Convection in horizontally vibrated granular material

We report observations of convective motion in a container filled with granular material when it is vibrated in the horizontal direction. We find that the roughness of the boundaries and the container dimensions play an important role in determining the shape and number of the convection cells. When the container bottom and lateral walls are rough, the system typically exhibits four counter-rotating rolls stacked in two pairs on top of each other; for very low filling height, it is possible to observe a single row of rolls arranged laterally along the bottom of the container. With smooth walls, on the other hand, we find that the system typically forms only a single pair of counter-rotating convection rolls that originate in the two upper corners of the vibrated material; when the filling height is increased to a level that depends on the container width, we observe a transition to the four-roll state. (c) 1999 American Institute of Physics.     

Kink-induced transport and segregation in oscillated granular layers

We use experiments and molecular dynamics simulations of vertically oscillated granular layers to study horizontal particle segregation induced by a kink (a boundary between domains oscillating out of phase). Counterrotating convection rolls carry the larger particles in a bidisperse layer along the granular surface to a kink, where they become trapped. The convection originates from avalanches that occur inside the layer, along the interface between solidified and fluidized grains. The position of a kink can be controlled by modulation of the container frequency, making possible systematic harvesting of the larger particles.     

垂直振动颗粒混合气体的振荡现象研究

运用事件驱动算法研究颗粒混合物在垂直振动容器中的振荡现象.容器被具有一定高度的隔板分成相等大小的两个小室,并采用半径相差一倍的两种颗粒.研究结果表明,颗粒振荡周期随两种颗粒密度比的减少而急剧增加.通过计算在垂直方向上两种颗粒高度之比随颗粒密度的变化关系,说明决定颗粒振荡与否的主要因素并不是"巴西坚果效应"或"反巴西坚果效应".通过计算颗粒温度,发现颗粒振荡取决于颗粒混合气体的小颗粒温度.当小颗粒温度大于一定值时,颗粒混合气体发生颗粒振荡现象.根据Viridi等提出的流体动力学模型,文中对该模型做出相应的修改,加入密度因子,从而可以解释颗粒振荡周期与颗粒密度比的关系.     

Spontaneous ratchet effect in a granular gas

The spontaneous clustering of a vibrofluidized granular gas is employed to generate directed transport in two different compartmentalized systems: a granular fountain in which the transport takes the form of convection rolls, and a granular ratchet with a spontaneous particle current perpendicular to the direction of energy input. In both instances, transport is not due to any system-intrinsic anisotropy, but arises as a spontaneous collective symmetry breaking effect of many interacting granular particles. The experimental and numerical results are quantitatively accounted for within a flux model.     

Different localized states of travelling-wave convection in a rectangular container

We have performed numerical simulations of localized travelling-wave convection in a binary fluid mixture heated from below in a long rectangular container. Calculations are carried out in a vertical cross section of the rolls perpendicular to their axes. For a negative enough separation ratio, two types of quite different confined states were documented by applying different control processes. One branch of localized travelling waves survives only in a very narrow band within subcritical regime, while another branch straddles the onset of convection existing both in subcritical and supercritical regions. We elucidated that concentration field and its current are key to understand how confined convection is sustained when conductive state is absolutely unstable. The weak structures in the conducting region are demonstrated too.     

窄振动颗粒床中的运动模式

实验研究了竖直振动情况下,窄容器中颗粒的运动模式.发现运动模式与颗粒床厚度及振动加速度有很强的依赖关系.实验表明横向尺寸较小的容器可以抑制对流卷及拱起现象.对于足够厚的颗粒床,即使振动加速度很大,颗粒床下部仍然存在着颗粒聚集态.出现聚集态时,颗粒床对容器底的冲击力是倍周期分岔的.实验表明倍周期分岔点与颗粒床厚度无关.对于较薄的颗粒床,颗粒可以是聚集态或对流卷,视颗粒尺寸而定.如果使用尺寸分布非常窄的球形颗粒,可以观察到颗粒的有序排列.出现同心的圆筒形“壳”结构,每个“壳”上的颗粒是二维六角密排列的. 关键词： 颗粒物质 倍周期分岔 颗粒聚集态 球堆积     

Thermal convection in fluidized granular systems

Thermal convection is observed in molecular dynamic simulations of a fluidized granular system of nearly elastic hard disks moving under gravity, inside a square box. Boundaries introduce no shearing or time dependence, but the energy injection comes from a slip (shear-free) thermalizing base. The top wall is perfectly elastic and lateral boundaries are either elastic or periodic. The spontaneous temperature gradient appearing in the system due to the inelastic collisions, combined with gravity, produces a buoyancy force that, when dissipation is large enough, triggers convection.     

