Experimental investigation of viscoelastic effects in wavy-microchannel flow

We examine Newtonian and viscoelastic flows through slit microchannels depth d with a sinusoidal wall profile amplitude A<< d, wavelength λ and a range of dimensionless depths 0.6< α = 2πd/λ <10. Dilute solutions of high molecular weight polymer in solvents of various viscosity provide fluids with elasticity numbers 0.001<El <44. Flow velocimetry is performed in the channels over a range of flow rates. For all fluids, the wavy wall causes small perturbations (~3 %) to the Poiseuille base flow. A subtle interplay between El, α, and the imposed flow rate affects the form of the perturbation and its depth of penetration P into the channel. Our experiments support recent theoretical predictions of a ‘critical layer’ in the channel located at a dimensionless depth Σ~El^0.5. Our results are consistent with the existence of a phase diagram in α-Σ parameter space showing three regimes classified as “shallow-elastic”, “deep-elastic” and “transcritical”. In the transcritical regime (defined by α > Σ, Σ < 1), the critical layer drives a surprising nonlocal amplification of the perturbation, significantly influencing P.