In this study, falling ferrofluid droplet behavior in nonmagnetic viscous fluid under the uniform magnetic field in two-phase flow is studied numerically. To this approach, a hybrid lattice-Boltzmann based Shan-Chen model 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 the finite volume method to calculate the magnetic field. To validate the flow field solution,

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... two tests have been considered: the free bubble rising and Laplace law. In order to validate the magnetic field, permeable circle and deformation of static drop under magnetic field is simulated. The comparison of results between present study and previous researches shows that there is a good agreement between the results. The effects of the magnetic Bond number, susceptibility and magnetic field direction on deformation of the falling droplet are investigated. The results show that increase in the magnetic Bond number or susceptibility leads to a larger deformation of the droplet. Also, in horizontal magnetic field, the falling process takes longer time compared to the vertical magnetic field. Keywords: Two phase flow lattice-Boltzmann method Shan-Chen model Ferroflu id, Un iform ma gnetic f ield -1 ‫ﻣﻘﺪﻣﻪ‬ ‫ﻣﻨﻈﻮر‬ ‫ﺑﻪ‬ ‫ﮐﻨﺘﺮل‬ ‫رﻓﺘﺎر‬ ‫ﻗﻄﺮات‬ ‫روش‬ ‫ﻫﺎي‬ ‫ﻣﺘﻌﺪدي‬ ‫ﺗﻮﺳﻂ‬ ‫ﻣﺤﻘﻘﯿﻦ‬ ‫ﭘﯿﺸﻨﻬﺎد‬ ‫ﺷﺪه‬ ‫اﺳﺖ.‬ ‫رﻓﺘﺎر‬ ‫ﻗﻄﺮه‬ ‫ﻣﯿﺘﻮان‬ ‫را‬ ‫ﺗﻮﺳﻂ‬ ‫ﮔﺮادﯾﺎن‬ ‫ﺷﯿﻤﯿﺎﯾﯽ،‬ ‫ﺗﺮﻣﻮﮐﭙﯿﻼري،‬ ‫و‬ ‫ﻧﯿﺮوﻫﺎي‬ ‫اﻟﮑﺘﺮواﺳﺘﺎﺗﯿﮏ‬ ‫و‬ ‫ﻣﻐﻨﺎﻃﯿﺴﯽ‬ ‫ﮐﻨﺘﺮل‬ ] ‫ﻧﻤﻮد‬ 1 -3 .[ ‫ﻣﻮﺛﺮﺗﺮﯾﻦ‬ ‫ﺟﻤﻠﻪ‬ ‫از‬ ‫روش‬ ‫اﯾﻦ‬ ‫ﻣﯽ‬ ‫ﻫﺎ‬ ‫ﮐﻨﺘﺮل‬ ‫اﻣﮑﺎن‬ ‫ﮐﻪ‬ ‫ﺑﺮد‬ ‫ﻧﺎم‬ ‫را‬ ‫ﻣﻐﻨﺎﻃﯿﺴﯽ‬ ‫ﻣﯿﺪان‬ ‫اﻋﻤﺎل‬ ‫ﺗﻮان‬ ‫ﻏﯿﺮﺗﻤﺎﺳﯽ‬ ‫ﺻﻮرت‬ ‫ﺑﻪ‬ ‫ﻗﻄﺮه‬ ‫ﺣﺮﮐﺖ‬ 1 ‫ﻣﯽ‬ ‫ﻓﺮاﻫﻢ‬ ‫را‬ ‫و‬ ‫ﻓﺮو‬ ‫ﺳﯿﺎل‬ ‫ﻗﻄﺮه‬ ‫اﮔﺮ‬ ‫آورد.‬ ‫ﻣﯿﺪان‬ ‫ﻣﻌﺮض‬ ‫در‬ ‫ﻣﺘﻔﺎوت‬ ‫ﻣﻐﻨﺎﻃﯿﺴﯽ‬ ‫ﺧﺼﻮﺻﯿﺎت‬ ‫ﺑﺎ‬ ‫دﯾﮕﺮ‬ ‫ﺳﯿﺎل‬ ‫ﯾﮏ‬ ‫دﺳﺘﺨﻮ‬ ‫ﮔﯿﺮﻧﺪ،‬ ‫ﻗﺮار‬ ‫ﻣﻐﻨﺎﻃﯿﺴﯽ‬ ‫ﻣﯽ‬ ‫ﺷﮑﻞ‬ ‫ﺗﻐﯿﯿﺮ‬ ‫ش‬ ] ‫ﻓﺮوﺳﯿﺎل‬ ‫ﯾﮏ‬ ‫ﺷﻮﻧﺪ.‬ 4 ،[ ‫ﻧﺎﻧﻮ‬ ‫ﺑﺎﺷﺪ.‬ ‫ﻣﯽ‬ ‫ﺣﺎﻣﻞ‬ ‫ﺳﯿﺎل‬ ‫ﯾﮏ‬ ‫در‬ ‫ﻣﻐﻨﺎﻃﯿﺴﯽ‬ ‫ذرات‬ ‫از‬ ‫ﮐﻠﻮﺋﯿﺪي‬ ‫ﻣﺨﻠﻮﻃﯽ‬ ‫روﮐﻨﺸﮕﺮ‬ ‫ﻣﺎده‬ ‫ﯾﮏ‬ ‫ﺑﺎ‬ ‫ﻣﻌﻤﻮﻻ‬ ‫ذرات‬ 2 ‫ﻣﯽ‬ ‫ﭘﻮﺷﺎﻧﺪه‬ ‫ﻧﺎﻧﻮذرات‬ ‫اﻧﺒﺎﺷﺘﮕﯽ‬ ‫از‬ ‫ﺗﺎ‬ ‫ﺷﻮﻧﺪ‬ 1 Contactless control 2 Surfactant