Instability Of Plane Poiseuille Flow In A Fluid-Porous System

The instability of Poiseuille flow in a fluid-porous system is investigated. The system consists of a fluid layer overlying porous media and is subjected to a horizontal plane Poiseuille flow. We use Brinkman's model instead of Darcy's law to describe the porous layer. The eigenvalue problem is solved by means of a Chebyshev collocation method. We study the influence of the depth ratio (d) over cap and the Darcy number delta on the instability of the system. We compare systematically the instability of Brinkman's model with the results of Darcy's model. Our results show that no satisfactory agreement between Brinkman's model and Darcy's model is obtained for the instability of a fluid-porous system. We also examine the instability of Darcy's model. A particular comparison with early work is made. We find that a multivalued region may present in the (k, Re) plane, which was neglected in previous work. Here k is the dimensionless wavenumber and Re is the Reynolds number. (C) 2008 American Institute of Physics. [DOI: 10.1063/1.3000643]

Pull-In Instability Of Micro-Switch Actuators: Model Review

The existing three widely used pull-in theoretical models (i.e., one-dimensional lumped model, linear supposition model and planar model) are compared with the nonlinear beam mode in this paper by considering both cantilever and fixed-fixed type micro and nano-switches. It is found that the error of the pull-in parameters between one-dimensional lumped model and the nonlinear beam model is large because the denominator of the electrostatic force is minimal when the electrostatic force is computed at the maximum deflection along the beam. Since both the linear superposition model and the slender planar model consider the variation of electrostatic force with the beam's deflection, these two models not only are of the same type but also own little error of the pull-in parameters with the nonlinear beam model, the error brought by these two models attributes to that the boundary conditions are not completely satisfied when computing the numerical integration of the deflection.

Hydrothermal Instability Of Thermocapillary Convection In Large-Prandtl-Number Liquid Bridges Under Microgravity

Linear stability analysis was performed to study the mechanism of transition of thermocapillary convection in liquid bridges with liquid volume ratios ranging from 0.4 to 1.2, aspect ratio of 0.75 and Prandtl number of 100. 2-D governing equations were solved to obtain the steady axi-symmetric basic flow and temperature distributions. 3-D perturbation equations were discretized at the collocation grid points using the Chebyshev-collocation method. Eigenvalues and eigenfunctions were obtained by using the Q-R. method. The predicted critical Marangoni numbers and critical frequencies were compared with data from space experiments. The disturbance of the temperature distribution on the free surface causes the onset of oscillatory convection. It is shown that the origin of instability is related to the hydrothermal origin for convections in large-Prandtl-number liquid bridges. (C) 2007 COSPAR. Published by Elsevier Ltd. All rights reserved.

Thermovibrational Instability Of Rayleigh-Marangoni-Benard Convection In Two-Layer Fluid Systems

The thermovibrational instability of Rayleigh-Marangoni-Benard convection in a two-layer system under the high-frequency vibration has been investigated by linear instability analysis in the present paper. General equations for the description of the convective flow and within this framework, the generalized Boussinesq approximation are formulated. These equations are dealt with using the averaging method. The theoretical analysis results show that the high-frequency thermovibrations can change the Marangoni-Benard convection instabilities as well as the oscillatory gaps of the Rayleigh-Marangoni-Benard convection in two-layer liquid systems. It is found that vertical high-frequency vibrations can delay convective instability of this system, and damp the convective flow down. (C) 2007 COSPAR. Published by Elsevier Ltd. All rights reserved.

Dynamic Fracture Instability Of Tough Bulk Metallic Glass

We report the observations of a clear fractographic evolution from vein pattern, dimple structure, and then to periodic corrugation structure, followed by microbranching pattern, along the crack propagation direction in the dynamic fracture of a tough Zr41.2Ti13.8Cu12.5Ni10Be22.5 (Vit.1) bulk metallic glass (BMGs) under high-velocity plate impact. A model based on fracture surface energy dissipation and void growth is proposed to characterize this fracture pattern transition. We find that once the dynamic crack propagation velocity reaches a critical fraction of Rayleigh wave speed, the crack instability occurs; hence, crack microbranching goes ahead. Furthermore, the correlation between the critical velocity of amorphous materials and their intrinsic strength such as Young's modulus is uncovered. The results may shed new insight into dynamic fracture instability for BMGs. (C) 2008 American Institute of Physics.

