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

The flow behavior of polymer solutions near a solid surface (either neutral or adsorbing) is modeled through a new, hierarchical (macroscopic and micr oscopic) 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, v ariables defining the state of the system at the macroscopic level is chose n, and a complete set of transport and constitutive equations is constructe d for them through a two fluid, Hamiltonian model. In the present work, the macroscopic variables include the polymer chain concentration, the macrosc opic 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, t o solve them one needs to specify H. This is done in a second step, by invo king a microscopic model, which consistently takes into account the simulta neous effect on chain conformations of both the solid boundary and the impo sed flow field. Solid boundary effects are taken into account in the soluti on of a diffusion equation for the chain propagator G(r, n; r(0)) which rep resents the weighted probability that an n-segment long chain which starts at r(0) will end at position r. Flow field effects are taken into account t hrough the definition of a generalized propagator G'(r, n; r(0), alpha), wh ich further depends on the apparent strain tensor alpha, representing chain deformation effects due to flow. The present part of the paper describes t he general formulation of the approach and its relevance with previous work s. Results from applying the methodology to the case of a polymer solution flowing past a purely repulsive surface (a wall) are presented in the secon d part of this work. (C) 1999 American Institute of Physics. [S0021-9606(99 )50701-0].