(483d) The Measurement of Solute Mixing Rates in the Flow of Concentrated Suspensions through Straight Conduits

The transport of solutes in sheared non-Brownian, particulate suspensions is a problem of great interest in industrial operations such drilling and hydraulic fracturing for oil and gas production. But, while there are several studies in the literature of the particle distribution in the pressure-driven flow of suspensions, there are relatively few experimental studies of the mechanisms and rates by which solutes are transported in such flows. In this work, we characterize the mass transfer properties of the simplest suspension - spherical, rigid particles dispersed in a Newtonian suspending medium at moderate volume fractions (30% to 50%) sheared at high Brownian Peclet numbers, flowing through a straight channel with a rectangular cross-section.

In the absence of flow, the mixing of a passive solute in the presence of a concentration gradient can be attributed only to molecular diffusion. On imposing shear, flow-induced inter-particle collisions lead to particulate self-diffusion, which in turn, leads to solute shear-induced self diffusion and can enhance the mixing rate. A third mass transfer mechanism is the secondary convection accompanying the flow of a concentrated suspension through a non-axisymmetric geometry, arising from the second-normal stress differences exhibited by suspensions. To elucidate these mechanisms, we carried out experiments in a silicon-glass microchannel designed in the shape of a Y-Junction, and mounted on a laser scanning confocal microscope. A suspension containing a fluorescently-labeled dye in the medium was introduced through one branch of the Y-junction, while an identical suspension without the dye was introduced through the other. The mixing of the dye as the two suspensions flowed through the straight, downstream channel was monitored using confocal microscopy.

For the case of suspension streams flowing at equal flow rates into the Y-junction, the cross-sectional mixing followed a pattern governed by secondary convection, and ultimately distributed by molecular diffusion in the region of maximum packing. However, the rate of mixing of the solute was significantly faster than predictions based on the suspension balance model. For a flow rate ratio of 2:1, the solute was initially present only in, approximately, the left one-third segment of the cross-section. Here, the mixing was, once again, much faster than the numerical predictions, but we observed another interesting result - the solute travelled in a direction opposite to the predictions of secondary current profile! Perhaps the most interesting observation was that the miscible interface between the dyed and undyed suspension streams undulated in the flow direction. The reasons for the faster mixing, the counterintuitive circulation pattern exhibited by the solute, and the apparent instability of the miscible interface will be elucidated in the presentation.