The effect of Joule-heating-induced buoyancy on the electrohydrodynamic instability in a fluid layer with electrical conductivity gradient. (English) Zbl 1219.80027
Summary: Applying an electric field across a fluid layer with a conductivity gradient can induce an electrical body force destabilizing the flow and simultaneously generate Joule-heating effect. For microfluidic devices with high surface area to volume ratio, the Joule heating can be removed and the onset of instability occurs only when the electrical body force overcomes the viscous force. For mini-scale devices containing conducting solutions, the Joule heating can induce thermal buoyancy sufficiently to affect the stability. This paper performs an analysis to examine the possible impact on the stability due to the presence of Joule-heating-induced buoyancy. Results show that for the cases of low conductivity gradient, the induced buoyancy always appears to enhance the electrohydrodynamic instability regardless of the direction of buoyancy. However, at high conductivity gradients, the buoyancy may become a stabilizing mechanism if the electrical field and the buoyancy are on the opposite direction.
MSC:
| 80A20 | Heat and mass transfer, heat flow (MSC2010) |
| 76W05 | Magnetohydrodynamics and electrohydrodynamics |
| 76R10 | Free convection |
| 76E25 | Stability and instability of magnetohydrodynamic and electrohydrodynamic flows |
References:
| [1] | Melcher, J. R.; Taylor, G. I.: Electrohydrodynamics: a review of the role of interfacial shear stresses, Annu. rev. Fluid mech. 1, 11-146 (1969) |
| [2] | Hoburg, J. F.; Melcher, J. R.: Internal electrohydrodynamic instability and mixing of fluids with orthogonal field and conductivity gradients, J. fluid mech. 73, 333-351 (1976) · Zbl 0341.76018 · doi:10.1017/S0022112076001390 |
| [3] | Hoburg, J. F.; Melcher, J. R.: Electrohydrodynamic mixing and instability induced by collinear field and conductivity gradients, Phys. fluids 20, 903-911 (1977) · Zbl 0361.76045 · doi:10.1063/1.861967 |
| [4] | Hoburg, J. F.: Internal electrohydrodynamic instability of liquids with collinear field and conductivity gradients, J. fluid mech. 84, 291-303 (1978) · Zbl 0369.76096 · doi:10.1017/S0022112078000178 |
| [5] | Manz, A.; Graber, N.; Widmer, H.: Miniaturized total chemical analysis systems: a novel concept for chemical sensing, Sens. actuators, B 1, 244 (1990) |
| [6] | Reyes, D. R.; Iossifidis, D.; Auroux, P. A.; Manz, A.: Micro total analysis systems. 1. Introduction, theory, and technology, Anal. chem. 74, 2623-2636 (2002) |
| [7] | Stone, H. A.; Stroock, A. D.; Ajdari, A.: Engineering flow in small devices: microfluidics toward a lab-on-a-chip, Annu. rev. Fluid mech. 36, 381-411 (2004) · Zbl 1076.76076 · doi:10.1146/annurev.fluid.36.050802.122124 |
| [8] | Turnbull, R. J.: Effect of dielectrophoretic forces on the bernard instability, Phys. fluids 12, 1809-1815 (1969) |
| [9] | Melcher, J. R.; Firebaugh, M. S.: Traveling-wave bulk electroconvection induced across a temperature gradient, Phys. fluids 10, 1178-1185 (1967) |
| [10] | Baygents, J. C.; Baldessari, F.: Electrohydrodynamic instability in a thin fluid layer with an electrical conductivity gradient, Phys. fluids 10, 301-311 (1998) |
| [11] | Chang, M. H.; Ruo, A. C.; Chen, F.: Electrohydrodynamic instability in a horizontal fluid layer with electrical conductivity gradient subject to a weak shear flow, J. fluid mech. 634, 191-215 (2009) · Zbl 1183.76735 · doi:10.1017/S0022112009007782 |
| [12] | Ruo, A. C.; Chang, M. H.; Chen, F.: Effect of rotation on the electrohydrodynamic instability of a fluid layer with an electrical conductivity gradient, Phys. fluids 22, 024102 (2010) · Zbl 1183.76444 · doi:10.1063/1.3308542 |
| [13] | Cetin, B.; Li, D.: Effect of joule heating on electrokinetic transport, Electrophoresis 29, 994-1005 (2008) |
| [14] | Xuan, X.: Joule heating in electrokinetic flow, Electrophoresis 298, 33-43 (2008) |
| [15] | Cao, J.; Cheng, P.; Hong, F. -J.: Applications of electrohydrodynamics and joule heating effects in microfluidic chips: a review, Sci. China ser. E-technol. Sci. 52, 3477-3490 (2009) · Zbl 1252.76089 |
| [16] | Boyd, J. P.: Chebyshev and Fourier spectral methods, (2001) · Zbl 0994.65128 |
| [17] | Yuan, Q.; He, Z.; Leng, H.: An improvement for Chebyshev collocation method in solving certain Sturm – Liouville problems, Appl. math. Comput. 195, 440-447 (2008) · Zbl 1132.65072 · doi:10.1016/j.amc.2007.04.113 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
