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Shape curvature effects in viscous streaming

Published online by Cambridge University Press:  03 July 2020

Yashraj Bhosale ,
Tejaswin Parthasarathy  and
Mattia Gazzola Open the ORCID record for Mattia Gazzola [Opens in a new window]
Yashraj Bhosale
Affiliation:
Mechanical Sciences and Engineering and National Center for Supercomputing Applications, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
Tejaswin Parthasarathy
Affiliation:
Mechanical Sciences and Engineering and National Center for Supercomputing Applications, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
Mattia Gazzola*
Affiliation:
Mechanical Sciences and Engineering, National Center for Supercomputing Applications and Carl R. Woese Institute for Genomic Biology, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
*
†Email address for correspondence: mgazzola@illinois.edu
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Abstract

Viscous streaming flows generated by objects of constant curvature (circular cylinders, infinite plates) have been well understood. Yet, characterization and understanding of such flows when multiple body length scales are involved has not been looked into in rigorous detail. We propose a simplified setting to understand and explore the effect of multiple body curvatures on streaming flows, analysing the system through the lens of bifurcation theory. Our set-up consists of periodic, regular lattices of cylinders characterized by two distinct radii, so as to inject discrete curvatures into the system, which in turn affect the streaming field generated due to an oscillatory background flow. We demonstrate that our understanding based on this system, and in particular the role of bifurcations in determining the local flow topology, can be then generalized to a variety of individual convex shapes presenting a spectrum of curvatures, explaining prior experimental and computational observations. Thus, this study illustrates a route towards the rational manipulation of viscous streaming flow topology, through regulated variation of object geometry.

JFM classification

Micro-/Nano-fluid dynamics: Microfluidics Nonlinear Dynamical Systems: Bifurcation Mathematical Foundations: General fluid mechanics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 898 , 10 September 2020 , A13
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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