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

TL;DR

This study analyzes how oscillatory squeeze flow of viscoelastic fluids enhances time-averaged transport of heat and solutes, revealing resonance effects and the influence of fluid elasticity on transport efficiency.

Contribution

It introduces a homogenization approach to derive a one-dimensional model capturing effective diffusion, advection, and reaction mechanisms in oscillatory squeeze flows of viscoelastic fluids.

Findings

Effective dispersion coefficient exceeds molecular diffusivity, especially near resonance.

Fluid elasticity and oscillation frequency significantly enhance transport efficiency.

Resonant modes cause peaks in velocity and transport, depending on Womersley number.

Abstract

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.