Experimental Investigations on Interaction of Two Drops by Thermocapillary-Buoyancy Migration

Experiments were performed, in a terrestrial environment, to study the migration and interaction of two drops with different diameters in matrix liquid under temperature gradient field. Pure soybean oil and silicon oil were used as matrix liquid and the drop liquid, respectively. The information on the motions of two drops was recorded by CCD camera system in the experiments to analyze the trajectories and velocities of the drops. Our experiments showed that, upon two drops approaching each other, the influence of the larger drop on the motion of the smaller one became significant. Meanwhile the smaller drop had a little influence on the larger one all the time. The oscillation of migration velocities of both drops was observed as they were approaching. For a short period the smaller drop even moved backward when it became side by side with the larger one during the migration. Although our experimental results on the behavior of two drops are basically consistent with the theoretical predictions, there are also apparent differences. 2006 Elsevier Ltd. All rights reserved. Keywords: Thermocapillary migration; Drop; Interaction; Oscillation 1. Introduction A bubble or drop will move when placed in another fluid with temperature gradient. This motion happens as a consequence of the variation of interfacial tension with temperature. Such a phenomenon is already known as Marangoni migration problem. With the development of microgravity science, bubble dynamics and droplet dynamics became a hot point problem of research because this investigation is very important for basic research as well as for applications in reduced gravity environment, such as space material science, chemical engineering and so on. Young et al. first investigated the thermocapillary migration of

Dynamic behavior of a cylindrical crack in a functionally graded interlayer under torsional loading

In this paper the problem of a cylindrical crack located in a functionally graded material (FGM) interlayer between two coaxial elastic dissimilar homogeneous cylinders and subjected to a torsional impact loading is considered. The shear modulus and the mass density of the FGM interlayer are assumed to vary continuously between those of the two coaxial cylinders. This mixed boundary value problem is first reduced to a singular integral equation with a Cauchy type kernel in the Laplace domain by applying Laplace and Fourier integral transforms. The singular integral equation is then solved numerically and the dynamic stress intensity factor (DSIF) is also obtained by a numerical Laplace inversion technique. The DSIF is found to rise rapidly to a peak and then reduce and tend to the static value almost without oscillation. The influences of the crack location, the FGM interlayer thickness and the relative magnitudes of the adjoining material properties are examined. It is found among others that, by increasing the FGM gradient, the DSIF can be greatly reduced.

Instability Analysis of Nonlinear Surface Waves in a Circular Cylindrical Container Subjected to a Vertical Excitation

Singular perturbation theory of two-time scale expansions was developed both in inviscid and weak viscous fluids to investigate the motion of single surface standing wave in a liquid-filled circular cylindrical vessel, which is subject to a vertical periodical oscillation. Firstly, it is assumed that the fluid in the circular cylindrical vessel is inviscid, incompressible and the motion is irrotational, a nonlinear evolution equation of slowly varying complex amplitude, which incorporates cubic nonlinear term, external excitation and the influence of surface tension, was derived from solvability condition of high-order approximation. It shows that when forced frequency is low, the effect of surface tension on mode selection of surface wave is not important. However, when forced frequency is high, the influence of surface tension is significant, and can not be neglected. This proved that the surface tension has the function, which causes free surface returning to equilibrium location. Theoretical results much close to experimental results when the surface tension is considered. In fact, the damping will appear in actual physical system due to dissipation of viscosity of fluid. Based upon weakly viscous fluids assumption, the fluid field was divided into an outer potential flow region and an inner boundary layer region. A linear amplitude equation of slowly varying complex amplitude, which incorporates damping term and external excitation, was derived from linearized Navier-Stokes equation. The analytical expression of damping coefficient was determined and the relation between damping and other related parameters (such as viscosity, forced amplitude and depth of fluid) was presented. The nonlinear amplitude equation and a dispersion, which had been derived from the inviscid fluid approximation, were modified by adding linear damping. It was found that the modified results much reasonably close to experimental results. Moreover, the influence both of the surface tension and the weak viscosity on the mode formation was described by comparing theoretical and experimental results. The results show that when the forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when the forcing frequency is high, the surface tension of the fluid is prominent. Finally, instability of the surface wave is analyzed and properties of the solutions of the modified amplitude equation are determined together with phase-plane trajectories. A necessary condition of forming stable surface wave is obtained and unstable regions are illustrated. (c) 2005 Elsevier SAS. All rights reserved.

