Min-Hsing Chang

Instability of Poiseuille flow in a fluid overlying a porous layer

The problem of Poiseuille flow in a fluid overlying a porous medium saturated with the same fluid is studied. A careful linear instability analysis is carried out. It is shown that there are three modes of instability, two belong to one eigenvalue and persist in small ranges of parameters, while beyond these parameter ranges a third corresponding to another eigenvalue prevails. These three modes are of different stability characteristics, but are triggered by the shear stress of the Poiseuille flow in the fluid layer.

Stability of Taylor–Dean flow in a small gap between rotating cylinders

A linear stability analysis has been implemented for Taylor-Dean flow, a viscous flow between rotating concentric cylinders with a pressure gradient acting in the azimuthal direction. The analysis is made under the assumption that the gap spacing between the cylinders is small compared to the mean radius (small-gap approximation). A parametric study covering wide ranges of μ, the ratio of angular velocity of the outer cylinder to that of inner cylinder, and β, a parameter characterizing the ratio of representative pumping and rotation velocities is conducted

Effect of rotation on the electrohydrodynamic instability of a fluid layer with an electrical conductivity gradient

The electrohydrodynamic instability of a horizontal rotating fluid layer with a vertical electrical conductivity gradient is considered. An external electric field is applied across the fluid layer to induce an unstably stratified electrical body force. A linear stability analysis has been performed to study the effect of rotation on the onset of electrohydrodynamic instability in the fluid layer. Results show that the instability behaviors depend heavily on the boundary condition of bottom surface. In the case of stress-free condition, rotation enhances the stability and the onset of instability will be dominated by the oscillatory mode once the speed of rotation (or Taylor number) exceeds a critical value. In contrast, in the case of rigid bottom surface, rotation also tends to stabilize the fluid layer and the stationary mode will prevail eventually with increasing Taylor number. However rotation becomes destabilizing as the critical mode shifts from oscillatory to stationary. Moreover, under the same ...

Thermal convection in superposed fluid and porous layers subjected to a plane Poiseuille flow

Thermal convection in a two-layer system comprised by a fluid layer overlying a layer of porous media saturated with the same fluid has been investigated. The system is heated from below and subjected to a horizontally plane Poiseuille flow. The interaction between both instability mechanisms, the unstably stratification and the shear arising from the plane Poiseuille flow, is studied and a completely linear stability analysis has been carried out by considering both longitudinal rolls (LRs) and transverse rolls (TRs). It is found that the neutral curves of both modes may be bimodal, which is dependent on the depth ratio, the ratio of the depth of fluid layer to that of the porous layer. The stability characteristics of LRs are found to be invariant with the Reynolds number based on the horizontal Poiseuille velocity and the Prandtl number of the fluid, and the instability is always dominated by this mode if the Reynolds number is within low or moderate strength. The superimposed Poiseuille flow seems to ...

Stability of hydromagnetic dissipative Couette flow with non-axisymmetric disturbance

A linear stability analysis has been implemented for hydromagnetic dissipative Couette flow, a viscous electrically conducting fluid between rotating concentric cylinders in the presence of a uniform axial magnetic field. The small-gap equations with respect to non-axisymmetric disturbances are derived and solved by a direct numerical procedure. Both types of boundary conditions, conducting and non-conducting walls, are considered. A parametric study covering wide ranges of μ, the ratio of angular velocity of the outer cylinder to that of inner cylinder, and Q, the Hartmann number which represents the strength of axial magnetic field, is conducted

On the nonaxisymmetric instability of round liquid jets

A fully temporal linear stability analysis for round liquid jets is accomplished in this study. Three-dimensional disturbances are considered and a detailed parametric investigation is performed. The results indicate that only the nonaxisymmetric mode with azimuthal wavenumber m=1 may prevail over the axisymmetric mode and appear to dominate the maximum growth rate. The domain in which the nonaxisymmetric modes may start to grow is also clarified. A comparison with experimental observations in the literature is also presented. The results provide a complete understanding of the stability characteristics of round liquid jets.

