Electromechanical Costreaming and Counterstreaming Instabilities

The dynamics of two highly conducting, finite length streams in relative motion, coupled by a transverse electric or longitudinal magnetic field, are examined in detail. The systems may be mathematically described by two second‐order coupled, hyperbolic, partial differential equations. Four classes of flow exist: (I) subcapillary, (II) supercapillary costreaming, (III) supercapillary counterstreaming, and (IV) subcapillary‐supercapillary flow. The first three are considered in the present paper. The Bers‐Briggs stability criterion is applied to the dispersion relation for the infinitely long system. The eigenvalue problem is formulated for class I and III flows (no eigenvalues exist for class II flow) and the complex eigenfrequencies computed. Electrohydrodynamic experiments on these systems are described and compared with the theory. Physical explanations are given for the observed instabilities.