Experimental Study on Liquid Free Surface in Buoyant-Thermocapillary Convection

We investigate the surface deformations of buoyant-thermocapillary convection in a rectangular cavity due to gravity and temperature gradient between the two sidewalls. The cavity is 52mm×42 mm in horizontal cross section, the thickness of liquid layer h is changed from 2.5 mm to 6.5 mm. Surface deformations of h = 3.5 mm and 6.0mm are discussed and compared. Temperature difference is increased gradually, and the flow in the liquid layer will change from stable convection to unstable convection. Two kinds of optical diagnostic system with image processor are developed for study of the kinetics of buoyant-thermocapillary convection, they give out the information of liquid free surface. The quantitative results are calculated by Fourier transform and correlation analysis, respectively. With the increasing temperature gradient, surface deformations calculated are more declining. It is interesting phenomenon that the inclining directions of the convections in thin and thick liquid layers are different. For a thin layer, the convection is mainly controlled by thermocapillary effect. However, for a thick layer, the convection is mainly controlled by buoyancy effect. The surface deformation theoretically analysed is consistent with our experimental results. The present experiment proves that surface deformation is related to temperature gradient and thickness of the liquid layer. In other words, surface deformation lies on capillary convection and buoyancy convection.     

Universality in crossover function for convection in fluids with a free surface

We show that in the onset of convection in a thin fluid layer with a free surface, the passage from surface tension driven to buoyancy driven convection with changing thickness of the fluid layer follows a universal curve and can be calculated very accurately using a variational method. We have shown that the balance between surface tension traction to buoyancy force determines the crossover length scale of the fluid which is independent of viscosity or thermal diffusivity. We suggest a scenario near critical point of fluids in which this crossover can be observed.     

Experimental Investigation of Influence of Interfacial Tension on Convection of Two-Layer Immiscible Liquid

Bdnard-Marangoni convections of two-layer fluids heated from the bottom are investigated experimentally with a particle imagine velocimetry. The flows are visualized from the side, and various velocity fields near the onset of convection, such as three-layer vortex convective patterns, are observed when the depth ratio varies in a wide range. A new classification of the convective patterns is proposed with more detail than in previous studies. The analysis of the results indicates that the interface tension greatly influences the motion intensities of the bottom and top layers. The dimensionless wave number increases with the Bond number when the motion in the top layer is not more intense than that in the bottom layer, which agrees with the theoretical prediction.     

Chevron patterns and defect lattices in an anisotropic model for electroconvection

Chevron patterns and defect lattices are unique patterns found in the electrohydrodynamic convection of nematic liquid crystals. We study numerically the stability and bifurcations of the chevron patterns and the limit-cycle oscillation of defect lattices using a two-dimensional anisotropic model equation. Simplified one dimensional models are derived by truncating Fourier modes from the two-dimensional model to qualitatively understand the chevron patterns and the defect lattices. The pattern formation and the dynamical behaviors in the one-dimensional models are compared with the numerical simulations of the two-dimensional model.     

Role of Convection Flow on the Pattern Formation in the Drying Process of Colloidal Suspension

We study the macroscopic drying patterns of aqueous suspensions of colloidal silica spheres. It was found that convection strength can influence pattern formation. Uniformed films are obtained at weaker convection strength. In addition, we make clear that it is not reasonable to discuss individually the effect of temperature and humidity on the colloid self-assembly. The physical mechanism is that these factors have relationship with the evaporation rate, which can affect the convection strength.     

Spatio-temporal patterns in the thermoconvection of a planar nematic layer: I. Weakly nonlinear models

We study theoretically the formation of convection patterns in a laterally extended planar nematic layer heated from below, in the linear and weakly nonlinear regimes. By reformulating the viscous coupling terms of the basic nematohydrodynamic equations, a simple interpretation of the flow effects on the director dynamics can be proposed. A detailed linear analysis of the problem is presented. A systematic method to investigate nonlinear mechanisms is developed, and exemplified by the study of the nonlinear saturation in rolls. The extension of the roll amplitude equation with the envelope formalism is used to characterize the dynamics of the roll modulations near threshold. Coupled envelope equations are shown to describe the structure of the point defects in zig-zags observed experimentally. Finally the bifurcation to the bimodal varicose is studied. The secondary wavevector in the bimodal appears to be selected by a rotation of the director in the horizontal plane. Quantitative predictions concerning the amplitude of this rotation are given. Received: 1st December 1997 / Revised: 25 May 1998 / Accepted: 2 June 1998     

