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Diffuse-interface approach to competition between viscous flow and diffusion in pinch-off dynamics

Fukeng Huang* and Weizhu Bao2,†

Tiezheng Qian‡

  • Department of Mathematics, National University of Singapore, Singapore, 119076

  • Department of Mathematics, The Hong Kong University of Science and Technology and Clear Water Bay, Kowloon, Hong Kong, People's Republic of China

  • *hfkeng@nus.edu.sg
  • †matbaowz@nus.edu.sg
  • ‡Corresponding author: maqian@ust.hk
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Phys. Rev. Fluids 7, 094004 – Published 28 September, 2022

DOI: https://doi.org/10.1103/PhysRevFluids.7.094004

Abstract

The pinch-off dynamics of a liquid thread has been studied through numerical simulations and theoretical analysis. Occurring at small length scales, the pinch-off dynamics admits similarity solutions that can be classified into the Stokes regime and the diffusion-dominated regime, with the latter being recently experimentally observed in aqueous two-phase systems [Phys. Rev. Lett. 123, 134501 (2019)]. Derived by applying Onsager's variational principle, the Cahn–Hilliard–Navier–Stokes model is employed as a minimal model capable of describing the interfacial motion driven by not only advection but also diffusion. By analyzing the free energy dissipation mechanisms in the model, a characteristic length scale is introduced to measure the competition between diffusion and viscous flow in interfacial motion. This length scale is typically of nanometer scale for systems far from the critical point, but can approach micrometer scale for aqueous two-phase systems close to the critical point. The Cahn–Hilliard–Navier–Stokes model is solved by using an accurate and efficient spectral method in a cylindrical domain with axisymmetry. Ample numerical examples are presented to show the pinch-off processes in the Stokes regime and the diffusion-dominated regime respectively. In particular, the crossover between these two regimes is investigated numerically and analytically to reveal how the scaling behaviors of similarity solutions are to be qualitatively changed as the characteristic length scale is inevitably accessed by the pinching neck of the interface. Discussions are also provided for numerical examples that are performed for the breakup of long liquid filaments and show qualitatively different phenomena in different scaling regimes.

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Phys. Rev. Fluids 7, 094004– Published 28 September, 2022
  • Received 7 June 2022
  • Accepted 29 August 2022
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