Experimental Study on Thermocapillary Convection

In the present paper, the experimental studies on thermocapillary convection are reviewed. The author's interest is mainly focused on the onset of oscillatory thermocapillary convection, the features of oscillatory flow pattern, and the critical Marangoni number related with temperature and free surface oscillation. The coordinated measurement in a microgravity environment of a drop shaft is also addressed.

Experimental Study on the Transition Process to the Oscillatory Thermocapillary Convections in a Floating Half Zone

The transition process of the thermocapillary convection from a steady and axisymmetric mode to the oscillatory mode in a liquid bridge with a fixed aspect ratio and varied volume ratio was studied experimentally. To ensure the surface tension to play an important role in the ground-based experiment, the geometrical configuration of the liquid bridge was so designed that the associated dynamic Bond number Bd ≈ 1. The velocity fields were measured by Particle Image Velocimetry (PIV) technique to effectively distinguish the different flow modes during the transition period in the experiments. Our experiments showed that as the temperature difference increased the slender and fat bridges presented quite different features on the evolution in their flow feature: for the former the thermocapillary convection transformed from a steady and axisymmetric pattern directly into an oscillatory one; but for the latter a transition flow status, characterized by an axial asymmetric steady convection, appeared before reaching the oscillatory mode. Experimental observations agree with the results of numerical simulations and it is obvious that the volume of liquid bridge is a sensitive geometric parameter. In addition, at the initial stage of the oscillation, for the former a rotating oscillatory convection with azimuthal wave number m = 1 was observed while for the latter a pulsating oscillatory pattern with azimuthal wave number m = 2 emerged, and then with further increase of the temperature difference, the pulsating oscillatory convection with azimuthal wave number m = 2 evolved into a rotating oscillatory pattern with azimuthal wave number m = 2.

Fourth order accurate compact scheme with group velocity control (GVC)

For solving complex flow field with multi-scale structure higher order accurate schemes are preferred. Among high order schemes the compact schemes have higher resolving efficiency. When the compact and upwind compact schemes are used to solve aerodynamic problems there are numerical oscillations near the shocks. The reason of oscillation production is because of non-uniform group velocity of wave packets in numerical solutions. For improvement of resolution of the shock a parameter function is introduced in compact scheme to control the group velocity. The newly developed method is simple. It has higher accuracy and less stencil of grid points.

A simulation model of a floating half zone

A simulation model of a floating half zone was suggested by steady numerical simulation and experiment respectively, in the previous papers [Q.S. Chen, W.R. Hu, Int. J. Mass Heat Transfer 40 (1997) 757; J.H. Han, Y. Ar, R. Zhou, W.R. Hue, Int. J. Mass Heat Transfer 40 (1997) 2671]. In the present paper, the simulation model is studied by using the method of unsteady and three-dimensional numerical simulation, and the transient process from steady convection to oscillatory convection is especially analyzed. Comparison of onsets of oscillation for both simulation model and the usual model were obtained, and the results show that the critical Marangoni number of the simulation model is obviously smaller than that of the usual model for the same slender liquid bridge. This implies that the usual model of a floating half zone gives a lower estimation on the onset of oscillation for floating zone convection.

Two bifurcation transitions of the floating half zone convection in a fat liquid bridge of larger Pr

The transient process of the thermocapillary convection was obtained for the large Pu floating half zone by using the method of three-dimensional and unsteady numerical simulation. The convection transits directly from steady and axisymmetric state to oscillatory flow for slender liquid bridge, and transits first from steady and axisymmetric convection to the steady and non-axisymmetric convection, then, secondly to the oscillatory convection for the fatter liquid bridge. This result implies that the volume of liquid bridge is not only a sensitive critical parameter for the onset of oscillation, but also relates to the new mechanism for the onset of instability in the floating half zone convection even in case of large Prandtl number fluid.

