Bead-spring models for an adsorbed polymer molecule in a shear flow

A bead-spring (Rouse-type) model is used to model an adsorbed fragment of a long-chain polymer attached to a surface in a steady shear flow. Analytic solution of the moment equations for the case of linear Hookean springs gives the mean configuration, wall traction, and power dissipation of the segment. A Monte Carlo method based on simulation of the stochastic differential equations of motion is used to deal with nonlinear finite-extension springs. The large increase in hydrodynamic thickness with shear rate found by some experimenters cannot be obtained with these models, although some increase can be obtained if there is an elongational component in the flow, due perhaps to surface nonuniformity or interference between segments.