Oscillatory Instabilities of Two-Layer Rayleigh-Marangoni-Benard Convection

The Rayleigh–Marangoni–Bénard convective instability (R–M–B instability) in the two-layer systems such as Silicone oil (10cSt)/Fluorinert (FC70) and Silicone oil (2cSt)/water liquids are studied. Both linear instability analysis and nonlinear instability analysis (2D numerical simulation) were performed to study the influence of thermocapillary force on the convective instability of the two-layer system. The results show the strong effects of thermocapillary force at the interface on the time-dependent oscillations at the onset of instability convection. The secondary instability phenomenon found in the real two-layer system of Silicone oil over water could explain the difference in the comparison of the Degen’s experimental observation with the previous linear stability analysis results of Renardy et al.

可压剪切层线性稳定性特征直接数值模拟=Direct Simulation of the Linear Instabilities in Compressible Shear Layers

基于伪随机数生成技术促生白噪声扰动,以高精度迎风/对称紧致混合差分算法求解二维/三维非定常可压Navier-Stokes方程,揭示了可压自由剪切层初始剪切过程中扰动的线性演化特征,以及该过程对扰动波数和方向的内在选择性.验证了所用算法的有效性,表明线性理论同数值模拟相结合是可压剪切层研究的合理途径之一.

Analysis of Instabilities in Non-Equilibrium Plasmas

Plasma instabilities with charged particle production processes in non-equilibrium plasma are analysed. A criterion on plasma instabilities is deduced by 6rst-order perturbation theory. The relationship between plasma instabilities and certain factors (degree of non-equilibrium in Plasma, the electron attachment rate coefficient and electron temperature) are described.

Snap-through and pull-in instabilities of an arch-shaped beam under an electrostatic loading

The snap-through and pull-in instabilities of the micromachined arch-shaped beams under an electrostatic loading are studied both theoretically and experimentally. The pull-in instability that results in a system collision with an electrode substrate may lead to a system failure and, thus, limits the system maximum displacement. The beam/plate structure with a flat initial configuration under an electrostatic loading can only experience the pull-in instability. With the different arch configurations, the structure may experience either only the pull-in instability or the snap-through and pull-in instabilities together. As shown in our computation and experiment, those arch-shaped beams with the snap-through instability have the larger maximum displacement compared with the arch-shaped beams with only the pull-in stability and those with the flat initial configuration. The snap-through occurs by exerting a fixed load, and the structure experiences a discontinuous displacement jump without consuming power. Furthermore, after the snap-through jump, the structures are demonstrated to have the capacity to withstand further electrostatic loading without pull-in. Those properties of consuming no power and increasing the structure deflection range without pull-in is very useful in microelectromechanical systems design, which can offer better sensitivity and tuning range.

Oscillatory Instabilities of Two-Layer Rayleigh-Marangoni-Benard Convection

The Rayleigh-Marangoni-Benard convective instability (R-M-B instability) in the two-layer systems such as Silicone oil (10cSt)/Fluorinert (FC70) and Silicone oil (2cSt)/water liquids are studied. Both linear instability analysis and nonlinear instability analysis (2D numerical simulation) were performed to study the influence of thermocapillary force on the convective instability of the two-layer system. The results show the strong effects of thermocapillary force at the interface on the time-dependent oscillations at the onset of instability convection. The secondary instability phenomenon found in the real two-layer system of Silicone oil over water could explain the difference in the comparison of the Degen's experimental observation with the previous linear stability analysis results of Renardy et al.

A Continuation Method Applied to the Study of Thermocapillary Instabilities in Liquid Bridges

A continuation method is applied to investigate the linear stability of the steady, axisymmetric thermocapillary flows in liquid bridges. The method is based upon an appropriate extended system of perturbation equations depending on the nature of transition of the basic flow. The dependence of the critical Reynolds number and corresponding azimuthal wavenumber on serval parameters is presented for both cylindrical and non-cylindrical liquid bridges.