受水压振荡时饱和砂床的液化与变形特性

为考察饱和砂土地基受到水压振荡作用时的动力响应,根据两相连续介质理论,分析了液化发展、液化区厚度、颗粒速度等.研究结果表明,随着土强度和渗透性的降低与载荷强度的增加,液化发展速率加快;随着土强度的降低和渗透性、载荷强度的增加,变形量增加;如果土的初始分布不均匀,则在渗透性小的位置,应变和孔隙水压力将剧烈变化,这可以解释为什么在一定条件下土中会出现断裂和水层.

Instability from steady and axisymmetric to steady and asymmetric floating half zone convection in a fat liquid bridge of larger Prandtl number

The linear instability analysis of the present paper shows that the thermocapillary convection in a half floating zone of larger Prandtl number has a steady instability mode w(i) = 0 and m = 1 for a fat liquid bridge V = 1.2 with small geometrical aspect ratio A = 0.6. This conclusion is different from the usual idea of hydrothermal instability, and implies that the instability of the system may excite a steady and axial asymmetric state before the onset of oscillation in the ease of large Prandtl number.

Experimental Study of Surface Deformation and Flow Pattern on Buoyant-Thermocapillary Convection

Free surface deformation is one of the most important physical phenomena in fluids with free surface. In the present paper, convection and surface deformation caused by thermocapillary effect in a rectangular cavity were investigated. In ground experiments, the convection was also affected by gravity. The cavity has a horizontal cross section of 52mm×42mm and the thikkness of the liquid layer is 4mm. Temperature difference between two sides of the liquid layer was increased gradually, and the flow in liquid layer will develop from steady to unstable convection. An optical diagnostic system consisting of a revised Michelson interferometer with image processor was developed to study fluid surface deformation in convection, and the displacements of free surface oscillation were determined. PIV technique was adopted to observe the evolution of flow pattern, and the velocity fields were obtained quantitatively. The present experiments demonstrate that surface deformation is quite distinct in buoyant-thermocapillary convection. in order to understand the mechanism of buoyant-thermocapillary convection, not only the hydrothermal wave instability but also the surface wave instability should be discussed.

Two Bifurcation Transition Processes in Floating Half Zone Convection of Larger Prandtl Number Fluid

Processes of the onset oscillation in the thermocapillaxy convection under the Earth's gravity are investigated by the numerical simulation and experiments in a floating half zone of large Prandtl number with different volume ratio. Both computational and experimental results show that the steady and axisymmetric convection turns to the oscillatory convection of m=1 for the slender liquid bridge, and to the oscillatory convection before a steady and 3D asymmetric state for the case of a fat liquid bridge. It implies that, there are two critical Marangoni numbers related, respectively, to these two bifurcation transitions for the fat liquid bridge. The computational results agree with the results of ground-based experiments.

Influence of Liquid Bridge Volume on the Floating Zone Convection

The liquid bridge volume is a critical geometrical parameter in addition to the aspect ratio for onset of oscillation in the floating zone convection. The oscillatory features are generally divided into two characteristic regions: slender liquid bridge region and fat liquid bridge region. The oscillatory modes in two regions are discussed in the present paper.

Thermocapillary Convection in Floating Zones

This paper provides an overview of ongoing studies in the area of thermocapillary convection driven by a surface tension gradient parallel to the free surface in a floating zone. Here, research interests are focused around the onset of oscillatory thermocapillary convection, also known as the transition from quasisteady convection to oscillatory convection. The onset of oscillation depends on a set of critical parameters, and the margin relationship can be represented by a complex function of the critical parameters. The experimental results indicate that the velocity deviation of an oscillatory flow has the same order of magnitude as that of an average flow, and the deviations of other quantities, such as temperature and free surface radii fluctuations, are much smaller when compared with their normal counterparts. Therefore, the onset of oscillation should be a result of the dynamic process in a fluid, and the problem is a strongly nonlinear one. In the past few decades, several theoretical models have been introduced to tackle the problem using analytical methods, linear instability analysis methods, energy instability methods, and unsteady 3D numerical methods. The last of the above mentioned methods is known to be the most suitable for a thorough analysis of strong nonlinear processes, which generally leads to a better comparison with the experimental results. The transition from oscillatory thermocapillary convection to turbulence falls under the studies of chaotic behavior in a new system, which opens a fascinating new frontier in nonlinear science, a hot research area drawing many recent works. This paper reviews theoretical models and analysis, and also experimental research, on thermocapillary connection in floating zones. It cites 93 references.