A combined experimental, numerical and theoretical investigation of the geometric scaling of the onset of a purely elastic flow instability in serpentine channels is presented. Good qualitative agreement is obtained between experiments, using dilute solutions of flexible polymers in microfluidic devices, and three-dimensional numerical simulations using the upper-convected Maxwell model. The results are confirmed by a simple theoretical analysis, based on the dimensionless criterion proposed by Pakdel & McKinley (Phys. Rev. Lett., vol. 77, 1996, pp. 2459–2462) for onset of a purely elastic flow instability. Three-dimensional simulations show that the instability is primarily driven by the curvature of the streamlines induced by the flow geometry and not due to the weak secondary flow in the azimuthal direction. In addition, the simulations also reveal that the instability is time-dependent and that the flow oscillates with a well-defined period and amplitude close to the onset of the supercritical instability.
We propose a novel device capable of measuring relaxation times of viscoelastic fluids as small as 1 ms. In contrast to most rheometers, which by their very nature are concerned with producing viscometric or nearly-viscometric flows, here we make use of an elastic instability that occurs in the flow of viscoelastic fluids with curved streamlines. To calibrate the rheometer we combine simple scaling arguments with relaxation times obtained from first normal-stress difference data measured in a classical shear rheometer. As an additional check we also compare these relaxation times to those obtained from Zimm theory and good agreement is observed. Once calibrated, we show how the serpentine rheometer can be used to access smaller polymer concentrations and lower solvent viscosities where classical measurements become difficult or impossible to use due to inertial and/or resolution limitations. In the absence of calibration, the serpentine channel can still be a very useful comparative or index device.
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