Interfacial instability of ferrofluid flow under the influence of a vacuum magnetic field

Mingjun LI, Li ZHU

doi:10.1007/s10483-021-2758-7

Applied Mathematics and Mechanics >

2021 , Vol. 42 >Issue 8: 1171 - 1182

DOI: https://doi.org/10.1007/s10483-021-2758-7

Articles

Interfacial instability of ferrofluid flow under the influence of a vacuum magnetic field

Expand

1. School of Mathematics and Computation Science, Xiangtan University, Xiangtan 411105, Hunan Province, China;
2. Hunan National Center for Applied Mathematics, Xiangtan 411105, Hunan Province, China

Received date: 2021-04-08

Revised date: 2021-05-27

Online published: 2021-07-28

Supported by

the National Natural Science Foundation of China (No. 11971411) and the Research Foundation of Education Bureau of Hunan Province of China (No. 18A067)

Fold

Abstract

This study is to numerically test the interfacial instability of ferrofluid flow under the presence of a vacuum magnetic field. The ferrofluid parabolized stability equations (PSEs) are derived from the ferrofluid stability equations and the Rosensweig equations, and the characteristic values of the ferrofluid PSEs are given to describe the ellipticity of ferrofluid flow. Three numerical models representing specific cases considering with/without a vacuum magnetic field or viscosity are created to mathematically examine the interfacial instability by the computation of characteristic values. Numerical investigation shows strong dependence of the basic characteristic of ferrofluid Rayleigh-Taylor instability (RTI) on viscosity of ferrofluid and independence of the vacuum magnetic field. For the shock wave striking helium bubble, the magnetic field is not able to trigger the symmetry breaking of bubble but change the speed of the bubble movement. In the process of droplet formation from a submerged orifice, the collision between the droplet and the liquid surface causes symmetry breaking. Both the viscosity and the magnetic field exacerbate symmetry breaking. The computational results agree with the published experimental results.

Key words： interfacial instability; ferrofluid; vacuum magnetic field; parabolized stability equation (PSE)

Cite this article

Mingjun LI, Li ZHU . Interfacial instability of ferrofluid flow under the influence of a vacuum magnetic field[J]. Applied Mathematics and Mechanics, 2021 , 42(8) : 1171 -1182 . DOI: 10.1007/s10483-021-2758-7

References

[1] HERBERT, T. Parabolized stability equations. Annual Review of Fluid Mechanics, 29(1), 245-283(1997)
[2] RUDMAN, S. and RUBIN, S. G. Hypersonic viscous flow over slender bodies with sharp leading edges. AIAA Journal, 6(10), 1883-1890(1968)
[3] ZHANG, Y. M. and ZHOU, H. Verification of parabolized stability equations for its application to compressible boundary layers. Applied Mathematics and Mechanics (English Edition), 28(8),987-998(2007) https://doi.org/10.1007/s10483-007-0801-3
[4] HAJ-HAFIRI, H. Characteristics analysis of the parabolic stability equations. Studies in Applied Mathematics, 92(1), 41-53(1994)
[5] LI, M. J. and GAO, Z. Analysis and application of ellipticity of stability equations on fluid mechanics. Applied Mathematics and Mechanics (English Edition), 24(11), 1334-1341(2003) https://doi.org/10.1007/BF02439657
[6] JEFFREY, D. Z. Interfacial Instability, Encyclopedia of Microfluidics and Nanofluidics, Springer, Boston, 866-871(2008)
[7] COWLEY, M. D. and ROSENSWEIG, R. E. The interfacial stability of a ferromagnetic fluid. Journal of Fluid Mechanics, 30(4), 671-688(1967)
[8] ZELAZO, R. E. and MELCHER, J. R. Dynamics and stability of ferrofluids:surface interactions. Journal of Fluid Mechanics, 39(1), 1-24(1969)
[9] ANJALI-DEVI, S. P. and HEMAMALINI, P. T. Nonlinear Rayleigh-Taylor instability of two superposed magnetic fluids under parallel rotation and a normal magnetic field. Journal of Magnetism and Magnetic Materials, 314(2), 135-139(2006)
[10] XU, H., LOMBARD, J. E. W., and SHERWIN, S. J. Influence of localised smooth steps on the instability of a boundary layer. Journal of Fluid Mechanics, 817(1), 138-170(2017)
[11] YAGHOOBI, A. and SHADMEHRI, M. Magnetic Rayleigh-Taylor instability in radiative flows. Monthly Notices of the Royal Astronomical Society, 477(1), 412-420(2018)
[12] CARVALHO, D. D. and GONTIJO, R. G. Magnetization diffusion in duct flow:the magnetic entrance length and the interplay between hydrodynamic and magnetic timescales. Physics of Fluids, 32(7), 072007(2020)
[13] BALLA, M., TRIPATHI, M. K., and SAHU, K. C. Shape oscillations of a nonspherical water droplet. Physical Review E, 99(2), 023107(2019)
[14] SUN, D. L. and TAO, W. Q. A coupled volume-of-fluid and level set (VOSET) method for computing incompressible two-phase flows. International Journal of Heat and Mass Transfer, 53(4), 645-655(2010)
[15] TRIPATHI, M. K., SAHU, K. C., and GOVINDARAJAN, R. Dynamics of an initially spherical bubble rising in quiescent liquid. Nature Communications, 6, 6268(2015)
[16] ZHANG, T. W., WU, J., and LIN, X. J. An interface-compressed diffuse interface method and its application for multiphase flows. Physics of Fluids, 31(12), 122102(2019)
[17] ZHANG, T. W., WU, J., and LIN, X. J. Numerical investigation on formation andmotion of bubble or droplet in quiescent flow. Physics of Fluids, 32(3), 032106(2020)
[18] YAMAGUCHI, H. Engineering Fluid Mechenics, Springer, Netherlands, 497-503(2008)
[19] CRAVERO, I., PUPPO, G., SEMPLICE, M., and VISCONTI, G. Cool WENO schemes. Computers and Fluids, 169, 71-86(2018)
[20] GLIMM, J., MARCHESIN, D., and MCBRYAN, O. Subgrid resolution of fluid discontinuities, II. Journal of Computational Physics, 37(3), 336-354(1980)
[21] WANG, C. W., LIU, T. G., and KHOO, B. C. A real ghost fluid method for the simulation of compressible flow. SIAM Journal on Scientific Computing, 28(1), 278-302(2006)
[22] LIU, T. G., KHOO, B. C., and YEO, K. S. Ghost fluid method for strong shock impacting on interface. Journal of Computational Physics, 190(2), 651-681(2003)
[23] LI, F. C., OISHI, M., KAWAGUCHI, Y., OSHIMA, N., and OSHIMA, M. Experimental study on symmetry breaking in a swirling free-surface cylinder flow influenced by viscoelasticity. Experimental Thermal and Fluid Science, 31(3), 237-248(2006)

Options

Outlines

模态框（Modal）标题

Abstract

Cite this article

References