We present a systematic experimental investigation of the onset of instability in the flow of concentrated, shear-thinning, polyethylene oxide (PEO) solutions through rigid microtubes (diameters $\sim 500\mu \mathrm{m}$ and $2840\mu \mathrm{m}$). Micro-PIV measurements are performed for the flow of PEO solutions ($\sim 2000–6000\mathrm{ppm}$ in water) in the $500\mu \mathrm{m}$ tube to obtain the magnitude of normalized velocity fluctuations, which show a jump at Reynolds number ${\text{Re}}_s$ as low as $\sim 10$, indicative of an instability of the laminar flow, where ${\text{Re}}_s=\left(DV\rho \right)/{\eta }_s$ is the Reynolds number based on the viscosity ${\eta }_s$ evaluated at the maximum shear rate prevailing in the flow, $D$ is the tube diameter, $V$ is the cross-sectional average velocity, and $\rho$ is the fluid density. However, the ratio of peak to center-line velocity does not show any significant shift from the laminar value. Experiments are also carried out to obtain friction factor data for the flow of $2000–4000\mathrm{ppm}$ PEO solutions through a $2.84\mathrm{mm}$ glass tube. Here the transition is inferred from the deviation of the experimental data from the friction factor associated with the laminar flow obtained by fitting the shear-thinning rheology of the polymer solution using the Carreau model. The data for transition Reynolds number ${\text{Re}}_{s,t}$ inferred from micro-PIV and friction factor measurements, for polymer solutions of varying concentrations and for two different tube diameters, collapse reasonably well to yield a scaling law ${\text{Re}}_{s,t}\sim {\left[E_s(1-\beta )\right]}^{-3/4}$, where $E_s=4{\lambda }_s{\eta }_s/\rho D^2$ is the elasticity number based on the fluid relaxation time ${\lambda }_s$ estimated at the maximum shear rate of the flow, and $\beta$ is the ratio of solvent to (shear-rate dependent) total viscosity of the polymer solution. The scaling exponent of $-3/4$ inferred from the present experiments for concentrated polymer solutions is very different from the $-1/2$ exponent reported in previous studies for relatively dilute solutions concerning the onset of elastoinertial turbulence. This suggests that the instability observed in this study for concentrated polymer solutions is qualitatively different from the instability leading to elastoinertial turbulence in relatively dilute solutions. Our study further shows that even rectilinear laminar flows of concentrated polymer solutions become unstable at a relatively low ${\text{Re}}_s\sim 10$, provided the fluid is both sufficiently shear thinning and elastic.

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• Complex fluids
• Flow instability
• Microfluidics
• Non-Newtonian fluids