Fluctuating hydrodynamics and the Rayleigh–Plateau instability

Journal Article · Tue Jul 18 00:00:00 EDT 2023 · Proceedings of the National Academy of Sciences of the United States of America

DOI:https://doi.org/10.1073/pnas.2306088120· OSTI ID:1991116

Barker, Bryn ^[1]; Bell, John B. ^[2]; Garcia, Alejandro L. ^[3]

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1. Department of Mathematics, The University of North Carolina, Chapel Hill, NC 27599
2. Center for Computational Sciences and Engineering, Applied Mathematics and Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94703
3. Department of Physics and Astronomy, San Jose State University, San Jose, CA 95192

The Rayleigh–Plateau instability occurs when surface tension makes a fluid column become unstable to small perturbations. At nanometer scales, thermal fluctuations are comparable to interfacial energy densities. Consequently, at these scales, thermal fluctuations play a significant role in the dynamics of the instability. These microscopic effects have previously been investigated numerically using particle-based simulations, such as molecular dynamics (MD), and stochastic partial differential equation–based hydrodynamic models, such as stochastic lubrication theory. In this paper, we present an incompressible fluctuating hydrodynamics model with a diffuse-interface formulation for binary fluid mixtures designed for the study of stochastic interfacial phenomena. An efficient numerical algorithm is outlined and validated in numerical simulations of stable equilibrium interfaces. We present results from simulations of the Rayleigh–Plateau instability for long cylinders pinching into droplets for Ohnesorge numbers of Oh = 0.5 and 5.0. Both stochastic and perturbed deterministic simulations are analyzed and ensemble results show significant differences in the temporal evolution of the minimum radius near pinching. Short cylinders, with lengths less than their circumference, were also investigated. As previously observed in MD simulations, we find that thermal fluctuations cause these to pinch in cases where a perturbed cylinder would be stable deterministically. Finally, we show that the fluctuating hydrodynamics model can be applied to study a broader range of surface tension–driven phenomena.

• Sponsoring Organization: USDOE
• Grant/Contract Number: AC02-05CH11231; SC0022158
• OSTI ID: 1991116
• Journal Information: Proceedings of the National Academy of Sciences of the United States of America, Journal Name: Proceedings of the National Academy of Sciences of the United States of America Journal Issue: 30 Vol. 120; ISSN 0027-8424
• Publisher: Proceedings of the National Academy of Sciences
• Country of Publication: United States
• Language: English