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Time-averaged transport in oscillatory squeeze flow of a viscoelastic fluid

Rui Yang1, Ivan C. Christov2, Ian M. Griffiths3, and Guy Z. Ramon1,*

  • 1Department of Civil and Environmental Engineering, Technion—Israel Institute of Technology, Haifa 32000, Israel
  • 2School of Mechanical Engineering, Purdue University, West Lafayette, Indiana 47907, USA
  • 3Mathematical Institute, University of Oxford, Radcliffe Observatory Quarter, Oxford OX2 6GG, United Kingdom

  • *ramong@technion.ac.il
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Phys. Rev. Fluids 5, 094501 – Published 15 September, 2020

DOI: https://doi.org/10.1103/PhysRevFluids.5.094501

Abstract

Periodically driven flows are known to generate nonzero, time-averaged fluxes of heat or solute species, due to the interactions of out-of-phase velocity and temperature/concentration fields, respectively. Herein, we investigate such transport (a form of the well-known Taylor-Aris dispersion) in the gap between two parallel plates, one of which oscillates vertically, generating a time-periodic squeeze flow of either a Newtonian or a Maxwell fluid. Using the method of multiple time-scale homogenization, the mass/heat balance equation describing transport in this flow is reduced to a one-dimensional advection-diffusion-reaction equation. This result indicates three effective mechanisms in the mass/heat transfer in the system: an effective diffusion that spreads mass/heat along the concentration/temperature gradient, an effective advective flux, and an effective reaction that releases or absorbs mass/heat—in the time-averaged frame. Our results demonstrate that there exist resonant modes under which the velocity peaks when the dimensionless plate oscillation frequency (embodied by the Womersley number, the ratio of the transient inertia to viscous forces) approaches specific values. As a result, transport in this flow is significantly influenced by the dimensionless frequency. On the one hand, the effective, time-averaged dispersion coefficient is always larger than the molecular diffusivity and is sharply enhanced near resonance. The interaction between the fluid elasticity and the oscillatory forcing enhances the efficiency of transport in the system. On the other hand, the identified effective advection and reaction mechanisms may transport mass/heat from regions of high concentration/temperature to those of low concentration/temperature, or vice versa, depending on the value of the dimensionless frequency. Ultimately, it is shown that the oscillatory squeeze flow can either enhance or diminish transport, depending on the interplay of these three effective (homogenized) mechanisms.

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Phys. Rev. Fluids 5, 094501– Published 15 September, 2020
  • Received 27 May 2020
  • Accepted 18 August 2020
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