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Viscoelastic effects in circular edge waves

Published online by Cambridge University Press:  25 May 2021

X. Shao ,
P. Wilson ,
J.B. Bostwick Open the ORCID record for J.B. Bostwick [Opens in a new window]  and
J.R. Saylor
X. Shao
Affiliation:
Department of Mechanical Engineering, Clemson University, Clemson, SC29634, USA
P. Wilson
Affiliation:
Department of Mechanical Engineering, Clemson University, Clemson, SC29634, USA
J.B. Bostwick*
Affiliation:
Department of Mechanical Engineering, Clemson University, Clemson, SC29634, USA
J.R. Saylor
Affiliation:
Department of Mechanical Engineering, Clemson University, Clemson, SC29634, USA
*
†Email address for correspondence: [email protected]
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Abstract

Surface waves are excited at the boundary of a mechanically vibrated cylindrical container and are referred to as edge waves. Resonant waves are considered, which are formed by a travelling wave formed at the edge and constructively interfering with its centre reflection. These waves exhibit an axisymmetric spatial structure defined by the mode number $n$. Viscoelastic effects are investigated using two materials with tunable properties; (i) glycerol/water mixtures (viscosity) and (ii) agarose gels (elasticity). Long-exposure white-light imaging is used to quantify the magnitude of the wave slope from which frequency-response diagrams are obtained via frequency sweeps. Resonance peaks and bandwidths are identified. These results show that for a given $n$, the resonance frequency decreases with viscosity and increases with elasticity. The amplitude of the resonance peaks are much lower for gels and decrease further with mode number, indicating that much larger driving amplitudes are needed to overcome the elasticity and excite edge waves. The natural frequencies for a viscoelastic fluid in a cylindrical container with a pinned contact-line are computed from a theoretical model that depends upon the dimensionless Ohnesorge number ${Oh}$, elastocapillary number ${Ec}$ and Bond number ${Bo}$. All show good agreement with experimental observations. The eigenvalue problem is equivalent to the classic damped-driven oscillator model on linear operators with viscosity appearing as a damping force and elasticity and surface tension as restorative forces, consistent with our physical interpretation of these viscoelastic effects.

JFM classification

Waves/Free-surface Flows: Capillary waves Non-Newtonian Flows: Viscoelasticity Waves/Free-surface Flows: Elastic waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 919 , 25 July 2021 , A18
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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