Influence of the surface deformability and variable viscosity on buoyant - thermocapillary instability in a liquid layer

The primary stationary and oscillatory Bénard-Marangoni instability is investigated in a fluid layer of infinite horizontal extent, bounded below by a rigid plane and above by a deformable upper surface, subjected to a vertical temperature gradient. Since the viscosity is temperature-dependent the consequences of relaxing Oberbeck-Boussinesq approximation and free surface deformability are theoretically examined by means of small disturbance analysis. The problem has been solved numerically by the Taylor series expansion method. The results obtained confirm that when the free surface is undeformable, stationary convection develops in the form of polygonal cells, and oscillatory motion cannot be detected. When the surface deformability is considered, stationary convection sets in, either as a short-wavelength hexagonal instability or as a long-wavelengh mode or as both, and oscillatory convection is also possible. The stability threshold for the short-wavelength mode depends mainly on the viscosity variation while the long-wavelength mode is determined by the surface deformation. Numerically, it is found that the neutral oscillatory Marangoni numbers are only negative. When a variable-viscosity model is used the theoretical and experimental results are in better agreement. Received 15 May 1997     

A domain decomposition method for two-phase transport model in the cathode of a polymer electrolyte fuel cell

Using Kirchhoff transformation, we develop a Dirichlet–Neumann alternating iterative domain decomposition method for a 2D steady-state two-phase model for the cathode of a polymer electrolyte fuel cell (PEFC) which contains a channel and a gas diffusion layer (GDL). This two-phase PEFC model is represented by a nonlinear coupled system which typically includes a modified Navier–Stokes equation with Darcy’s drag as an additional source term of the momentum equation, and a convection–diffusion equation for the water concentration with discontinuous and degenerate diffusivity. For both cases of dry and wet gas channel, we employ Kirchhoff transformation and Dirichlet–Neumann alternating iteration with appropriate interfacial conditions on the GDL/channel interface to treat the jump nonlinearities in the water equation. Numerical experiments demonstrate that fast convergence as well as accurate numerical solutions are obtained simultaneously owing to the implementation of the above-described numerical techniques along with a combined finite element-upwind finite volume discretization to automatically control the dominant convection terms arising in the gas channel.     

Nonlinear-driven instability of dynamical plasma in solids: Emergence of spatially self-organized order and chaotic-like behavior

We analyze in detail the nonlinear kinetics of a carrier system in a photoinjected plasma in semiconductors under the action of constant illumination with ultraviolet light. We show that the spatially homogeneous steady-state becomes unstable, and a charge density wave emerges after a critical intensity of the incident radiation is achieved. It is shown that this instability can only follow in doped p-type materials. In bulk systems the critical intensity was found to be too high making the phenomenon not observable under realistic experimental conditions. However, a more efficient electron excitation can be obtained in low dimensional p-type systems, like some molecular and biological polymers, where the interaction may follow by chemical interaction with the medium. We show that for intensities beyond the critical threshold an increasing number of modes provide further contributions (subharmonics) to the space inhomogeneity. It is conjectured that this process could lead the system to display chaotic-like behavior. Received 8 July 1998 and Received in final form 6 May 1999     

Derivation of the amplitude equation for a hydromagnetic convective problem

The amplitude equation for a convective system under a vertical magnetic field is derived. The coefficients in these equations have been numerically calculated for infinite Prandtl number fluids and for boundary conditions both free and rigid top and bottom. The results confirm that, for realistic parameter values only stationary convection can be present and the pattern is made by convective rolls.     

Onset of Unsteady Horizontal Convection in Rectangular Tank at Pr=1

The horizontal convection within a rectangular tank is numerically simulated. The flow is found to be unsteady at high Rayleigh numbers. There is a Hopf bifurcation of Ra from steady solutions to periodic solutions, and the critical Rayleigh number Rac is obtained to be Rac = 5.5377×10^8 for the middle plume forcing at Pr = 1, which is much larger than the value previously obtained. In addition, the unstable perturbations are always generated from the central jet, which implies that the onset of instability is due to velocity shear （shear instability） other than thermally dynamics （thermal instability）. Finally, Paparella and Young＇s first hypotheses [J. Fluid Mech. 466 （2002） 205] about the destabilization of the flow is numerically proven, i.e. the middle plume forcing can lead to a destabilization of the flow.     

