ABSTRACT
The temporal linear instability of a coaxial jet with two immiscible Newtonian liquids in both the axial and radial electric fields is studied. The outer liquid is supposed to be a leaky dielectric and the inner liquid a perfect dielectric. The eigenvalue problem for both axisymmetric instability and helical instability is formulated and solved using the spectral method. Different from axisymmetric instability, for helical instability there is only one unstable mode, i.e., the helical mode, located in the long wave region. The axial electric field is found to have a strong stabilization effect on both the axisymmetric and helical modes, and the radial electric field has a great destabilization effect on them. The competition between the axisymmetric and helical instability under the action of the axial and radial electric fields is calculated. The boundary curve separating the stabilization and destabilization regions of the parasinuous mode, the neutral stability curve of the helical mode, and the boundary curve between the dominant regions of the axisymmetric and helical instability are plotted on the Q0-Eu plane and Pi-Eu plane, respectively (Q0 is the dimensionless surface charge density; Eu is the electrical Euler number representing the characteristic tangential electrostatic force; and Pi=Q0;2Eu is the dimensionless parameter representing the characteristic normal electrostatic force). In general, when surface charge density is small, the helical mode is stable, and the parasinuous mode is dominant; however, when surface charge density is sufficiently large, the helical mode is destabilized and becomes dominant in jet instability. Liquid viscosity influences the predominance of the helical mode significantly. Although liquid viscosity decreases the growth rates of both the axisymmetric and helical modes, it suppresses the axisymmetric instability much more than the helical instability, and therefore favors the realization of the helical instability in experiments.
ABSTRACT
A temporal linear stability analysis is carried out for a coflowing jet with two immiscible inviscid liquids under a uniform axial electric field. According to the electrical properties of the inner and outer liquids, four cases, i.e., IDOC (inner: dielectric; outer: conductor), ICOD (inner: conductor; outer: dielectric), ICOC (inner and outer: conductor), and IDOD (inner and outer: dielectric), are considered. The analytical dimensionless dispersion relation is derived for both axisymmetric and nonaxisymmetric perturbations and is solved for axisymmetric ones. Three unstable modes, i.e., the paravaricose, parasinuous and transitional modes, are identified in the Rayleigh regime. The influences of the axial electric field, liquid electrical properties, and Weber number are studied at length. The results show that the axial electric field has a generally stabilizing effect on the unstable modes. The effects of the liquid electrical properties are quite different but all great for each case. The change of dominant mode is detected with the variation of the electric field intensity, electrical properties or Weber number. It is found that the parasinuous instability is the easiest to realize in IDOC. And the comparison with the experiment validates that the parasinuous mode is predominant in coaxial electrospray.
ABSTRACT
Three-dimensional steady Rayleigh-Bénard convection in a vertical cylinder is investigated by numerical simulation and bifurcation analysis. The complex pattern formation beyond the onset of the convection is presented by a bifurcation diagram. The coexistence of multiple stable states is observed near the threshold of the first bifurcation and two group symmetries are summarized for the corresponding primary branches. The first stable target pattern originates through a subcritical bifurcation. A multiplicity of flow states for the Rayleigh number of 14200 is validated numerically in comparison with the experiment, and a four-spoke pattern is observed.
