2002 -02 -13
10 :15 at ML J 21

A hierarchical model for surface effects on chain conformation and rheology of polymer solutions

Vlasis Mavrantzas

Institute of Polymers, ETH Zurich

The flow behavior of polymer solutions near a solid surface is modeled through a hierarchical (macroscopic microscopic) approach which enables the thermodynamically consistent extension of static (equilibrium) considerations to flow (non-equilibrium) conditions. The approach involves two steps:
First, the vector of primary variables is chosen and a complete set of transport and constitutivee quations is constructed through a two-fluid Hamiltonian model. The governing equations involve the extended (free energy) or hamiltonian of the system, are valid both in the bulk and in the intefacial area and are written in terms of the polymer chain number density, the macroscopic fluid velocity and the conformation tensor.
To solve the equations, one needs to specify H. This is done in a second step by invoking a micsroscopic model. Solid boundary effects are taken into account through the solution of a diffusion equation for the chain propagator that determines chain conformations near the wall. Flow field effects are taken into account by further allowing the propagator to depend on an apparent strain tensor, representing chain deformation due to flow.
Results will be presented for a polymer solution flowing past a non- interacting surface (a wall). The equations are solved numerically with a spectral collocation technique and reveal the existence of a boundary layer near the wall, of a length scale on the order of the equilibrium chain radius of gyration, where:
a) the solution is depleted in polymer molecules,
b) the fluid velocity increases rapidly from its zero value exactly on the wall to its asymptotic bulk profile, giving rise to an apparent slip phenoemenon, and
c) polymer conformations are significantly altered relative to the boundary-free case.
Shear stress is found to enhance depletion phenomena, while the slip velocity is found to depend linearly on the applied shear stress.