Study on MHD Cylindrical Couette Flow and Rheological Properties of Some Magnetic Suspensions

  • S.E. E. Hamza Physics Department, Faculty of Science, Benha University, Benha, Egypt
Keywords: MHD flow, Concentric cylinders, Couette flow, Bessel function, Magnetic suspensions, Ferrofluids, Giesekus model, Nano-particles


The study of magnetic suspensions (MS) and magnetic field effects on their rheological properties is of evident practical importance due to its ability to orient and change their physical properties, especially their viscosity, by magnetic fields. This research presents the effect of a uniform magnetic field on the flow of MS in the annular region between two concentric cylinders. The motion of the fluid is due to the rotation of the inner cylinder with a constant angular velocity. An exact solution of the governing equations is obtained in the form of modified Bessel functions of the first and second kinds. The torque, which must be applied to the inner cylinder in order to maintain the rotation, is also calculated. The results show that as the magnetic parameter increases, the velocity profile decreases, while the torque increases due to the effect of magnetic force against the flow direction.

In order to model the magnetoviscous effects, experiments were performed for different shear rates and different magnetic field strengths by using specially designed rheometers. The studied samples are iron oxide-water-glycerol system,  ferrofluid nanoparticles, MAG DX biocompatible ferrofluid. The theoretical analysis is based on Giesekus model for MS. This model gives more accurate results and takes into account the effects of viscoelastic shear thinning characteristics. It is found that a magnetic field increases the viscosity of all suspensions under consideration. Finally, new proposed correlation for the viscosity of MS as a function of both shear rate and magnetic field has been suggested.


Download data is not yet available.


Bird, R.B., Armstrong, R.C. and Hassager, O. Dynamics of polymeric liquids. Wiley-Interscience, New York (1987).

Dery, J.P., Borra, E.F. and Ritcey, A.M. Ethylene glycol based ferrofluid for the fabrication of magnetically deformable liquid mirrors. Chemistry of Materials, 20 (2008) 6420–2426.

Sansom, C.L., Jones, P., Dorey, R.A., Beck, C., Stanhope-Bosumpim, A. and Peterson, J. Synthesis and characterization of Mn0.5Zn0.5Fe2O4 and Fe3O4 nanoparticle ferrofluids for thermo-electric conversion. Journal Magnetism and Magnetic Materials, 335 (2013) 159–162.

Atif, S.M., Hussain, S. and Sagheer, M. Numerical study of MHD micropolar carreau nanofluid in the presence of induced magnetic field. AIP Adv, 8 (2018) 1–20.

Rinaldi, C., Chaves, A., Elborai, S., He, X. and Zahn, M. Magnetic ?uid rheology and ?ows. Curr Opin Colloid Interface Sci, 10 (2005) 141–157.

Pop, L.M., Hilljegerdes, J., Odenbach, S. and Wiedenmann, A. The microstructure of ferrofluids and their rheological properties. Appl Org Chem, 18 (2004) 523–528.

Odenbach, S. Recent progress in magnetic ?uid research. J Phys Condens Matter, 16 (2004) 1135–1150.

Gan Jia Gui, N., Stanley, C., Nguyen, N.T. and Rosengarten, G. Ferrofluids for heat transfer enhancement under an external magnetic field. Int J Heat Mass Trans, 123 (2018) 110–121.

Kimura, T. Study on the effect of magnetic fields on polymeric materials and its application. Polym J, 35 (2003) 823–843.

Vshivkov, S.A. and Rusinova, E. Effect of magnetic field on the rheological properties of poly(ethylene glycol) and poly(dimethylsiloxane) mixtures with aerosil and iron nanoparticles. Poly Sci A, 59 (2017) 764–771.

Ghasemi, E., Mirhabibi, A. and Edrissi, M. Synthesis and rheological properties of an iron oxide ferrofluid. J Magn Magn Mater, 320 (2008) 2635–2639.

Hong, R.Y., Ren, Z.Q., Han, Y.P., Li HZ, Zheng, Y. and Ding, J. Rheological properties of water-based Fe3O4 ferrofluids. Chem Eng Scie, 62 (2007) 5912–5924.

Odenbach, S. and Stork, H. Shear dependence of field-induced contributions to the viscosity of magnetic fluids at low shear rates. J Magn Magn Mater, 183 (1998) 188–194.

Yu Zubarev, A., Fleischer, J. and Odenbach, S. Towards a theory of dynamical properties of polydisperse magnetic fluids: Effect of chain-like aggregates. Physica A, 358 (2005) 475–491.

