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Two-layer channel flow involving a fluid with time-dependent viscosity

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Abstract

A pressure-driven two-layer channel flow of a Newtonian fluid with constant viscosity (top layer) and a fluid with a time-dependent viscosity (bottom layer) is numerically investigated. The bottom layer goes through an ageing process in which its viscosity increases due to the formation of internal structure, which is represented by a Coussot-type relationship. The resultant flow dynamics is the consequence of the competition between structuration and de-structuration, as characterised by the dimensionless timescale for structuration \((\tau )\) and the dimensionless material property \((\beta )\) of the bottom fluid. The development of Kelvin-Helmholtz type instabilities (roll-up structures) observed in the Newtonian constant viscosity case was found to be suppressed as the viscosity of the bottom layer increased over time. It is found that, for the set of parameters considered in the present study, the bottom layer almost behaves like a Newtonian fluid with constant viscosity for \(\tau >10\) and \(\beta >1\). It is also shown that decreasing the value of the Froude number stabilises the interfacial instabilities. The wavelength of the interfacial wave increases as the capillary number increases.

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Acknowledgements

I am grateful to Prof. Subhasish Dey (Guest Editor, Special Issue of Environmental Fluid Mechanics: Hydrodynamic and Fluvial Instabilities) for inviting me to contribute an article to this special issue. I also thank Mounika Balla for her help to plot some figures. The financial support from Science and Engineering Research Board, India through grant no. MTR/2017/000029 is gratefully acknowledged.

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  1. Department of Chemical Engineering, Indian Institute of Technology Hyderabad, Sangareddy, Telangana, 502 285, India

    Kirti Chandra Sahu

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  1. Kirti Chandra Sahu
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Correspondence to Kirti Chandra Sahu.

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Sahu, K.C. Two-layer channel flow involving a fluid with time-dependent viscosity. Environ Fluid Mech 22, 263–274 (2022). https://doi.org/10.1007/s10652-021-09803-8

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