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

Periodically-driven flows are known to generate non-zero, 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 th...

Full description

Bibliographic Details
Main Authors: Yang, R, Christov, IC, Griffiths, IM, Ramon, GZ
Format: Journal article
Language:English
Published: American Physical Society 2020
_version_ 1797071555073671168
author Yang, R
Christov, IC
Griffiths, IM
Ramon, GZ
author_facet Yang, R
Christov, IC
Griffiths, IM
Ramon, GZ
author_sort Yang, R
collection OXFORD
description Periodically-driven flows are known to generate non-zero, 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 Maxwellian 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 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 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.
first_indexed 2024-03-06T22:54:59Z
format Journal article
id oxford-uuid:6010751e-ed1d-47b4-a5ff-97e23ea6a64c
institution University of Oxford
language English
last_indexed 2024-03-06T22:54:59Z
publishDate 2020
publisher American Physical Society
record_format dspace
spelling oxford-uuid:6010751e-ed1d-47b4-a5ff-97e23ea6a64c2022-03-26T17:51:02ZTime-averaged transport in oscillatory squeeze flow of a viscoelastic fluidJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:6010751e-ed1d-47b4-a5ff-97e23ea6a64cEnglishSymplectic ElementsAmerican Physical Society2020Yang, RChristov, ICGriffiths, IMRamon, GZPeriodically-driven flows are known to generate non-zero, 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 Maxwellian 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 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 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.
spellingShingle Yang, R
Christov, IC
Griffiths, IM
Ramon, GZ
Time-averaged transport in oscillatory squeeze flow of a viscoelastic fluid
title Time-averaged transport in oscillatory squeeze flow of a viscoelastic fluid
title_full Time-averaged transport in oscillatory squeeze flow of a viscoelastic fluid
title_fullStr Time-averaged transport in oscillatory squeeze flow of a viscoelastic fluid
title_full_unstemmed Time-averaged transport in oscillatory squeeze flow of a viscoelastic fluid
title_short Time-averaged transport in oscillatory squeeze flow of a viscoelastic fluid
title_sort time averaged transport in oscillatory squeeze flow of a viscoelastic fluid
work_keys_str_mv AT yangr timeaveragedtransportinoscillatorysqueezeflowofaviscoelasticfluid
AT christovic timeaveragedtransportinoscillatorysqueezeflowofaviscoelasticfluid
AT griffithsim timeaveragedtransportinoscillatorysqueezeflowofaviscoelasticfluid
AT ramongz timeaveragedtransportinoscillatorysqueezeflowofaviscoelasticfluid