Electrolyte Flow in an External Magnetic Field: A Dimensionless Analysis

In this paper, some recent work on the flow induced by an external magnetic fields acting on electrochemical cell is reviewed. Although the influence of the magnetic field on the hydrodynamics has been studied for over 5 decades, the magnetohydrodynamics (MHD) remains relatively unfamiliar to all but a few research groups. There are nearly a countless number of dimensionless parameters in electrolytic flow (bubble induced flow) and MHD, but they have been introduced for convenience by different authors. The similitude parameter have been modified to provide a full set of parameters for electrolytic cell operating under external magnetic field. The bubble sliding characteristics underneath an inclined plane are studied using copper sulphate solution (as an electrolyte) in lab-based-scale and discussed.

[1] S. Das, Y. S. Morsi, G. Brooks, J. J. J. Chen and W. Yang, “Principal characteristics of a bubble formation on a horizontal downward facing surface,” Colloids and Surfaces A: Physicochemical and Engineering Aspects, vol. 411, pp. 94-104, 2012.
[2] S. Das, G. Littlefair, Y. Morsi and G. Brooks, “Tracking single bubble in Hall-Héroult aluminium cell: An experimental and numerical study,” in proc. of the 3rd International Science & Technology Conference ISTEC, 2012. Time (s) Deviation (mm) 34 L. D. Weerasiri, S. Das – Electrolyte Flow….. 2015
[3] S. Das and G. Littlefair, “Current distribution and lorentz field modelling using cathode designs: A parametric approach light metals,” John Wiley & Sons, Inc. 2012, pp. 845-851.
[4] T. Sele, “Instabilities of the metal surface in electrolytic alumina reduction cells,” Metallurgical Transactions B, vol. 8, no. 4, pp. 613-618, 1977.
[5] N. Urata, “Magnetics and metal pad instability,” in proc. of sessions, AIME annual meeting light metals, Pennsylvania, 1985.
[6] S. Das, G. Brooks and Y. Morsi, “Theoretical investigation of the inclined sidewall design on magnetohydrodynamic (MHD) forces in an aluminum electrolytic cell,” Metallurgical and Materials Transactions B, vol. 42, no. 1, pp. 243-253, 2011.
[7] M. Dupuis and V. Bojarevics, “Busbar sizing modeling tools: Comparing an ANSYS® based 3D model with the versatile 1D model part of MHD-Valdis”, Light Metals, pp. 341-346, 2006.
[8] C. C. Maneri and N. Zuber, “An experimental study of plane bubbles rising at inclination,” International Journal of Multiphase Flow, vol. 1, no. 5, 623-645, 1974.
[9] T. Maxworthy, “Bubble rise under an inclined plate,” Journal of Fluid Mechanics, vol. 229, pp. 659-674, 1991.
[10] T. Maxworthy, C. Gnann, M. Kürten and F. Durst, “Experiments on the rise of air bubbles in clean viscous liquids,” Journal of Fluid Mechanics, vol. 321, pp. 421-441, 1996.
[11] J. J. J. Chen, Z. Jian Chao and Q. Kang Xing, “Rise velocity of air bubble under a slightly inclined plane submerged in water,” Paper presented at the Fifth Asian Congr. of Fluid Mechanics Taejon, Korea.
[12] A. Caboussat, L. Kiss, J. Rappaz, K. Vékony, A. Perron, S. Renaudier and O. Martin, “Large gas bubbles under the anodes of aluminum electrolysis Cells,” In S. J. Lindsay (Ed.), Light metals 2011: John Wiley & Sons, Inc, 2012, pp. 581-586.
[13] D. Bhaga and M. E. Weber, “Bubbles in viscous liquids: Shapes, wakes and velocities,” Journal of Fluid Mechanics, vol. 105, pp. 61-85, 1981.
[14] J. Grace, T. Wairegi and T. Nguyen, “Shapes and velocities of single drops and bubbles moving freely through immiscible liquids,” Trans. Inst. Chem. Eng, vol. 54, no. 3, pp. 167-173, 1976.
[15] T. Maxworthy, “Experimental studies in magneto-fluid dynamics: Pressure distribution measurements around a sphere,” Journal of Fluid Mechanics, vol. 31, no. 04, pp. 801-814, 1968.
[16] S. Das, L. D. Weerasiri and V. Jegatheesan, “Bubble flow in a static magnetic field light metals,” John Wiley & Sons, Inc, 2015, pp. 789-793.
[17] A. Solheim, S. T. Johansen, S. Rolseth and J. Thonstad, “Gas induced bath circulation in aluminium reduction cells,” Journal of Applied Electrochemistry, vol. 19, no. 5, pp. 703-712, 1989.
[18] M. C. Ruzicka, “On dimensionless numbers”, Chemical Engineering Research and Design, vol. 86, no. 8, pp. 835-868, 2008.
[19] X. Miao, D. Lucas, Z. Ren, S. Eckert and G. Gerbeth, “Numerical modeling of bubble-driven liquid metal flows with external static magnetic field”, International Journal of Multiphase Flow, vol. 48, pp. 32-45, 2013.
[20] S. Das, “Convection in fluid overlying porous layer: An application to Hall-Heroult cell”, Materials Performance and Characterization, vol. 1, no. 1, pp. 1-22, 2012.
[21] D. Price and W. Davenport, “Densities, electrical conductivities and viscosities of CuSO4 /H2SO4 solutions in the range of modern electrorefining and electrowinning electrolytes”, Metallurgical Transactions B, vol. 11, no. 1, 159-163, 1980.
[22] Kuipers, J. A. M., W. Prins and W. P. M. V. Swaaij, “Theoretical and experimental bubble formation at a single orifice in a twodimensional gas-fluidized bed”, Chemical Engineering Science, vol. 46, no. 11, pp. 2881-2894, 1991.
[23] C. Heinicke, S. Tympel, G. Pulugundla, I. Rahneberg, T. Boeck and A. Thess, “Interaction of a small permanent magnet with a liquid metal duct flow”, Journal of Applied Physics, vol. 112, no. 12.

LANKA DINUSHKE WEERASIRI, SUBRAT DAS, “Electrolyte Flow in an External Magnetic Field: A Dimensionless Analysis ”,  International Journal ofApplied and Physical Sciences, Vol. 1, no. 1, pp. 27-34, 2015