Magneto-vibratory separation of glass and bronze granular mixtures immersed in a paramagnetic liquid

A fluid-immersed granular mixture may spontaneously separate when subjected to vertical vibration, separation occurring when the ratio of particle inertia to fluid drag is sufficiently different between the component species of the mixture. Here, we describe how fluid-driven separation is influenced by magneto-Archimedes buoyancy, the additional buoyancy force experienced by a body immersed in a paramagnetic fluid when a strong inhomogeneous magnetic field is applied. In our experiments glass and bronze mixtures immersed in paramagnetic aqueous solutions of MnCl₂ have been subjected to sinusoidal vertical vibration. In the absence of a magnetic field the separation is similar to that observed when the interstitial fluid is water. However, at modest applied magnetic fields, magneto-Archimedes buoyancy may balance the inertia/fluid-drag separation mechanism, or it may dominate the separation process. We identify the vibratory and magnetic conditions for four granular configurations, each having distinctive granular convection. Abrupt transitions between these states occur at well-defined values of the magnetic and vibrational parameters. In order to gain insight into the dynamics of the separation process we use computer simulations based on solutions of the Navier-Stokes' equations. The simulations reproduce the experimental results revealing the important role of convection and gap formation in the stability of the different states.     

Size segregation and convection of granular mixtures almost completely packed in a thin rotating Box

We simulate size segregation in granular mixtures which are almost completely packed in a rotating drum. Instead of a 3D drum, we simulate a 2D thin rotating box which is almost completely packed with granular mixtures. The phase inversion of a radially segregated pattern which was found in a 3D experiment is qualitatively reproduced with this simulation. A global convection appears after a radial segregation pattern is formed, and this convection induces an axially segregated pattern.     

A horizontal Brazil-nut effect and its reverse

Transport effects in a monolayer consisting of a binary granular mixture, confined in a horizontally vibrating circular dish, are studied experimentally and compared with a reduced theoretical model. Depending on the ratio of the particles' material density and size, migration of the larger particles occurs either towards the boundary or to the center of the circular container. These directed motions show similarities to the Brazil-nut effect and its reverse form.     

Reversing the Brazil-nut effect: competition between percolation and condensation

We report on experiments on vertically shaken binary granular mixtures, which separate into their components due to the external excitation. This well-known phenomenon, where large particles rise to the top of the mixture, is called the Brazil-nut effect. Recent theoretical findings predict also a reverse Brazil-nut effect, where large particles sink to the bottom of the container. We choose spherical beads of various diameters and materials in order to observe the transition from Brazil-nut effect to its reverse form. The direction of demixing depends sensitively on the external excitation, so that it is possible to switch between both effects for a given mass density ratio.     

Behavior of the Melt in the Vertical Bridgman Method with a Low Axial Temperature Gradient

The thermal conditions for the growth of Ge crystals with a diameter of 50 mm by the vertical Bridgman method in the case of low thermal-gravitational convection are studied using model experiments. Distilled water being hydrodynamically similar to the Ge melt is used as the model liquid. When modelling by means of the light cut method, it is established that mixture particles move along the heat flow direction from top to bottom. It is shown that an axial temperature gradient of 2 K/cm or more increases the contribution of thermal diffusion to mass transfer at a vertical flow rate of 0.09 mm/s or more. The numerical simulation of thermal convection in the Oberbeck–Boussinesq approximation confirms the absence of convection under the given thermal conditions. However, the deviation of the container axis from the vertical by 0.5° during the process of crystal growth contributes to the increase in the flow rates in the liquid phase up to 0.55 mm/s.     

Convection in a vibrated granular layer

When a granular layer is submitted to an oscillating acceleration with a peak value larger than gravity, a large scale motion develops. This movement is in some ways similar to the one displayed by a liquid heated from below, and it is called granular convection. Different conditions beside the parameters of the forcing can affect it, such as the presence of an interstitial gas or the roughness of the walls. We have carried out an experiment to study the convective movement of a granular layer with a temporal resolution high enough to describe the motion of individual grains within one oscillating period. We also present experimental results concerning the friction that the lateral walls exert on the grains and its relevance on granular convection.     

