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Controlled stabilization of rotating toroidal drops in viscous linear flow

Published online by Cambridge University Press:  01 December 2022

Sumit Malik Open the ORCID record for Sumit Malik [Opens in a new window] ,
Olga M. Lavrenteva Open the ORCID record for Olga M. Lavrenteva [Opens in a new window] ,
Moshe Idan Open the ORCID record for Moshe Idan [Opens in a new window]  and
Avinoam Nir Open the ORCID record for Avinoam Nir [Opens in a new window]
Sumit Malik*
Affiliation:
Faculty of Chemical Engineering, Technion-Israel Institute of Technology, Haifa 3200003, Israel
Olga M. Lavrenteva
Affiliation:
Faculty of Chemical Engineering, Technion-Israel Institute of Technology, Haifa 3200003, Israel
Moshe Idan
Affiliation:
Faculty of Aerospace Engineering, Technion-Israel Institute of Technology, Haifa 3200003, Israel
Avinoam Nir
Affiliation:
Faculty of Chemical Engineering, Technion-Israel Institute of Technology, Haifa 3200003, Israel
*
†Email address for correspondence: ssumitmalik@gmail.com
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Abstract

Toroidal drops, embedded in viscous flow, have a large range of stationary shapes that are challenging to compute numerically due to their inherent instability. When both the drop and the outer fluid are Newtonian liquids, the only reported cases of such stable configurations are of highly expanded drops rotating in an axisymmetrical extensional flow. In this study, we propose a method for stabilizing the stationary shapes of inherently unstable rotating toroidal drops, embedded in extensional or biextensional flow, by subjecting the system to feedback control stabilization. The proposed controller is designed using a two-state dynamic model of the system and is tested on a high-order nonlinear dynamic model of the drop deformation. It is demonstrated that, through this simplified feedback-control-centred approach, an extended collection of stabilized stationary solutions is generated, which spans the range from highly expanded drops to almost collapsed ones. In the latter region, that was never obtained in previous studies, multiplicity of solutions is identified. Furthermore, our method is more accurate and more efficient compared with the previously used ones.

JFM classification

Drops and Bubbles: Drops Flow Control: Instability control
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 952 , 10 December 2022 , A38
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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