Instabilities of a liquid film flowing down an inclined porous plane

The problem of a film flowing down an inclined porous layer is considered. The fully developed basic flow is driven by gravitation. A careful linear instability analysis is carried out. We use Darcy's law to describe the porous layer and solve the coupling equations of the fluid and the porous medium rather than the decoupled equations of the one-sided model used in previous works. The eigenvalue problem is solved by means of a Chebyshev collocation method. We compare the instability of the two-sided model with the results of the one-sided model. The result reveals a porous mode instability which is completely neglected in previous works. For a falling film on an inclined porous plane there are three instability modes, i.e., the surface mode, the shear mode, and the porous mode. We also study the influences of the depth ratio d, the Darcy number delta, and the Beavers-Joseph coefficient alpha(BJ) on the instability of the system.

The Convective Instabilities in a Liquid-Vapor System with a Non-equilibrium Evaporation Interface

Rayleigh-Marangoni-B,nard instability in a system consisting of a horizontal liquid layer and its own vapor has been investigated. The two layers are separated by a deformable evaporation interface. A linear stability analysis is carried out to study the convective instability during evaporation. In previous works, the interface is assumed to be under equilibrium state. In contrast with previous works, we give up the equilibrium assumption and use Hertz-Knudsen's relation to describe the phase change under non-equilibrium state. The influence of Marangoni effect, gravitational effect, degree of non-equilibrium and the dynamics of the vapor on the instability are discussed.

Instabilities in a grating feedback external cavity semiconductor laser

Output power fluctuations in a grating external cavity diode laser with Littman configuration are described, showing peculiar chaotic behaviors of self-pulsation at the L-I curve kink points. Different spectral characteristics with multiple peaks are observed at upper and lower state of the self-pulsation. It is found also that P-N junction voltage jumps in a same pace with the pulsation. The observed phenomena reflect competition between different longitudinal modes, and transient variation of transverse modes in addition. These experimental results may contain information about the mechanisms of the chaotic instability in strong filtered feedback semiconductor lasers. (C) 2008 Optical Society of America

Spatiotemporal instabilities in nonlinear Kerr media in the presence of arbitrary higher-order dispersions

Spatiotemporal instabilities in nonlinear Kerr media with arbitrary higher-order dispersions are studied by use of standard linear-stability analysis. A generic expression for instability growth rate that unifies and expands on previous results for temporal, spatial, and spatiotemporal instabilities is obtained. It is shown that all odd-order dispersions contribute nothing to instability, whereas all even-order dispersions not only affect the conventional instability regions but may also lead to the appearance of new instability regions. The role of fourth-order dispersion in spatiotemporal instabilities is studied exemplificatively to demonstrate the generic results. Numerical simulations confirm the obtained analytic results. (C) 2002 Optical Society of America.

Analytical method of predicating the instabilities of a micro arch-shaped beam under electrostatic loading

An arch-shaped beam with different configurations under electrostatic loading experiences either the direct pull-in instability or the snap-through first and then the pull-in instability. When the pull-in instability occurs, the system collides with the electrode and adheres to it, which usually causes the system failure. When the snap-through instability occurs, the system experiences a discontinuous displacement to flip over without colliding with the electrode. The snap-through instability is an ideal actuation mechanism because of the following reasons: (1) after snap-through the system regains the stability and capability of withstanding further loading; (2) the system flips back when the loading is reduced, i.e. the system can be used repetitively; and (3) when approaching snap-through instability the system effective stiffness reduces toward zero, which leads to a fast flipping-over response. To differentiate these two types of instability responses for an arch-shaped beam is vital for the actuator design. For an arch-shaped beam under electrostatic loading, the nonlinear terms of the mid-plane stretching and the electrostatic loading make the analytical solution extremely difficult if not impossible and the related numerical solution is rather complex. Using the one mode expansion approximation and the truncation of the higher-order terms of the Taylor series, we present an analytical solution here. However, the one mode approximation and the truncation error of the Taylor series can cause serious error in the solution. Therefore, an error-compensating mechanism is also proposed. The analytical results are compared with both the experimental data and the numerical multi-mode analysis. The analytical method presented here offers a simple yet efficient solution approach by retaining good accuracy to analyze the instability of an arch-shaped beam under electrostatic loading.

