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Acoustic streaming in Maxwell fluids generated by standing waves in two-dimensional microchannels

Published online by Cambridge University Press:  06 January 2022

C. Vargas Open the ORCID record for C. Vargas [Opens in a new window] ,
I. Campos-Silva ,
F. Méndez Open the ORCID record for F. Méndez [Opens in a new window] ,
J. Arcos Open the ORCID record for J. Arcos [Opens in a new window]  and
O. Bautista Open the ORCID record for O. Bautista [Opens in a new window]
C. Vargas
Affiliation:
ESIME Zacatenco, Instituto Politécnico Nacional, Calz. Ticoman 600, San José Ticoman, Del. Gustavo A. Madero, Ciudad de México 07738, Mexico
I. Campos-Silva
Affiliation:
ESIME Zacatenco, Instituto Politécnico Nacional, Calz. Ticoman 600, San José Ticoman, Del. Gustavo A. Madero, Ciudad de México 07738, Mexico
F. Méndez
Affiliation:
Universidad Nacional Autónoma de México, Coyoacan, Ciudad de México 04510, Mexico
J. Arcos
Affiliation:
ESIME Azcapotzalco, Instituto Politécnico Nacional, Av. de las Granjas 682, Col. Santa Catarina, Azcapotzalco, Ciudad de México 02250, Mexico
O. Bautista*
Affiliation:
ESIME Azcapotzalco, Instituto Politécnico Nacional, Av. de las Granjas 682, Col. Santa Catarina, Azcapotzalco, Ciudad de México 02250, Mexico
*
†Email address for correspondence: obautista@ipn.mx
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Abstract

In this work, a semianalytic solution for the acoustic streaming phenomenon, generated by standing waves in Maxwell fluids through a two-dimensional microchannel (resonator), is derived. The mathematical model is non-dimensionalized and several dimensionless parameters that characterize the phenomenon arise: the ratio between the oscillation amplitude of the resonator and the half-wavelength ($\eta =2A/\lambda _{a}$); the product of the fluid relaxation time times the angular frequency known as the Deborah number ($De=\lambda _{1}\omega$); the aspect ratio between the microchannel height and the wavelength ($\epsilon =2 H_{0}/\lambda _{a}$); and the ratio between half the height of the microchannel and the thickness of the viscous boundary layer ($\alpha =H_{0}/\delta _{\nu }$). In the limit when $\eta \ll 1$, we obtain the hydrodynamic behaviour of the system using a regular perturbation method. In the present work, we show that the acoustic streaming speed is proportional to $\alpha ^{2.65}De^{1.9}$, and the acoustic pressure varies as $\alpha ^{6/5}De^{1/2}$. Also, we have found that the growth of inner vortex is due to convective terms in the Maxwell rheological equation. Furthermore, the velocity antinodes show a high dependency on the Deborah number, highlighting the fluid's viscoelastic properties and the appearance of resonance points. Due to the limitations of perturbation methods, we will only analyse narrow microchannels.

JFM classification

Micro-/Nano-fluid dynamics: Microfluidics Micro-/Nano-fluid dynamics: Microscale transport Non-Newtonian Flows: Viscoelasticity
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 933 , 25 February 2022 , A59
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

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