Convection cell

These observations consummated in a growth model that confers on the millions of aligned zone 1 nanotubes the role of field emitters, a role they play so effectively that they are the dominant source of electron injection into the plasma. In response, the plasma structure, in which current flow becomes concentrated above zone 1, enhances and sustains the growth of the field emission source —that is, zone 1 nanotubes. A convection cell is set up in order to allow the inert helium gas, which is swept down by collisions with carbon ions toward zone 1, to return to the plasma. The helium flow carries unreacted carbon feedstock out of zone 1, where it can add to the growing zone 2 nanotubes. In the model, it is the size and spacing of these convection cells in the plasma that determine the spacing of the zone 1 columns in a hexagonal lattice. 

There is another type of bifurcation called Turing bifurcation, which results in a spatial pattern rather than oscillation. A typical example where a new spatial structure emerges from a spatially unique situation is Benard s convection cells. These have been well examined and are formed with increasing heat conduction.53 Prigogine called this type of structure a dissipative structure.54-56... 

As shown in Fig. 21, in this case, the entire system is composed of an open vessel with a flat bottom, containing a thin layer of liquid. Steady heat conduction from the flat bottom to the upper hquid/air interface is maintained by heating the bottom constantly. Then as the temperature of the heat plate is increased, after the critical temperature is passed, the liquid suddenly starts to move to form steady convection cells. Therefore in this case, the critical temperature is assumed to be a bifurcation point. The important point is the existence of the standard state defined by the nonzero heat flux without any fluctuations. Below the critical temperature, even though some disturbances cause the liquid to fluctuate, the fluctuations receive only small energy from the heat flux, so that they cannot develop, and continuously decay to zero. Above the critical temperature, on the other hand, the energy received by the fluctuations increases steeply, so that they grow with time this is the origin of the convection cell. From this example, it can be said that the pattern formation requires both a certain nonzero flux and complementary fluctuations of physical quantities. 

Benard convection cells [27, 28] a liquid with an inverse temperature gradient (hot below and cool on top) may exhibit thermal convection. Less dense parts of the liquid well upward whereas denser parts show down-welling. The convection cells may arrange in hexagonal order in which the center of each cell wells downwards and the rim wells upwards. The cells stem from the concerted movement of many molecules and cease when the temperature gradient is below a threshold at which the thermal equilibrium canbe reached solely bythermalconductionandnotconvection. 

Figure 11.2 (a) Microscope image of Benard from Ref 33). (b) Two microscope snapshots convection cells (indicated by the circle in the of an evaporating polystyrene solution on silicon upper left corner) and tears ofwine (indicated wafer. The time between the two frames is by the white arrows) in an evaporating approximately 100 ms. The polymer droplets... 

Figure 2.9.9(a) shows a schematic representation of a thermal convection cell in Rayleigh-Benard configuration [8]. With a downward temperature gradient one expects convection rolls that are more or less distorted by the tortuosity of the fluid filled pore space. In the absence of any flow obstacles one expects symmetrical convection rolls, such as illustrated by the numerical simulation in Figure 2.9.9(b). 

Fig. 2.9.9 (a) Schematic cross section of a compartments at the top and bottom, respec-convection cell in Rayleigh-Benard configura- tively. (b) Velocity contour plot of typical tion. In the version examined in Refs. [8, 44], a convection rolls expected in the absence of any fluid filled porous model object of section flow obstacles (numerical simulation). 

Fig. 2.9.10 Maps of the temperature and of the experimental data. The right-hand column convection flow velocity in a convection cell in refers to numerical simulations and is marked Rayleigh-Benard configuration (compare with with an index 2. The plots in the first row, (al) Figure 2.9.9). The medium consisted of a and (a2), are temperature maps. All other random-site percolation object of porosity maps refer to flow velocities induced by p = 0.7 filled with ethylene glycol (temperature thermal convection velocity components vx maps) or silicon oil (velocity maps). The left- (bl) and (b2) and vy (cl) and (c2), and the hand column marked with an index 1 represents velocity magnitude (dl) and (d2).

The formation of Benard convection cells takes place as follows if water is heated from below in a vessel, macroscopic convection currents occur under certain conditions seen from above, these have the structure of uniform, honeycombshaped cells. 

Kauffman also considers that autocatalytic reactions are a necessary precondition for biogenesis processes, as they can wind themselves up via self-amplifying feedback processes until a critical boundary has been reached. The next step would then be the transition from autocatalysis to self-organisation, similar to the transition from unstructured water to convection cells (the Benard instability) (Davies, 2000). 

Fleury and coworkers showed that cellular electrokineitc flow occurs under some conditions at the tips of the branches in the binary-electrolyte thin-layer experiments [37, 38], They constructed a model based on point charges at the growth tips to account for the shape of the induced convection cells. The streamlines of these cells form arcs between adjacent branches. By comparing deposits formed under an electrokineitc regime with deposits formed under a free-convection regime, Barkey et al. 

We can illustrate the salient features of convective dispersal by choosing a simple velocity distribution in a rectangular convection cell (0associated with the onset of Benard instability in the conditions of Boussinesq approximations (e.g., Turcotte and Schubert, 1982). Let us make the calculation for the so-called free-slip conditions, which permit free movement along the boundaries, both vertical and horizontal, such as a convection cell which would be limited by no rigid boundary. From Turcotte and Schubert (1982), we take the velocity field to be... 