Linear instability of compound jets with nonaxisymmetric disturbances

A three-dimensional linear instability analysis is carried out for a double infinitely, incompressible, and viscous compound jet moving in an inviscid surrounding gas. An analytical form of dispersion relation is derived and then solved by a direct numerical procedure. A detailed parametric study is performed to explore the instability mechanisms that cause the growth of nonaxisymmetric disturbances in compound jets. The results show that the Weber number defined on the outer interface between the ambient gas and the shell-liquid layer and the gas-to-shell density ratio both have significant influences on the growth of nonaxisymmetric instability modes, whereas the other parameters including the radius ratio, the core-to-shell density ratio, the Reynolds numbers, and the Weber number defined on the inner interface are relatively less important to the onset of the nonaxisymmetric modes. Particularly, it is found that the nonaxisymmetric sinuous mode may prevail over the axisymmetric mode for a compound jet...

Electrohydrodynamic instability in a horizontal fluid layer with electrical conductivity gradient subject to a weak shear flow

The stability of electrohydrodynamic flow between two horizontal plates with a vertical electrical conductivity gradient has been investigated in the presence of an imposed weak shear flow. The weak shear flow is driven by the horizontal pressure gradient, and the electrical conductivity gradient is generated by the concentration variation of the charge-carrying solute. An external electric field is applied across the fluid layer, and then the interaction between the unstable stratification of electrohydrodynamic flow and the shear arising from the plane Poiseuille flow is studied. A linear stability analysis has been implemented by considering both the longitudinal and transverse modes. Unlike the thermally stratified plane Poiseuille flow in which the longitudinal mode always dominates the onset of instability and is virtually unaffected by the superimposed shear flow, the instability of this mixed electrohydrodynamic– Poiseuille flow system is found to depend heavily on the shear flow, and the transverse mode may prevail over the longitudinal mode when the momentum of shear flow is sufficiently small. Particularly, an oscillatory longitudinal mode is found to exist, and it may become the critical mode when the conductivity gradient is small enough. The present results verify that an imposed weak shear flow may enhance the electrohydrodynamic instability in a fluid layer with electrical conductivity gradient.

Effects of Joule heating on the stability of time-modulated electro-osmotic flow

Effects of Joule heating and the induced variable viscosity are considered for time-modulated electro-osmotic flow in a two-dimensional microchannel confined between two infinitely parallel plates. Analytical expressions for both temperature and velocity profiles are obtained through asymptotic expansions for thin Debye layers, providing expressions for both the velocity and temperature “slip” outside these layers, and perturbation techniques for small viscosity variation. The amplitude variation of the temperature due to Joule heating is quite significant at low frequency electric fields, and decays gradually with increasing frequency. The induced variable viscosity effect changes the phase angle between velocity and harmonic electric field in comparison with the constant viscosity case, and reduces the shearing in the velocity profile. Results for the electrokinetic stability problem show that Joule heating generally exhibits a stabilizing effect.

Stability of micropolar fluid flow between concentric rotating cylinders

In this study, the theory of micropolar fluids is employed to study the stability problem of flow between two concentric rotating cylinders. The field equations subject to no-slip conditions (non-zero velocity and microrotation velocity components) at the wall surfaces are solved. The analytical solutions of the velocity and microrotation velocity fields as well as the shear stress difference, couple stress and strain rate for basic flow are obtained. The equations with respect to non-axisymmetric disturbances are derived and solved by a direct numerical procedure. It is found that non-zero wall-surface microrotation velocity makes the flow faster and more unstable. Moreover, it tends to reduce the limits of critical non-axisymmetric disturbances. The effect on the stability characteristics can be magnified by increasing the microstructure or couple-stress parameter or the microinertia parameter for the cases of corotating cylinders and a stationary outer cylinder or by decreasing the radius ratio or the microinertia parameter for the case of counterrotating cylinders.