(41e) Non-Boltzmann Distribution Of Polymers And Suspensions In Dissipative Systems: Cross-Stream Migration Vs. Differential Relaxation

Polymers and Brownian rods have been predicted and observed to migrate {\sl across} streamlines in flowing systems, impacting rheological measurements, material processing, and microfluidic systems. In particular, gradients in cross-stream diffusivity evidently give rise to cross-stream migration, in direct contrast with expectations from equilibrium statistical mechanics. Here, we provide a simple, physicially intuitive understanding of the subtle physics that underlies this counter-intuitive effect, and identify the three minimal ingredients: i) a cross-stream diffusivity that depends upon internal degrees of freedom of the suspended species; ii) internal d.o.f. that are driven non-conservatively and inhomogeneously, and iii) a mechanism for relaxation to steady state. Significantly, we argue that some inhomogeneous steady-state distributions that have been observed do not result from directed cross-stream migration; rather, from anisotropies in rates of relaxation. In fact, we show that no such migration occurs in systems without relaxation. We propose and predict analogous behavior in a variety of new systems, including colloidal models, externally-orientable Brownian rods, and externally-triggerable two-state molecules. Finally, we demonstrate that thermal gradients give rise to weak concentration gradients that might otherwise be interpreted in terms of thermophoresis.