Polymer dynamics in linear mixed flow

Recent simulations by Chu [Phys. Rev. E 66, 011915 (2002)] on the behavior of bead-spring and bead-rod models of polymers in linear mixed flows (flows with unequal amounts of extension and rotation) are compared with the predictions of a finitely extensible Rouse model that was used earlier [J. Chem. Phys. 112, 8707 (2000)] to describe the behavior of long flexible molecules of lambda-phage DNA in simple shear. The model is a generalization of the continuum Rouse model in which the "spring constant" of the bonds connecting near neighbor segments is allowed to become nonlinearly flow-dependent through a term involving the initially unknown mean square size of the chain, <R-2>. A self-consistent equation for this quantity is derived by using the flow-modified Hamiltonian to calculate it from its statistical mechanical definition. After solving this equation numerically, the mean fractional extension of the chain x can be obtained as a function of the Weissenberg number Wi and a mixing parameter alpha. The results compare favorably with data from the simulations of Chu , and suggest the existence of a scaling variable Wi(eff)=rootalpha Wi in terms of which separate curves of x versus Wi fall more or less on a single universal curve. (C) 2003 American Institute of Physics.