Numerical analysis of the Eckhaus instability in travelling-wave convection in binary mixtures

The Eckhaus stability boundaries of travelling periodic roll patterns arising in binary fluid convection is analysed using high-resolution numerical methods. We present results corresponding to three different values of the separation ratio used in experiments. Our results show that the subcritical branches of travelling waves bifurcating at the onset of convection suffer sideband instabilities that are restabilised further away in the branch. If this restabilisation is produced after the turning point of the travelling-wave branch, these waves do not become stable in a saddle node bifurcation as would have been the case in a smaller domain. In the regions of instability of the uniform travelling waves we expect to find either transitions between states of different wave number or modulated travelling waves arising in these bifurcations.     

Oscillatory convection in binary mixtures: Thermodiffusion,solutal buoyancy,and advection

The role of thermodiffusive generation of concentration fluctuations via the Soret effect, their contribution to the buoyancy forces that drive convection, the advective mixing effect of the latter, and the diffusive homogenisation are compared and elucidated for oscillatory convection. Numerically obtained solutions of the field equations in the form of spatially extended relaxed traveling waves, of standing waves, and of the transient growth of standing waves and their transition to traveling waves are discussed as well as spatially localized convective states of traveling waves that are surrounded by the quiescent fluid.     

Modelling the magnetorefractive effect in giant magnetoresistive granular and layered materials

The Zhang–Levy–Granovskii (Z–L–G) model of the magnetorefractive effect (MRE) in granular films and the Jacquet–Valet (J–V) model, originally developed for magnetic multilayers, are compared and their common origin demonstrated. Simulations in an extended Hagen–Rubens (H–R) model give new insight into the variation with wavelength of the MRE, and the relative dependence of giant magnetoresistance (GMR) and the MRE to material and experimental parameters such as bulk and interface scattering parameters, mean free paths, grain diameter, polarisation and reflection geometry is explored. The sensitivity of the size, wavelength dependence and the position of the depth of the minimum in the MRE spectra to the different parameters is verified. We establish powerful new equations to correlate the MRE and GMR, and we analyse their validity for a variety of film parameters. This suggests a new approach to the use of the MRE in sensing GMR in the films.     

Modeling film flows down inclined planes

A new model of film flow down an inclined plane is derived by a method combining results of the classical long wavelength expansion to a weighted-residuals technique. It can be expressed as a set of three coupled evolution equations for three slowly varying fields, the thickness h, the flow-rate q, and a new variable that measures the departure of the wall shear from the shear predicted by a parabolic velocity profile. Results of a preliminary study are in good agreement with theoretical asymptotic properties close to the instability threshold, laboratory experiments beyond threshold and numerical simulations of the full Navier-Stokes equations. Received: 16 April 1998 / Revised: 29 June 1998 / Accepted: 2 July 1998     

Direct pore-level modeling of incompressible fluid flow in porous media

We present a dynamic particle-based model for direct pore-level modeling of incompressible viscous fluid flow in disordered porous media. The model is capable of simulating flow directly in three-dimensional high-resolution micro-CT images of rock samples. It is based on moving particle semi-implicit (MPS) method. We modify this technique in order to improve its stability for flow in porous media problems. Using the micro-CT image of a rock sample, the entire medium, i.e., solid and fluid, is discretized into particles. The incompressible Navier–Stokes equations are then solved for each particle using the MPS summations. The model handles highly irregular fluid–solid boundaries effectively. An algorithm to split and merge fluid particles is also introduced. To handle the computational load, we present a parallel version of the model that runs on distributed memory computer clusters. The accuracy of the model is validated against the analytical, numerical, and experimental data available in the literature. The validated model is then used to simulate both unsteady- and steady-state flow of an incompressible fluid directly in a representative elementary volume (REV) size micro-CT image of a naturally-occurring sandstone with 3.398 μm resolution. We analyze the quality and consistency of the predicted flow behavior and calculate absolute permeability using the steady-state flow rate.     

A method to simulate linear stability of impulsively accelerated density interfaces in ideal-MHD and gas dynamics

We present a numerical method to solve the linear stability of impulsively accelerated density interfaces in two dimensions such as those arising in the Richtmyer–Meshkov instability. The method uses an Eulerian approach, and is based on an upwind method to compute the temporally evolving base state and a flux vector splitting method for the perturbations. The method is applicable to either gas dynamics or magnetohydrodynamics. Numerical examples are presented for cases in which a hydrodynamic shock interacts with a single or double density interface, and a doubly shocked single density interface. Convergence tests show that the method is spatially second-order accurate for smooth flows, and between first and second-order accurate for flows with shocks.