Polymer solution flow transitions and scaling laws for changing contraction ratios in planar constriction microchannels

Pores scale flows through contractions and expansions are relevant in geoengineering, microfluidics and material processing <i>etc.</i> These flows experience shearing and extensional kinematics near constrictions, where polymer solutions may demonstrate instabilities that arise from the fluid's nonlinear rheological characteristics even in creeping flows. The relative effect of shearing and extension can be controlled by the flow geometry. Following our earlier reports on the constriction length (M. K. Raihan <i>et al.</i>, <i>Soft Matter</i>, 2021, <b>17</b>, 9198-9209) and depth (M. K. Raihan <i>et al.</i>, <i>Soft Matter</i>, 2022, <b>18</b>, 7427-7440), we investigate here the flow responses to changing constriction width and in turn contraction ratio, CR, of the main channel width to the constriction width in planar constriction microchannels. We test water and three polymer solutions including shear thinning xanthan gum, viscoelastic polyethylene oxide (PEO), and shear thinning/viscoelastic polyacrylamide solutions. Overall, the contraction and expansion flows in all tested fluids demonstrate destabilization with increasing CR except for the PEO solution, where the threshold Reynolds number for the onset of contraction flow instability first increases and then decreases. Such nonmonotonic CR dependence is also observed from the vortex length in the contraction PEO flow. In contrast, the vortex length for every other case has a fixed-order (either zero or a positive number based on fluid rheology) dependence on CR. The insights obtained here will benefit the designing of lab-on-a-chip devices as well as the harnessing of pore-scale flows for enhanced mixing, material recovery and sequestration purposes.