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A magnetic field coupling lattice Boltzmann model and its application on the merging process of multiple-ferrofluid-droplet system

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  • Li, Xiang
  • Yu, Peng
  • Niu, Xiao-Dong
  • Li, De-Cai
  • Yamaguchi, Hiroshi

Abstract

The present study concerns the dynamics of ferrofluid droplets in a Newtonian fluid. The incompressible Navier-Stokes (NS) equations are applied for the dynamics of the immiscible magnetic and Newtonian fluids while the Cahn-Hilliard (C-H) equation is adopted to describe the behavior of their interface. A magnetic field coupling lattice Boltzmann (LB) model is developed to solve both the NS equations and the C-H equation. Specially, a mass-correcting term is introduced into the C-H equation, which strongly enforces the mass conservation. The magnetic field is evaluated by a Poisson equation solver with a self-correcting procedure for the static Maxwell equations. The magnetic dipole force is transformed into the magnetic surface force by a rigorous mathematical procedure, which can physically describe the magnetic effect on the interface. Moreover, the magnetic force after this treatment becomes easy-to-implement, which can be directly incorporated into the external force term of the LB model. The capability of the present combination method to simulate the magnetic multiphase flows is demonstrated by three typical numerical examples, i.e., Laplace law for a stationary droplet, a stationary cylinder under an external uniform magnetic field, the deformation of a single ferrofluid droplet. Further, the merging process of multiple-ferrofluid-droplet system in organic oil is investigated. It is found that the elongation of ferrofluid droplet in the direction of magnetic field shows positive impact on the merging process when the orientation of ferrofluid droplets is parallel to the external magnetic field, while negative impact on the merging process when their orientation is perpendicular to the external magnetic field.

Suggested Citation

  • Li, Xiang & Yu, Peng & Niu, Xiao-Dong & Li, De-Cai & Yamaguchi, Hiroshi, 2021. "A magnetic field coupling lattice Boltzmann model and its application on the merging process of multiple-ferrofluid-droplet system," Applied Mathematics and Computation, Elsevier, vol. 393(C).
    • Handle: RePEc:eee:apmaco:v:393:y:2021:i:c:s0096300320307220
    DOI: 10.1016/j.amc.2020.125769
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    References listed on IDEAS

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    1. Karami, Naser & Rahimian, Mohammad Hassan & Farhadzadeh, Mohsen, 2017. "Numerical simulation of droplet evaporation on a hot surface near Leidenfrost regime using multiphase lattice Boltzmann method," Applied Mathematics and Computation, Elsevier, vol. 312(C), pages 91-108.
    2. Khademi, Ramin & Razminia, Abolhassan & Shiryaev, Vladimir I., 2020. "Conjugate-mixed convection of nanofluid flow over an inclined flat plate in porous media," Applied Mathematics and Computation, Elsevier, vol. 366(C).
    3. Mehrez, Zouhaier & Cafsi, Afif El, 2021. "Heat exchange enhancement of ferrofluid flow into rectangular channel in the presence of a magnetic field," Applied Mathematics and Computation, Elsevier, vol. 391(C).
    4. Bourantas, G.C. & Loukopoulos, V.C. & Joldes, G.R. & Wittek, A. & Miller, K., 2019. "An explicit meshless point collocation method for electrically driven magnetohydrodynamics (MHD) flow," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 215-233.
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    1. Djukic, Tijana & Topalovic, Marko & Filipovic, Nenad, 2023. "Validation of lattice Boltzmann based software for blood flow simulations in complex patient-specific arteries against traditional CFD methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 957-976.

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