A hierarchical model for surface effects on chain conformation and rheology of polymer solutions. I. General formulation

Abstract

The flow behavior of polymer solutions near a solid surface (either neutral or adsorbing) is modeled through a new, hierarchical (macroscopic and microscopic) approach which enables the thermodynamically consistent extension of equilibrium (static) considerations to nonequilibrium (flow) conditions. The approach involves two steps: First, the set of primary, independent, variables defining the state of the system at the macroscopic level is chosen, and a complete set of transport and constitutive equations is constructed for them through a two fluid, Hamiltonian model. In the present work, the macroscopic variables include the polymer chain concentration, the macroscopic fluid velocity, and the conformation tensor (defined as the tensor of the second moment of the chain end-to-end vector). The governing equations involve the (extended) free energy or Hamiltonian of the system, H, and are valid both in the bulk of the fluid and in the interfacial region. Thus, to solve them one needs to specify H. This is done in a second step, by invoking a microscopic model, which consistently takes into account the simultaneous effect on chain conformations of both the solid boundary and the imposed flow field. Solid boundary effects are taken into account in the solution of a diffusion equation for the chain propagator G(r,n;r0) which represents the weighted probability that an n-segment long chain which starts at r0 will end at position r. Flow field effects are taken into account through the definition of a generalized propagator G′(r,n;r0,α), which further depends on the apparent strain tensor α, representing chain deformation effects due to flow. The present part of the paper describes the general formulation of the approach and its relevance with previous works. Results from applying the methodology to the case of a polymer solution flowing past a purely repulsive surface (a wall) are presented in the second part of this work.