THERMAL SCIENCE

International Scientific Journal

Atena Ghaderi

,

Mohammad Hassan Kayhani

,

Mohsen Nazari

SIMULATION OF THE CO-AXIAL FERROFLUID DROPLETS INTERACTION UNDER UNIFORM MAGNETIC FIELD

ABSTRACT
In this study, falling and the coalescence of a pair ferrofluid droplets subjected to uniform magnetic field are investigated numerically. For this approach, a two dimensional hybrid approach combined of lattice-Boltzmann and Finite-volume method is used. The lattice Boltzmann equation with the magnetic force term is solved to update the flow field while the magnetic induction equation is solved using finite volume method to calculate the magnetic field. To validate current simulations, three test cases have been considered: Laplace, multiple rising bubbles and deformation of static drop under magnetic field are analyzed. The comparison of results between the present study and previous researches shows a good agreement. The effects of different parameters: magnetic Bond number, magnetic susceptibility and magnetic field direction are comprehensively studied. The results show that the coalescence of droplets becomes fast with the increasing Bond number and susceptibility in y-direction magnetic field. Also, the coalescence and falling process of droplets takes more time in the horizontal magnetic field in comparison with the vertical magnetic field.
KEYWORDS
Lattice Boltzmann Method, Shan-Chen Model, ferrofluid, magnetic field
PAPER SUBMITTED: 2017-03-18
PAPER REVISED: 2017-06-08
PAPER ACCEPTED: 2017-06-28
PUBLISHED ONLINE: 2017-07-08
DOI REFERENCE: https://doi.org/10.2298/TSCI170318158G
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2019, VOLUME 23, ISSUE Issue 2, PAGES [1027 - 1042]
REFERENCES
  1. Delnoij, E., et al. Numerical Simulation of Bubble Coalescence using a Volume of Fluid (VOF) Model In: Third International Conference on Multiphase Flows,1998, June 8-12, Lyon, France.
  2. Guido, S., Simeone, M.: Binary collision of drops in simple shear flow by computer assisted video optical microscopy, J. Fluid Mech. 357, 1-20, (1998).
  3. Yang, H., et al. The coalescence of two equal-sized drops in a two dimensional linear flow, Phys. Fluids, 13, 5 (2001).
  4. Ha, J. W., et al. Effect of compatibilizer on the coalescence of two drops in flow, Phys. Fluids, 15, 4 (2003).
  5. Annaland, M.V.S., et al. Numerical simulation of gas bubbles behavior using a three dimentional volume of fluid method, Journal of Chmical Engineering Science, 60, 2999-3011 (2005).
  6. Yoon, Y., et al. Coalescence of Two Equal-sized Deformable Drops in an Axisymmetric Flow, Physics of Fluids, (2007) doi: dx.doi.org/10.1063/1.2772900.
  7. Burns, A., et al. Microfabricated structures for integrated DNA, Proc. Nat. Acad. Sci. U.S.A., 93 , 5556-5561, (1996).
  8. Cordero, M.L., et al. Thermocapillary manipulation of droplets using holographic beam shaping: Microfluidic pin ball, Appl. Phys. Lett., Vol. 93, (2008).
  9. Cho, S.K., et al. Creating, transporting, cutting, and merging liquid droplets by electrowetting-based actuation for digital microfluidic circuits., J. Microelectromech. Syst., 12 , 70-80, (2003).
  10. Rosensweig, R.E.: Ferrohydrodynamics, Cambridge University Press, Cambridge, 1985.
  11. Flament, C., et al. Measurements of ferrofluid surface tension in confined geometry, Journal of physic review E, 53, 4801- 4806, 1996.
  12. Afkhami, S., et al. St: Field induced motion of ferrofluid droplets through immiscible viscous media,J. Fluid Mech., 610, 363 (2008).
  13. Tian, X. H., et al. Influence of Vertical Static Magnetic Field on Behavior of Rising Single Bubble in a Conductive Fluid, Journal of Iron and steel Institute of Japan, 56, 195-204 (2016).
  14. Kie, H. Level Set Method for Two-Phase Incompressible Flows under Magnetic Fields, Journal of Computer Physics Communications, 181, 999-1007 (2010).
  15. Hadidi, A., Jalali-Vahid, D. Numerical study of the uniform magnetic field effect on the interaction of Bubbles in viscous liquid column, Theor. Comput. Fluid Dyn. 30, 165-184 (2016).
