretically calculated slip coefficient is found to be of the same order of magnitude w ith the experimentally measured one, as reported in the literature for a di lute polymer solution of polymethylacrylate flowing near a glass surface [H . Mueller-Moehnssen Et al., J. Rheol. 34, 223 (1990)]. (C) 1999 American In stitute of Physics. [S0021-9606(99)50801-5].