Birefringence in strong flows of polymer solutions

The constitutive relation for the refractive index of dilute solutions of f lexible polymer molecules is obtained, and calculations of the intrinsic bi refringence exhibited in uniaxial elongational flow are presented. The poly mer molecules are modeled as chains of beads connected by finitely extensib le nonlinear elastic springs under the Peterlin approximation. It is found that at very low elongation rates there is very little birefringence, but t here is a critical elongation rate above which there is substantial birefri ngence. This critical elongation rate scales as the inverse square of the n umber of beads in the chain. At this elongation rate the individual springs in the chains are stretched and oriented with the flow, but the chains hav e not uncoiled. It is found that the stress-optic relation holds for elonga tion rates below the critical elongation rate. However, the stress-optic co efficient is not constant above the critical rate. In the instantaneous inc eption of the flow above the critical elongation rate, the stress optic coe fficient initially takes on the value that it would have below the critical elongation rate, but it decays to a much lower value as the strain increas es. (C) 1999 Elsevier Science Ltd. All rights reserved.