Electrohydrodynamic instability of miscible core–annular flows with electrical conductivity stratification

Abstract

AbstractThis paper investigates the electrohydrodynamical instability of two miscible flows in a micro-pipe subject to an axial electric field. There is an electrical conductivity stratification between the two layers. A weak shear flow arises from a constant axial pressure gradient. The three-dimensional linear stability analysis is studied under the assumption of a quasi-steady state. The influences of the conductivity ratio ${\it\eta}$, the interface location $a$, the interface thickness ${\it\delta}$, the Reynolds number $\mathit{Re}$ and the Schmidt number $\mathit{Sc}$ on the linear stability of the flows are investigated. The flow becomes more unstable for a larger conductivity contrast. When the conductivity in the inner layer is larger, the critical unstable mode can be dominated by either the corkscrew mode (the azimuthal wavenumber $m=1$) or the axisymmetric mode ($m=0$), which is dependent on the interface location $a$. It is observed that, when the interface is proximal to pipe’s wall, the critical unstable mode shifts from the corkscrew mode to the axisymmetric mode. When the conductivity is larger in the outer layer, the instability is dominated by the axisymmetric mode. A detailed parametric study shows that the flow is least stable when the interface between the two liquids is located at approximately $a=0.3$ and $a=0.2$ for conductivity ratios of ${\it\eta}=0.5$ and ${\it\eta}=2$ respectively. The flow becomes more stable as the interface becomes thicker, and the shear flow and ionic diffusion are found to have a stabilizing effect due to the enhancement of dissipation mechanisms.