On the structure of the velocity field due to wave motion at a uniformly charged interface between two viscous immiscible liquids

An analytical solution to the problem of evolution of a capillary-gravitational wave on the uniformly charged interface between viscous immiscible liquids is found. It is shown that, away from the interface, both the total liquid flows and their wave-related eddy components on both sides of the interface decrease rapidly. The amplitude of the velocity field curl changes stepwise in going through the interface. The ratio between the amplitudes of the velocity field eddy components in the media being considered depends on the charge density at the interface, ratio of the kinematic viscosities, and densities of the upper and lower liquids.     

Surface electromagnetic waves at the interface between a homogeneous medium and a system of coupled waveguides

An analysis is made of the experimental investigations of the surface waves existing at the interface between a homogeneous medium and a periodically stratified medium that represents a bounded system of coupled waveguides. It is shown that, in all cases of the observation of surface waves, the bounded system of coupled waveguides has its own spectrum of guided modes and a spectrum of leaky modes that become surface waves of the system. It is also demonstrated that a biosensor can successfully operate when two surface waves serve as leaky modes of a Bragg waveguide in which the periodic system of waveguides is used as a distributed Bragg mirror of this waveguide. A structure supporting surface waves is designed on the basis of ten pairs of Nb₂O₅-SiO₂ layers and implemented experimentally. The surface waves are detected with a K8 glass prism according to the Kretschmann scheme.     

Wave propagation along the boundary between a saturated porous medium and a liquid

The frequency dependences of the velocity and attenuation of waves propagating along the boundary between a saturated porous medium and a liquid are investigated. It is shown that, depending on the parameters of the saturated porous medium and the boundary conditions, the propagation of one, two, or three surface waves is possible, each of them being either a true mode or a pseudomode. The results of the study agree well with other investigations carried out in the high-frequency approximation.     

Reflexion of a spherical wave by the plane interface between a perfect fluid and a porous medium

By using the Fourier transform of the system of equations and continuity conditions, it is easy to obtain the Fourier transform of the solution. This last function is decomposed into several terms which are identified as Fourier images of known functions. An exact representation of the scattered sound pressure field is obtained as a combination of the radiation of the image source and layer potentials. Approximations are given when the point spherical source is located on the interface.     

A fractal approach to low velocity non-Darcy flow in a low permeability porous medium

In this paper, the mechanism for fluid flow at low velocity in a porous medium is analyzed based on plastic flow of oil in a reservoir and the fractal approach. The analytical expressions for flow rate and velocity of non-Newtonian fluid flow in the low permeability porous medium are derived, and the threshold pressure gradient （TPG） is also obtained. It is notable that the TPG （J） and permeability （K） of the porous medium analytically exhibit the scaling behavior J ~ K-D＇r/（l＋Or）, where DT is the fractal dimension for tortuous capillaries. The fractal characteristics of tortuosity for capillaries should be considered in analysis of non-Darcy flow in a low permeability porous medium. The model predictions of TPG show good agreement with those obtained by the available expression and experimental data. The proposed model may be conducible to a better understanding of the mechanism for nonlinear flow in the low permeability porous medium.     

On the structure of the velocity field under the free spheroidal surface of a viscous liquid drop oscillating in an electrostatic field

An asymptotic analytical solution to an initial boundary-value problem considering (i) the time evolution of the capillary oscillation amplitude as applied to a viscous spheroidal liquid drop placed in a uniform electrostatic field and (ii) the liquid flow velocity field inside the drop is found. The problem is solved in an approximation that is linear in two small parameters: the dimensionless oscillation amplitude and the dimensionless field-induced constant deformation of the equilibrium (spherical) shape of the drop. Terms proportional to the product of the small parameters are retained. In this approximation, interaction between oscillation modes is revealed. It is shown that the intensity of the eddy component of the oscillation-related velocity field depends on the liquid viscosity and the external uniform electrostatic field strength. The intensity of the eddy component decays rapidly with distance from the free surface. The depth to which the eddy flow (which is caused by periodical flows on the free surface) penetrates into the drop is a nonmonotonic function of the polar angle and increases with dimensionless viscosity and field strength.     

