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Streamwise-travelling viscous waves in channel flows.

Pierre Ricco1, Peter D Hicks2

  • 11Department of Mechanical Engineering, University of Sheffield, Sheffield, S1 3JD UK.

Journal of Engineering Mathematics
|April 19, 2019
PubMed
Summary

Investigating unsteady viscous flow in channels, this study finds analytical solutions for wall-induced waves. These findings aid microfluidic manipulation and friction reduction in turbulent flows.

Keywords:
BiosensorsElectro-osmosisElectro-osmotic wavesLove wavesMicrofluidicsMixingShear-horizontal surface acoustic wavesTurbulent drag reduction

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Area of Science:

  • Fluid dynamics
  • Non-Newtonian fluid mechanics
  • Microfluidics

Background:

  • Streamwise-travelling waves of spanwise wall velocity have practical applications.
  • These include microfluidic flow manipulation and turbulent friction reduction.

Purpose of the Study:

  • To investigate unsteady viscous flow induced by streamwise-travelling wall velocity waves.
  • To develop analytical and numerical solutions for this flow regime.
  • To explore the physical balances and near-wall flow characteristics.

Main Methods:

  • Analytical solutions using classical Poiseuille flow and parabolic cylinder functions.
  • Boundary-layer theory to analyze near-wall flow.
  • Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) theory for channel-wide solutions.
  • WKBJ composite expansion and Langer method for turning-point analysis.
  • Matched asymptotic expansion for electro-osmosis.

Main Results:

  • An analytical solution dependent on Reynolds number, wavelength, and wave speed was found.
  • Boundary-layer theory quantified near-wall flow thickness.
  • WKBJ analysis revealed turning-point behavior and distinct flow regimes.
  • Langer method provided a simpler, accurate solution for the turning-point region.

Conclusions:

  • The study provides a comprehensive analysis of unsteady viscous flow induced by wall waves.
  • The findings offer insights into microfluidic applications like flow mixing and friction reduction.
  • The developed methods are applicable to various flow manipulation techniques.