  16. Nazari M., et al. Lattice Boltzmann Simulation of Natural Convection in an Open End Cavity with Inclined Hot Wall, Applied Math. and Mech., 36, 523-540 (2015).
  17. Nazari, M, et al. Lattice Boltzmann Simulation of Double Diffusive Natural Convection in a Square Cavity with a Hot Square Obstacle, Chin. J. Chemical Eng., 23, 22-30 (2015).
  18. .Ashorynejad, H.R., Hoseinpour, B., Investigation of Different Nanofluids Effect on entropy generation on natural convection in a porous cavity, European Journal of Mechanics B/Fluids, 62: 86-93 (2017).
  19. Fallah, K., et al. Simulation of Natural Convection Heat Transfer Using Nanofluid in a Concentric Annulus, Thermal science International Scientific Journal, (2015) doi:10.2298/TSCI150118078F
  20. Alinejad, J., Fallah, K.: Taguchi Optimization Approach for Three-Dimensional Nanofluid Natural Convection in a Transformable Enclosure, Journal of Thermophysics and Heat Transfer, 31 (1), 211-217 (2016).
  21. Hoseinpour, B., et al. Entropy Generation of Nanofluid in a Porous Cavity by Lattice Boltzmann Method, Journal of Thermophysics and Heat Transfer, 31(1) 20-27 (2017).
  22. Fallah, K., et al. Numerical simulation of planar shear flow passing a rotating cylinder at low Reynolds numbers, Acta Mechanica, 223, 221-236 (2012).
  23. Fallah, et al. Multiple-relaxation-time lattice Boltzmann simulation of non-Newtonian flows past a rotating circular cylinder, Journal of Non-Newtonian Fluid Mechanics, 177-178, 1-14 (2012).
  24. Amiri Delouei, A., et al. Non-Newtonian Unconfined Flow and Heat Transfer over a Heated Cylinder Using the Direct Forcing Immersed Boundary-Thermal Lattice Boltzmann Method, Physical Review E (APS), (2014) doi: 10.4208/cicp.060414.220115a
  25. Nazari, M., et al. Power-Law Fluid Flow and Heat Transfer in a Channel with a Built-In Porous Square Cylinder: Lattice Boltzmann Simulation, J. Non-Newtonian Fluid Mechanics, 204, 38-49, (2014).
  26. Fallah, K. et al. Drop formation in cross-junction microchannel, using lattice Boltzmann method, Thermal science International Scientific Journal, (2016), doi: 10.2298/TSCI160322230F.
  27. Fallah, K., Taeibi, M., Lattice Boltzmann Simulation of Drop formation in T-junction Microchannel, Journal of Molecular Liquids, Article in press, 2017.
  28. Gunstensen, A.K., et al. Lattice Boltzmann Model of Immiscible Fluids, Journal of Physic Review A, 43, 4320-4330 (1991).
  29. Shan, X., Chen, H.: Lattice Boltzmann Model for Simulating Flows with Multiple Phases and Components, Journal of Physic Review E, 47,1815-1819 (1993).
  30. He, X., et al. A Discrete Boltzmann Equation Model for Non-ideal Gases, Journal of Physic Review E, (1998) doi: dx.doi.org/10.1103/PhysRevE.57.R13.
  31. Swift, M. R., et al. Lattice Boltzmann Simulation of Nonideal Fluids, Journal of Physic Review Letters, Vol.75, 830-840 (1995).
  32. Shan, X., Chen, H., Lattice Boltzmann Model for Simulating Flows with Multiple Phases and Components, Journal of Physic Review E, 47, 1815-1819 (1993).
  33. Mousavi Tilehboni, S.E., et al. M. Numerical Simulation of Droplet Detachment from Solid Walls under Gravity Force Using Lattice Boltzmann Method, Journal of Molecular Liquids, 212, 544-556 (2015).
  34. Afkhami, S., et al. Deformation of a Hydrophobic Ferrofluid Droplet Suspended in a Viscous Medium under Uniform Magnetic Fields, Journal of Fluid Mechanics,663 358-384 (2010).
  35. Ansari, M.R., et al. M.E., Effect of a Uniform Magnetic Field on Dielectric Two-phase Bubbly Flows Using the Level Set Method. J. Mag. Mag. Mater., 324 4094-4101 (2012).
  36. Ghaffari, A., et al. CFD Simulation of Equilibrium Shape and Coalescence of Ferrofluid Droplets Subjected to Uniform Magnetic Field, Colloids and Surfaces A: Physicochem. Eng. Aspects, 481 186-198 (2015).
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Simulation of the co-axial ferrofluid droplets interaction under uniform magnetic field

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