Non-modal instabilities of two-dimensional disturbances in plane Couette flow of a power-law fluid

Instabilities of fluid flows have traditionally been investigated by normal mode analysis, i.e. by linearizing the equations of flow and testing for unstable eigenvalues of the linearized problem. However, the results of eigenvalue analysis agree poorly in many cases with experiments, especially for shear flows. In this paper we study the instabilities of two-dimensional Couette flow of a polymeric fluid in the framework of non-modal stability theory rather than normal mode analysis. A power-law model is used to describe the polymeric liquid. We focus on the response to external excitations and initial conditions by examining the pseudospectra structures and the transient energy growths. For both Newtonian and non-Newtonian flows, the results show that there can be a rather large transient growth even though the linear operator of Couette flow has no unstable eigenvalue. The effects of non-Newtonian viscosity on the transient behaviors are examined in this study. The results show that the "shear-thinning/shear-thickening" effect increases/decreases the amplitude of responses to external excitations and initial conditions. (C) 2010 Elsevier B.V. All rights reserved.

Instabilities and transient behaviors of a liquid film flowing down a porous inclined plane

The nonmodal linear stability of a falling film over a porous inclined plane has been investigated. The base flow is driven by gravity. We use Darcy's law to describe the flow in the porous medium. A simplified one-sided model is used to describe the fluid flow. In this model, the influence of the porous layer on the flow in the film can be identified by a parameter beta. The instabilities of a falling film have traditionally been investigated by linearizing the governing equations and testing for unstable eigenvalues of the linearized problem. However, the results of eigenvalue analysis agree poorly in many cases with experiments, especially for shear flows. In the present paper, we have studied the linear stability of three-dimensional disturbances using the nonmodal stability theory. Particular attentions are paid to the transient behavior rather than the long time behavior of eigenmodes predicted by traditional normal mode analysis. The transient behaviors of the response to external excitations and the response to initial conditions are studied by examining the pseudospectral structures and the energy growth function G(t) Before we study the nonmodal stability of the system, we extend the results of long-wave analysis in previous works by examining the linear stabilities for streamwise and spanwise disturbances. Results show that the critical conditions of both the surface mode and the shear mode instabilities are dependent on beta for streamwise disturbances. However, the spanwise disturbances have no unstable eigenvalue. 2010 American Institute of Physics. [doi:10.1063/1.3455503]

Instabilities in a non-transferred direct current plasma torch operated at reduced pressure

Using an oscilloscope, a high-speed video camera and a double-electrostatic probe system, the periodicity and amplitude of the fluctuations in arc voltage, jet luminance and ion saturation current of a plasma jet were monitored to investigate various sources of instabilities and their effects in a non-transferred dc plasma torch operated at reduced pressure. The results show that besides a 300 Hz main fluctuation inherited from the power supply, arc voltage fluctuation of 3–4 kHz with an amplitude less than 5% of the mean voltage was mainly affected by the total gas flow rate. The arc voltage fluctuation can affect the energy distribution of the plasma jet which is detectable by electrostatic probes and a high-speed video camera. The steadiness of energy transfer is also affected by the laminar or turbulent flow state of the plasma.

Spin and spin-isospin instabilities and Landau parameters of Skyrme interactions with tensor correlations

The Landau parameters of Skyrme interactions in the spin and spin-isospin channels are studied using various Skyrme effective interactions with and without tensor correlations. We focus on the role of the tensor terms on the spin and spin-isospin instabilities that can occur in nuclear matter above saturation density. We point out that these instabilities are realized in nuclear matter at the critical density of about two times the saturation density for all the adopted parameter sets. The critical density is shown to be very much dependent not only on the choice of the Skyrme parameter set, but also on the inclusion of the tensor terms.