Experimental Observation Of Electrical Instability Of Droplets On Dielectric Layer

Polydimethylsiloxane ( PDMS) has become the most widely used silicon-based organic polymer in bio-MEMS/NEMS devices. However, the inherent hydrophobic nature of PDMS hinders its wide applications in bio-MEMS/NEMS for efficient transport of liquids. Electrowetting is a useful tool to reduce the apparent contact angle of partially wetting conductive liquids and has been utilized widely in bio-MEMS/NEMS. Our experimental results show that the thin PDMS membranes exhibit good properties in electrowetting-on-dielectric. The electrical instability phenomenon of droplets was observed in our experiment. The sessile droplet lying on the PDMS membrane will lose its stability with the touch of the wire electrode to make the apparent contact angle change suddenly larger than 35 degrees. Contact mode can protect the dielectric layer from electrical breakdown effectively. Electrical breakdown process of dielectric layer was recorded by a high speed camera. It is found experimentally that a PDMS membrane of 4.8 mu m thick will not be destroyed due to the electric breakdown even at 800 V in the contact mode.

Direct Numerical Simulation Of Three-Dimensional Richtmyer-Meshkov Instability

Direct numerical simulation (DNS) is used to study flow characteristics after interaction of a planar shock with a spherical media interface in each side of which the density is different. This interfacial instability is known as the Richtmyer-Meshkov (R-M) instability. The compressible Navier-Stoke equations are discretized with group velocity control (GVC) modified fourth order accurate compact difference scheme. Three-dimensional numerical simulations are performed for R-M instability installed passing a shock through a spherical interface. Based on numerical results the characteristics of 3D R-M instability are analysed. The evaluation for distortion of the interface, the deformation of the incident shock wave and effects of refraction, reflection and diffraction are presented. The effects of the interfacial instability on produced vorticity and mixing is discussed.

An experimental study for wave-induced instability of pipelines: the breakout of pipelines

In this paper, a series of experiments have been conducted in a U-shaped oscillatory flow tunnel, which provides a more realistic simulation than the previous actuator loading methods. Based on the experimental data of pipe displacement with two different constraint conditions (freely laid pipelines and anti-rolling pipelines), three characteristic times in the process of pipeline losing stability are identified. The effects of sand size on the pipeline lateral stability are examined for freely laid pipelines. The empirical relationships between non-dimensional pipeline weight (G) and Fronde number (Fr-b) are established for different constraint conditions, which will provide a guide for engineering practice. (C) 2002 Elsevier Science Ltd. All rights reserved.

Instability of the vertically forced surface wave in a circular cylindrical container

The nonlinear amplitude equation, which was derived by Jian Yongjun employing expansion of two-time scales in inviscid fluids in a vertically oscillating circular cylindrical vessel, is modified by introducing a damping term due to the viscous dissipation of this system. Instability of the surface wave is analysed and properties of the solutions of the modified equation are determined together with phase-plane trajectories. A necessary condition of forming a stable surface wave is obtained and unstable regions are illustrated. Research results show that the stable pattern of surface wave will not lose its stability to an infinitesimal disturbance.

Effects of adiabatic exponent on Richtmyer-Meshkov instability

We present a systematical numerical study of the effects of adiabatic exponent gamma on Richtmyer-Meshkov instability (RMI) driven by cylindrical shock waves, based on the gamma model for the multi-component problems and numerical simulation with high-order and high-resolution method for compressible Euler equations. The results show that the RMI of different gamma across the interface exhibits different evolution features with the case of single gamma. Moreover, the large gamma can hold back the development of nonlinear structures, such as spikes and bubbles.

Numerical simulation of Richtmyer-Meshkov instability

The compressible Navier-Stokes equations discretized with a fourth order accurate compact finite difference scheme with group velocity control are used to simulate the Richtmyer-Meshkov (R-M) instability problem produced by cylindrical shock-cylindrical material interface with shock Mach number Ms = 1.2 and density ratio 1:20 (interior density/outer density). Effect of shock refraction, reflection, interaction of the reflected shock with the material interface, and effect of initial perturbation modes on R-M instability are investigated numerically. It is noted that the shock refraction is a main physical mechanism of the initial phase changing of the material surface. The multiple interactions of the reflected shock from the origin with the interface and the R-M instability near the material interface are the reason for formation of the spike-bubble structures. Different viscosities lead to different spike-bubble structure characteristics. The vortex pairing phenomenon is found in the initial double mode simulation. The mode interaction is the main factor of small structures production near the interface.

The plastic instability behaviour of laser-textured steel sheet

As the production of a new technique that can offer both good formability and high image clarity for texturing metal sheet, laser-textured sheet has attracted the attention of many manufacturers and users. Among the many subjects to be studied, plastic instability behaviour of the laser-textured sheet is one of most important to understand its ability in extending material ductility and to appropriately control this technique. Experimental investigations are carried out in this paper to study the macroscopic behaviour and microstructural mechanism of the laser-textured sheet, and comparison is made with the normal sheet taken from the same coil of metal sheet. It is demonstrated that, the difference in the behaviour of plastic instability obviously shows tendency to delay strain localization and the onset of thickness necking. Shear banding and internal void damage are spread to a much wider region in the sheet being laser-textured. The prestrained microcraters enforced on the surface of the textured sheet act as hardening spots, which are likely to share out deformation and inhibit the increasing rate of voiding, and eventually favouring the ductility of the material used.