Hydromagnetic free convection flow through a porous medium between two parallel plates

Steady hydromagnetic free convective flow of a conducting fluid through a porous medium bounded by two parallel plates is considered and effects of G (Grashof number) and the K (permeability parameter) on the velocity field are discussed.     

Sink flow deforms the interface between a viscous liquid and air into a tip singularity

In our experiment, an interface between a viscous liquid and air is deformed by a sink flow of constant flow rate to form a sharp tip. Using a microscope, the interface shape is recorded down to a tip size of 1 microm. The curvature at the tip is controlled by the distance h between the tip and the sink. As a critical distance h*is approached, the curvature diverges like 1/(h-h*)3and the tip becomes cone shaped. As the distance to the sink is decreased further, the opening angle of the cone vanishes like h2. No evidence for air entrainment was found, except when the tip was inside the orifice.     

On MHD transient flow of a Maxwell fluid in a porous medium and rotating frame

Analytic solution for unsteady magnetohydrodynamic (MHD) flow is constructed in a rotating non-Newtonian fluid through a porous medium. Constitutive equations for a Maxwell fluid have been taken into consideration. The hydromagnetic flow in the uniformly rotating fluid is generated by a suddenly moved infinite plate in its own plane. Analytic solution of the governing flow problem is obtained by means of the Fourier sine transform. It is shown that the obtained solution satisfies both the associate partial differential equation and the initial and boundary conditions. The solution for a Navier-Stokes fluid is recovered if λ→0. The steady state solution is also obtained for t→∞.     

Temperature and velocity measurement of a 3-D thermal flow field using thermo-sensitive liquid crystals

It is an important challenge to analyze a three-dimensional thermal flow field in engineering, science, and agriculture. For such an analysis, it is essential to measure physical quantities such as temperature and velocity over the entire thermal flow field. This paper presents a measurement system based on color image processing for temperature and velocity vector distributions in a three-dimensional thermal flow field. Flow visualization is accomplished by the use of thermo-sensitive liquid crystal tracers. An algorithm for the color-to-temperature transformation using a multi-layer feed-forward neural network is applied to three-dimensional natural convection in a rotating cylindrical cell. Two-dimensional temperature distributions in a slit plane are obtained by using the algorithm. A three-dimensional temperature distribution is consequently constructed by interpolating the two-dimensional distributions using the B-spline function. In addition, the Spatio-Temporal correlation method is applied to the natural convection to obtain a three-dimensional velocity vector distribution.     

Atmospheric-dispersion experiments in the near and medium field

Summary In September 1979, the Turbigo power plant of ENEL hosted the fourth European experiment on the remote sensing of atmospheric dispersion and boundary layer structure sponsored by the Commission of the European Communities (CEC). The exercise was particularly aimed at studying nonstationary diffusion processes, under low wind and convectively unstable conditions; other situations, typical of up- and down-valley breeze regimes, were observed as well. The campaign produced a large amount of information, the analysis of which is still under development. This paper highlights the overall results obtained by the joint effect of many teams, simultaneously operating both conventional and advanced remote-sensing instruments. In particular, it describes and discusses the results connected to a few specific objectives, representing the main characteristics of the conditions peculiar to this experiment and to the site climatology.     

MHD natural convective flow through a porous medium in a square cavity filled with liquid gallium

This article contains a computational study of free convective flow through a square enclosure filled with liquid gallium saturated porous medium in the presence of a uniform inclined magnetic field. Lower boundary of enclosure is considered to be heated uniformly, upper horizontal boundary is taken insulated, left wall of the cavity is heated linearly, and right wall is heated linearly or taken cold. Navier–Stokes equations governing the flow problem are first exposed to penalty method to eliminate the pressure terms and then Galerkin FEM is employed to solve reduced equations. Grid independent results are achieved and shown in tabular form for numerous ranges of physical flow parameters. To ensure the accuracy of developed code, computed results are compared with those available in earlier studies through figures. It is found that the strength of streamlines circulation is increased due to increase in Darcy number while imposition of vertical magnetic field instead of horizontal magnetic field causes slow rate of increase in strength of streamlines circulation. Whereas, in the case of linearly heated right wall, the average Nusselt number is an increasing function of the Darcy number, and vertical magnetic field causes higher values for average Nusselt number as compared to horizontal magnetic field along bottom and side walls of cavity. Contrarily, in the case of cold right wall, the horizontal magnetic field results in higher values of average Nusselt number as compared to the vertical magnetic field case, and the average Nusselt number reduces as we move along lower and right boundary while increases along left wall with increase in distance.     