SYMMETRIY ANALYSIS OF CONVECTION PATTERNS

In this paper, we carry out a symmetry analysis of convection patterns of Newton-Boussinesg fluid in some finite containers. We also discuss, from the viewpoint of symtry analysis, the behaviour of infinitely extended fluid layer, as a limit of that in finite container, near convection threshold.     

Reversals of large-scale circulation in turbulent convection in rectangular cavities

The behavior of large-scale circulation appearing against the background of Rayleigh-Bénard turbulent convection in rectangular cavities of various geometries (from a thin layer to a cubic cell) has been experimentally investigated. It has been shown that the regimes of large-scale circulation with spontaneous reversals separated by long periods of quasistationary circulation appear both in a limited range of the Rayleigh number and in a limited range of the aspect ratio, which determines the ratio of the thickness of a cell to the side in the circulation plane. A regime without reversals is established in a thick layer, whereas a regime characterized by numerous changes in the direction of circulation, which are not separated by intervals with the stable direction of the large-scale flow, arises in a thin layer. The spectra of oscillations of the amplitude of large-scale circulation have been analyzed. It has been shown that a dominant frequency appears in the spectrum of oscillations of the cubic cell.     

Universal power-law decay of the impulse energy in granular protectors

Protecting a big impulse from outside is one of the important issues of our everyday life. A granular medium is often used as a protecting material. The impulse inside a granular medium is a solitary wave which may be confined temporarily to a particular region of the medium, which we call the granular container that plays the role of the protector. We find a universal power-law behavior in time for the leakage of the impulse energy confined inside various granular containers.     

Noise, coherent fluctuations, and the onset of order in an oscillated granular fluid

We study fluctuations in a vertically oscillated layer of grains below the critical acceleration for the onset of ordered standing waves. As onset is approached, transient disordered waves with a characteristic length scale emerge and increase in power and coherence. The scaling behavior and the shift in the onset of order agrees with the Swift-Hohenberg theory for convection in fluids. However, the noise in the granular system is an order of magnitude larger than the thermal noise in the most sensitive convecting fluid experiments to date; the effect of the granular noise is observable 20% below the onset of order.     

The rotation-reptation transition under broken rotational symmetry

In a swirled circular container, granular particles can change their sense of rotation when the packing density is increased, exhibiting a transition from rotational to reptational motion. In addition, here we report a ‘snake mode’ that arises at a lower packing density, where particles form a chain like cluster that rotates with the same frequency as the container. We investigate experimentally transitions between these three modes under the influence of geometrical distortions which break the rotational symmetry of the container. The driving mechanism for the rotational motion of the clusters is also discussed.     

Variational model of granular flow in a three-dimensional rotating container

We considered a flow of a cohesionless granular material in a partially filled three-dimensional rotating container. A variational continuum mechanics model is suggested to describe the profile of the free surface of the granular material. A combination of a level set method and a variational form of energy conservation equation allows us to describe flow of granular material in arbitrary-shaped containers.     

The meridional circulation of the Sun: Observations,theory and connections with the solar dynamo

The meridional circulation of the Sun, which is observed to be poleward at the surface, should have a return flow at some depth. Since large-scale flows like the differential rotation and the meridional circulation are driven by turbulent stresses in the convection zone, these flows are expected to remain confined within this zone. Current observational(based on helioseismology)and theoretical(based on dynamo theory) evidences point towards an equatorward return flow of the meridional circulation at the bottom of the convection zone. Assuming the mean values of various quantities averaged over turbulence to be axisymmetric,we study the large-scale flows in solar-like stars on the basis of a 2D mean field theory. Turbulent stresses in a rotating star can transport angular momentum, setting up a differential rotation. The meridional circulation arises from a slight imbalance between two terms which try to drive it in opposite directions: a thermal wind term(arising out of the higher efficiency of convective heat transport in the polar regions) and a centrifugal term(arising out of the differential rotation). To make these terms comparable,the poles of the Sun should be slightly hotter than the equator. We discuss the important role played by the meridional circulation in the flux transport dynamo model. The poloidal field generated by the Babcock-Leighton process at the surface is advected poleward, whereas the toroidal field produced at the bottom of the convection zone is advected equatorward. The fluctuations in the meridional circulation(with coherence time of about 30-40 yr) help in explaining many aspects of the irregularities in the solar cycle. Finally, we discuss how the Lorentz force of the dynamo-generated magnetic field can cause periodic variations in the large-scale flows with the solar cycle.