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Color-gradient lattice Boltzmann model for immiscible fluids with density contrast

A. Subhedar*

  • Department of Chemical Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India

  • *amol.subhedar@iitb.ac.in
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Phys. Rev. E 106, 045308 – Published 21 October, 2022

DOI: https://doi.org/10.1103/PhysRevE.106.045308

Abstract

We present a color-gradient-based lattice Boltzmann model for immiscible fluids with a large density contrast. The model employs the velocity-based equilibrium distribution function, initially proposed for the phase-field-based model by Zu and He [Phys. Rev. E 87, 043301 (2013)], with a modification necessary to satisfy the kinematic condition at the interface. Different from the existing color-gradient models, the present model allows to specify interface mobility that is independent of the fluid density ratio. Further, we provide a unified framework, which uses the recursive representation of the lattice Boltzmann equation, to derive the governing equations of the system. The emergent color dynamics thus obtained, through an analysis of the segregation operator, is shown to obey the locally conservative Allen-Cahn equation. We use a series of benchmarks, which include a stationary drop, a layered Poiseuille flow, translation of a drop under a forced velocity field, the Rayleigh-Taylor instability, and the capillary intrusion test to demonstrate the model's ability in dealing with complex flow problems.

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Phys. Rev. E 106, 045308– Published 21 October, 2022
  • Received 7 June 2021
  • Revised 21 June 2022
  • Accepted 30 August 2022
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