Flow Resistance and Structures in Viscoelastic Channel Flows at Low Re

The flow of viscoelastic fluids in channels and pipes remains poorly understood, particularly at low Reynolds numbers. Here, we investigate the flow of polymeric solutions in straight channels using pressure measurements and particle tracking. The flow friction factor $f_{\eta }$ versus flow rate exhibits two regimes: a transitional regime marked by rapid increase in drag, and a turbulentlike regime characterized by a sudden decrease in drag and a weak dependence on flow rate. Lagrangian trajectories show finite transverse modulations not seen in Newtonian fluids. These curvature perturbations far downstream can generate sufficient hoop stresses to sustain the flow instabilities in the parallel shear flow.

Figure 1

(a) Schematic of the microchannel, showing location of pressure sensors and the dye injection scheme. [(b) and (c)] Spacetime dye patterns for $n=15$ and $x=200\mathrm{W}$ in the parallel shear region, (c) viscoelastic fluid at $\mathrm{Wi}=20$, and (b) the Newtonian case at identical flow rate.

Figure 2

Pressure drop per unit length as a function of flow rate $Q$ and Wi for $n=15$ and $n=0$ cases. The solid line represents estimation using wall shear rates and viscosity from rheology measurements. Error bars are less than marker size and not shown here.

Figure 3

(a) Pressure gradient signal $p_1^{\prime }(t)$ for the $n=15$ case, compared with the unperturbed $n=0$ case, $\mathrm{Wi}=18$. [(b) and (c)] Root-mean-square (rms) fluctuations versus Wi for $n=0$ and 15, (b) $p_1^{\prime }$, and (c) $p_2^{\prime }$. The dashed line is the average level for Newtonian fluid, experimentally found to be constant for increasing $Q$.

Figure 4

Viscous friction factor $f_{\eta }$ as a function of Wi for $n=0$ and 15 with four cases and types of polymeric fluids. Case I: 300 ppm PAA 90% glycerol, 0–50 W, II: 50–290 W, III: 250 ppm PAA 90% glycerol, 0–290 W, IV: 100 ppm PAA 93% glycerol, 0–290 W.

Figure 5

(a) Particle trajectories in the streamwise ($x$) and spanwise ($y$) direction; blue lines represent the $n=15$ viscoelastic case at $\mathrm{Wi}=18$ and the gray line is Newtonian at identical conditions. (b) Collection of trajectories colored by speed. Distributions of (c) cumulative transverse to streamwise displacements and (d) trajectory curvatures, where the dashed line represents population mean.