Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-19T03:10:09.709Z Has data issue: false hasContentIssue false
  • English
  • Français

Internal electrohydrodynamic instability and mixing of fluids with orthogonal field and conductivity gradients

Published online by Cambridge University Press:  29 March 2006

James F. Hoburg  and
James R. Melcher
James F. Hoburg
Affiliation:
Massachusetts Institute of Technology, Cambridge
James R. Melcher
Affiliation:
Massachusetts Institute of Technology, Cambridge
Get access Rights & Permissions [Opens in a new window]

Abstract

The interface between two miscible fluids which have identical mechanical properties but disparate electrical conductivities and are stressed by an equilibrium tangential electric field is studied experimentally and theoretically. A bulk-coupled electrohydrodynamic instability associated with the diffusive distribution of fluid conductivity at the interface is experimentally observed.

The configuration is modelled using a layer of exponentially varying conductivity spliced on each surface to a constant-conductivity fluid half-space. Over-stable (propagating) modes are discovered and characterized in terms of the complex growth rate and fastest growing wavenumber, with the conductivity ratio and an inertia-viscosity time-constant ratio as parameters. In the low inertia limit, growth rates are governed by the electric-viscous time τ = η/εE2. Instability is found also with the layer of varying conductivity bounded by rigid equipotential walls. A physical mechanism leading to theoretically determined fluid streamlines in the form of propagating cells is described.

At relatively high electric fields, large-scale mixing of the fluid components is observed. Photocell measurements of distributions of average fluid properties demonstrate evolution in time on a scale determined by τ.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 73 , Issue 2 , 27 January 1976 , pp. 333 - 351
Copyright
© 1976 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Betchov, R. & Criminale, W. O. 1967 Stability of Parallel Flows, p. 78. Academic.
Levich, V. G. 1962 Physicochemical Hydrodynamics, chap. 2. Prentice-Hall.
Melcher, J. R. 1972 Electrohydrodynamics. Applied Mechanics. Proc. 13th Int. Cong. Theor. Appl. Mech., Moscow, pp. 240–263. Springer.
Melcher, J. R. & Schwartz, W. J. 1968 Interfacial relaxation overstability in a tangential electric field Phys. Fluids, 11, 2604–2616.Google Scholar
Turnbuld, R. J. 1968a Electroconvective instability with a stabilizing temperature gradient. I. Theory Phys. Fluids, 11, 2588–2596.Google Scholar
Turnbull, R. J. 1968b Electroconvective instability with a stabilizing temperature gradient. II. Experimental results Phys. Fluids, 11, 2597–2603.Google Scholar
Uhl, V. W. & Gray, J. B. 1966 Mixing Theory and Practice, vol. I, chap. 1. Academic.
Woodson, H. H. & Melcher, J. R. 1968 Electromechanical Dynamics. Part II. Fields, Forces, and Motion, p. 383. Wiley.