Skumryev, V., Stoyanov, S., Zhang, Y., Hadjipanayis, G., Givord, D. and Nogues, J. Beating the superparamagnetic limit with exchange bias. Nature, 423 (2003) 850–853.

De Gans, B.J., Duin, N.J., Van den Ende, D. and Mellema J. The in?uence of particle size on the magnetorheological properties of an inverse ferro?uid. J Chem Phys, 113 (2000) 2032–2042.

Wang, J.M., Kang, J.F., Zhang, Y.J. and Huang, X.J. Viscosity monitoring and control on oil-?lm bearing lubrication with ferro?uids. Tribol Int, 75 (2014) 61–68.

Shchukin, D.G., Radtchenko, I.L. and Sukhorukov, G.B. Micron-scale hollow poly-electrolyte capsules with nanosized magnetic Fe3O4 inside. Mater Lett, 57 (2003) 1743–1747.

Chiriac, H. and Stoian, G. In?uence of the particles size and size distribution on the magnetorheological ?uids properties. IEEE Trans Magn, 45 (2009) 4049–4055.

Berger, P., Adelman, N.B., Beckman, K.J., Campbell, D.J., Ellis, A.B. and Lisensky, G.C. Preparation and properties of an aqueous ferro?uid. J Chem Educ, 76 (1999) 943–948.

Love, J.C., Urbach, A.R., Prentiss, M.G. and Whitesides, G.M. Three dimensional self-assembly of metallic rods with submicron diameters using magnetic interactions. J Am Chem Soc, 125 (2003) 12696–12697.

Shah, K., Oh, J.S., Choi, S.B. and Upadhyay, R. Plate-like iron particles based bidisperse magnetorheological ?uid. J Appl Phys, 114 (2013) 213904.

Dai, J., Yang, M., Li, X., Liu, H. and Tong, X. Magnetic ?eld sensor based on magnetic ?uid clad etched ?ber Bragg grating. Opt Fiber Tech, 17 (2011) 210–213.

Odenbach, S. and Colloids, J.S. Colloids and surfaces A: physicochemical and engineering aspects. Physicochem. Eng Aspects, 217 (2003) 171.

Sheparovych, R., Sahoo, Y., Motornov, M., Wang, S., Luo, H., Prasad, P.N., Sokolov, I. and Minko, S. Polyelectrolyte stabilized nanowires from Fe3O4 nanoparticles via magnetic ?eld induced self assembly. Chemistry of Materials, 18 (2006) 591–593.

Ding, X., Sun, Z., Zhang, W., Peng, Y., Chan, A.S.C. and Li, P. Characterization of Fe3O4/poly(styrene-co-N-isopropylacrylamide) magnetic particles with temperature sensitivity. Colloid Polym Sci, 278 (2000) 459–463.

Vshivkov, S.A., Rusinova, E.V. and Galyas, A.G. Effect of a magnetic field on the rheological properties of iron oxide-water-glycerol system. Rheol Acta, 55 (2016) 155–161.

Dhumal, J., Bandgar, S., Zipare, K. and Shahane, G. Fe3O4 ferrofluid nanoparticles: synthesis and rheological behavior. Int J of Materials Chem and Phys, 1 (2015) 141–145.

Nowak, J. and Odenbach, S. Magnetoviscous effect in a biocompatible ferrofluid. IEEE Trans on Magnetics, 49 (2013) 208–212.

Linke, J.M. and Odenbach, S. Anisotropy of the magnetoviscous effect in a ferro?uid with weakly interacting magnetite nanoparticles. J Phys Condens Matter, 27 (2015) 176001.

Hamza, S.E.E. A comparison of rheological models and experimental data of metallocene linear low density polyethylene solutions as a function of temperature and concentration. J Adv Phys, 12 (2016) 4322–4339.

Hamza, S.E.E. Modelling the effect of concentration on non–Newtonian apparent viscosity of an aqueous polyacrylamide solution. Global J Phys, 5 (2016) 505–517.

Hamza, S.E.E. MHD flow of cellulose derivatives and dilute suspensions rheology of its nanocrystals. American Journal of Fluid Dynamics, 7 (2017) 23–40.

How to Cite
E. Hamza, S. (2019). Study on MHD Cylindrical Couette Flow and Rheological Properties of Some Magnetic Suspensions. JOURNAL OF ADVANCES IN PHYSICS, 16(1), 119-140.