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Fluctuation-driven dynamics of liquid nano-threads with external hydrodynamic perturbations

Published online by Cambridge University Press:  30 September 2024

Zhao Zhang ,
Chengxi Zhao Open the ORCID record for Chengxi Zhao [Opens in a new window]  and
Ting Si Open the ORCID record for Ting Si [Opens in a new window]
Zhao Zhang
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
Chengxi Zhao*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
Ting Si
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
*
†Email address for correspondence: zhaochengxi@ustc.edu.cn
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Abstract

Instability and rupture dynamics of a liquid nano-thread, subjected to external hydrodynamic perturbations, are captured by a stochastic lubrication equation (SLE) incorporating thermal fluctuations via Gaussian white noise. Linear instability analysis of the SLE is conducted to derive the spectra and distribution functions of thermal capillary waves influenced by external perturbations and thermal fluctuations. The SLE is also solved numerically using a second-order finite difference method with a correlated noise model. Both theoretical and numerical solutions, validated through molecular dynamics, indicate that surface tension forces due to specific external perturbations overcome the random effects of thermal fluctuations, determining both the thermal capillary waves and the evolution of perturbation growth. The results also show two distinct regimes: (i) the hydrodynamic regime, where external perturbations dominate, leading to uniform ruptures, and (ii) the thermal-fluctuation regime, where external perturbations are surpassed by thermal fluctuations, resulting in non-uniform ruptures. The transition between these regimes, modelled by a criterion developed from linear instability theory, exhibits a strong dependence on the amplitudes and wavenumbers of the external perturbations.

JFM classification

Low-Reynolds-number flows: Lubrication theory

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Type
JFM Papers
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Journal of Fluid Mechanics , Volume 996 , 10 October 2024 , A29
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© The Author(s), 2024. Published by Cambridge University Press

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