This content will become publicly available on November 10, 2023

Reduced modelling and global instability of finite-Reynolds-number flow in compliant rectangular channels
Experiments have shown that flow in compliant microchannels can become unstable at a much lower Reynolds number than the corresponding flow in a rigid conduit. Therefore, it has been suggested that the wall's elastic compliance can be exploited towards new modalities of microscale mixing. While previous studies mainly focused on the local instability induced by the fluid–structure interactions (FSIs) in the system, we derive a one-dimensional (1-D) model to study the FSI's effect on the global instability. The proposed 1-D FSI model is tailored to long, shallow rectangular microchannels with a deformable top wall, similar to the experiments. Going beyond the usual lubrication flows analysed in these geometries, we include finite fluid inertia and couple the reduced flow equations to a novel reduced 1-D wall deformation equation. Although a quantitative comparison with previous experiments is difficult, the behaviours of the proposed model show, qualitatively, agreement with the experimental observations, and capture several key effects. Specifically, we find the critical conditions under which the inflated base state of the 1-D FSI model is linearly unstable to infinitesimal perturbations. The critical Reynolds numbers predicted are in agreement with experimental observations. The unstable modes are highly oscillatory, with frequencies close to the natural more »
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NSF-PAR ID:
10376754
Journal Name:
Journal of Fluid Mechanics
Volume:
950
ISSN:
0022-1120
3. This experimental study explores the physical mechanisms by which a transverse jet’s upstream shear layer can transition from being a convective instability to an absolute/global instability as the jet-to-cross-flow momentum flux ratio $J$ is reduced. As first proposed in computational studies by Iyer & Mahesh ( J. Fluid Mech. , vol. 790, 2016, pp. 275–307), the upstream shear layer just beyond the jet injection may be analogous to a local counter-current shear layer, which is known for a planar geometry to become absolutely unstable at a large enough counter-current shear layer velocity ratio, $R_{1}$ . The present study explores this analogy for a range of transverse jet momentum flux ratios and jet-to-cross-flow density ratios $S$ , for jets containing differing species concentrations (nitrogen, helium and acetone vapour) at several different jet Reynolds numbers. These studies make use of experimental data extracted from stereo particle image velocimetry as well as simultaneous stereo particle image velocimetry and acetone planar laser-induced fluorescence imaging. They provide experimental evidence for the relevance of the counter-current shear layer analogy to upstream shear layer instability transition in a nozzle-generated transverse jet.