Elastic Instabilities in Microchannels
"Elastic Instabilities of Polymer Solutions in Cross-Channel Flow" P.E. Arratia, C.C. Thomas, J. Diorio, and J. P. Gollub (under review, PRL). For a pre-print, please click here (Adobe PDF).
Abstract: When polymer molecules pass near the hyperbolic point of a microchannel cross flow, they are strongly stretched. As the strain rate is varied at low Reynolds number (<0.01), tracer and particle-tracking experiments show that molecular stretching produces two flow instabilities, one in which the velocity field becomes strongly asymmetric, and a second in which it fluctuates non-periodically in time. The flow is strongly perturbed even far from the region of instability, and this phenomenon can be used to produce mixing.
To illustrate one of the instabilities, we show the results of dye advection experiments in the cross-slot region, where the flow is strongly extensional. In the Newtonian case (Fig. 1a), the snapshot reveals a sharp interface at the center of the cross-slot region between the dye and undyed fluids.
Figure 1(b) reveals an entirely different behavior if we replace the Newtonian fluid by the dilute PAA solution. The snapshot at Deborah number (De)=1.5 shows that the interface is deformed (wavy), although still sharp. The pattern is steady and does not change significantly over several minutes. The mirror image of this pattern can also occur, depending on initial conditions. That is, the flow is bistable.
Figure 1. Dye advection patterns for a cross channel flow with two inputs and two outputs at low Re (<0.01) for (a) Newtonian fluid, and (b) PAA flexible polymer solution (De=1.5), where the interface between dyed and undyed fluid is deformed by an instability. (c,d) Particle streaklines and velocity field magnitudes corresponding to (a,b). Channel is 650 mm wide and 500 mm deep.
Figure 1(c) shows both typical particle paths and the magnitude of the time-independent velocity field of the Newtonian fluid in the cross-slot region: a well-defined symmetric extensional flow. Note that the velocity vanishes at the stagnation point at the center of the cross-slot, where the strain rate is highest, and the fluid is most strongly stretched. The velocity field (Fig. 1d) shows a deformed and asymmetric flow for the PAA solution.
In the movie below, we show how a dilute solution (200 ppm) of Polyacrylamide fluctuates in time and space at a Deborah number (De)= 8.0 in an extensional flow.