Localization of electric fields, currents, and superheating instability in a conductive liquid on the surface of ellipsoidal inhomogeneities

Abstract

It is well known [i] that the presence of inhomogeneities in a heated liquid may be the cause of formation of explosive boiling regions. According to [2], such regions may form in the vicinity of filaments heated by electric currents, or in the vicinity of spherical inclusions in the liquid, through which electrical currents also pass [3]. If the liquid surrounding the inhomogeneity is characterized by a nonlinear temperature dependence of electrical conductivity, the cause of explosive heterogeneous liquid boiling may be development of superheating instability, which, according to [4, 5], leads to current pinching on the electrode surfaces. Since macroscopic inclusions in the liquid may be maintained in a stable state by external magnetic [6] or electric [7] fields (the inclusions may serve as a means of discharge initiation in the liquid [8-10]), it is of interest to study in greater detail the localization of fields, currents, and Joulean energy dissipation on the surface of inhomogeneities, as well as the conditions for development of superheating instability on inclusions. It should be noted that these questions were partially considered in [3, 11-14], from which the following conclusions follow: I) Highly conductive inhomogeneities are more able to concentrate current and Joulean heat liberation than weakly conductive ones; 2) in the vicinity of highly conductive inclusions the current maximum is localized near points (poles) on the liquid-inclusion boundary, while for weakly conductive inclusions the maximum is in the zone of the equatorial line (Fig. i); an increase in the prolateness of conductive inclusions along the external electric field leads to an increase in concentration of field, current, and ~oulean heat dissipation in the surrounding liquid.