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The Quarterly Journal of Mechanics and Applied Mathematics 1992 45(1):25-46; doi:10.1093/qjmam/45.1.25
© 1992 by Oxford University Press
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THE ONSET OF OVERSTABLE MOTIONS IN A LAYER OF DIELECTRIC LIQUID SUBJECTED TO THE SIMULTANEOUS ACTION OF A WEAK UNIPOLAR INJECTION OF CHARGE AND A THERMAL GRADIENT

F. PONTIGA, A. CASTELLANOS and A. T. RICHARDSON

( Departmento de Electrónica y Electromagnetismo, Universidad de Sevilla Spain
Department of Engineering Mathematics, University of Bristol, University Walk Bristol BS8 1TR )

A linear instability analysis of a planar layer of dielectric liquid subjected to both an injection of ions and an applied temperature difference is performed. The variations of both the ionic mobility and the electrical permittivity are assumed to be linear in temperature. Whilst the injection of ions is expected to occur only from the lower electrode, heating may be applied at either the lower or the upper one. Special attention is given to the onset of oscillatory, is likely to prevail. The resulting bifurcation curves are determined by both semi-analytic and numerical analyses. If the thermally-induced variations across the liquid layer of mobility and permittivity are sufficiently weak then the domain where the oscillatory mode is preferred encroaches significantly into regions of parameter space where all the convective modes have a negative growth rate.


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