THE CONCENTRATION EQUATION OF POLYMER-SOLUTION IN NONHOMOGENEOUS FLOW-FIELD

We have derived formally exact equations for the concentration of poly mer in an externally imposed field using a time-dependent projection o perator formalism. Two different bases are chosen as projectors; the i nitial state basis (equilibrium) at t=0 and the final state basis (ste ady state) at t-->infinity. The initial state basis is natural for stu dying transient behavior at short time and the final state basis is go od for long time asymptotic behavior. Several methods have been sugges ted to obtain overall time dependences of the concentration, such as a n interpolation model for the approximate initial and final state form ulae. The general framework will be useful in studying the macroscopic characteristics of polymer solutions exposed to arbitrary flow fields in confined geometries using the molecular inputs. A simple illustrat ion of polymer migration caused by the flow geometry and hydrodynamic interactions is provided. Calculation of the steady state probability function of polymer chains is also given.