On the nonlinear dynamics of a saline boundary layer formed by throughflow near the surface of a porous medium

We consider gravitational instability of saline boundary layers, observed at the subsurface of salt lakes. This boundary layer is the result of the convective transport induced by the evaporation at the horizontal surface of a confined porous medium. When this upward transport is balanced by salt dispersion, a steady state boundary layer is formed. However, this boundary layer can be unstable when perturbed. This results in complex groundwater motion and density fields. The aim of this paper is to investigate the existence of finite amplitude solutions describing these resulting patterns (both the number of solutions and their structure), their stability, and their dependency on the system Rayleigh and Péclet numbers. For this purpose we construct a low-dimensional dynamical system (a reduced model) by projecting the nonlinear model equations onto a relatively small set of eigenfunctions of the problem linearized at criticality. The Galerkin projection approach is complicated by the fact that the problem under consideration is non-self-adjoint due to the existing evaporation. This implies that the eigenfunctions do not form an orthogonal set and therefore the adjoint eigenfunctions are used for the projection. The reduced model is constructed in such a way that it is capable of providing solutions in the strongly nonlinear regime as well. Convergence of these solutions towards the fully nonlinear model results is shown by means of direct numerical simulations. Further, the reduced model seems to partly capture the complex nonlinear behavior as seen in Hele-Shaw experiments by Wooding et al. [R.A. Wooding, S.W. Tyler, I. White, P.A. Anderson, Convection in groundwater below an evaporating salt lake: 2. evolution of fingers or plumes, Water Resour. Res. 33 (6) (1997) 1219-1228]. The physical transition mechanism that explains the occurrence of some observed bifurcation types is presented as well.     

MHD oscillatory flow on free convection–radiation through a porous medium with constant suction velocity

Unsteady two-dimensional hydromagnetic free convection and thermal radiation flow of an electrically conducting viscous-incompressible fluid, through a highly porous medium bounded by a vertical plane surface of constant temperature are presented. The Rosseland diffusion approximation is used to describe the radiative heat flux in the energy equation. Expressions for the velocity and temperature are obtained. The free-stream velocity of the fluid vibrates about a mean constant value and the surface absorbs the fluid with constant velocity. Effects of varying R (radiative parameter), G (Grashof number), k′ (permeability of the porous medium) and M (magnetic parameter upon the velocity field and the effect of varying R and Pr (Prandtl number) on the temperature are discussed.     

Simulation of flow through a two-dimensional random porous medium

The cellular automata approximation of two-dimensional hydrodynamics is used to model flow between randomly placed, partially overlapping circles. The flow resistance is first roughly proportional to the number of circles and then increases more strongly for higher numbers of such obstacles.     

双相多孔锂离子电池液/固界面的声反射与声透射

采用传递矩阵法,同步联立改进的Biot理论,对含液固界面的双相多孔锂离子电池的超声反射与透射系数进行理论求解。考虑锂离子的摇摆特性对电极力学性能的影响,计算了对应状态下液/固界面的双相多孔锂离子电池声反射及透射系数的角度谱与频率谱。同时,构建了不同荷电状态时含单元锂离子电池的频域仿真模型,以萃取对应的超声反射及透射角度谱及频率谱,并与理论计算结果对比吻合良好。随后,以多单元锂离子电池为例,在不同的荷电状态下,分析了反射与透射系数随斜入射角度、入射波频率的变化关系,并分别指出了其角度谱及频率谱特征点随荷电状态的变化特征,为锂离子电池运行状态的超声无损测量提供了理论基础。