The evolution of the simulation (Carr et al. 2008, their Figure 12) shows that the vent site farthest from the cell center develops first, at 700 years after intrusion. Weak convection cells develop over the center of the sill, but most of the high-temperature venting occurs where the circulation is driven by the edge of the cooling sill. Venting of 300°C fluid continues for 135,000 years. 

One of the most interesting aspects of the simulations is the way in which the convection cell that forms at the edge of the sill subsequently induces the formation of convection cells above the sill. Although... 

Russell, M.J. 1983. Major Sediment-Hosted Exhalative Zinc + Lead Deposits Formation From Hydrothermal Convection Cells That Deepen During Crustal Extension. In Sangster, D.F (ed.), MAC Short Course in Sediment-hosted stratiform iead-inc deposits. 

Turbulence also effects plume homogeneity. Turbulence interacts with the plume on different scales. It may be induced by the plume s flowing past a surface, by thermal convection cells, or by cross currents in the water. When the scale is large relative to the diameter of the plume, the effect is somewhat like twisting or rolling a ribbon. When the scale is comparable to the diameter of the plume, it directly affects the cross-sectional homogeneity of the plume. 

Screen Preparations, 100 micron thick x-ray intensifying screens were prepared using standard doctor blade coating techniques. The final phosphor volume was 50% when the coatings were dried. In most instances, the phosphor suspensions were prepared using polyvinyl butyral binders with viscosities adjusted to 2000 centipoise for the doctor blade operation and care was taken to avoid convection cell formation (9). A cross section of the screen construction is shown in Figure I. The completed screens consist of polyester (Mylar) base about 10 mil. thick, a 50 micron thick (TI02 (rutile) reflector layer, a 100 micron thick phosphor layer, a 10 micron thick clear cellulose acetate butyrate top protective layer. 

The large-scale bouyancy effects of an idealized heated repository have also been calculated (6). Expansion of the heated salt will result in a density differential with respect to the surrounding salt. This plus the reduced viscosity of the hot salt tends to form slow convective cells in the salt. Calculations of a repository in homogeneous salt loaded with 10-year old HLW at 100 kilowatts per acre show a peak upward velocity (approximately 1.5 cm/year) of the repository horizon would occur between 200 and 300 years and then slowly decrease. Displacement would be about 6.5 meters at 400 years. Incorporating a more viscous layer above the repository level to more closely simulate the actual WIPP site geology leads to maximum velocities about one-third those obtained in homogeneous salt. After 400 years the upward displacement for this latter case would be about 2.1 meters. More... 

Stommel, H., Trajectories of small bodies sinking slowly through convection cells , J. Mar. Res., 8, 24-29 (1949). 

BENARD CONVECTION CELLS. When a layer of liquid is heated from below, the onset of convection is marked by the appearance of a regular array of hexagonal cells, the liquid rising in the center and falling near the wall of each cell. The criterion for the appearance of the cells is that the Rayleigh number should exceed 1700 (for rigid boundaries). 

For case (a), the flow field consists of a single convective cell which circulates around an elliptic point (center) located at X= Y= 0 [28], For case (b) the flow field consists of two counter-rotating cells with centers at X = 0 and Y = 0.58. The cells are separated by the surface Y= 0. For case (c), the flow field is similar to (b) in the sense that the flow field consists of two counter-rotating cells separated by the surface at X= 0. The centers of rotation are at X= 1 and Y = 0. For case (d), the flow field consists of four counter-rotating cells separated by two surfaces at X = 0 and Y = 0. 

Figure 3. Streamlines (on right) and isotherms (on left) for growth of Si in a prototype Czochralski system. The volume of the melt, at the bottom in each drawing, changes among the calculations, affecting the qualitative form of the convection cell and the shape of the crystal interface. From Theory of Transport Processes in Single Crystal Growth from the Melt, by R. A. Brown, AIChE Journal, Vol. 34, No. 6, pp. 881 -911, 1988 [29]. Reproduced by permission of the American Institute of Chemical Engineers copyright 1988 AIChE.

Figure 1 illustrates conventional CVD reactors. These reactors may be classified according to the wall temperature and the deposition pressure. The horizontal, pancake, and barrel reactors are usually cold-wall reactors where the wall temperatures are considerably cooler than the deposition surfaces. This is accomplished by heating the susceptor by external rf induction coils or quartz radiant heaters. The horizontal multiple-wafer-in-tube (or boat) reactor is a hot-wall reactor in which the wall temperature is the same as that of the deposition surface. Therefore, in this type of reactor, the deposition also occurs on the reactor walls which presents a potential problem since flakes from the wall deposit cause defects in the films grown on the wafers. This is avoided in the cold-wall reactors, but the large temperature gradients in those reactors may induce convection cells with associated problems in maintaining uniform film thickness and composition. 

Example 12.3 Stability under both dissipative and convective effects In some cases, both dissipative as well as convective effects determine the stability of a system. Some examples of such stability are the onset of free convection in a layer of fluid at rest, leading to Benard convection cells, and the transition from laminar to turbulent flow. For stability considerations, two limiting cases exist (i) in the case of ideal fluids, dissipative processes are neglected, and (ii) in purely dissipative systems, no convection effects occur. 

Let us define the distance of a system from global equilibrium by parameter ji (e.g., a temperature or a concentration gradient). After a value of /J, is reached, the system displays ordering characterized by a certain frequency or a wavelength. Figure 13.1 shows the bifurcation in the velocity in Bernard convection cells. If the parameter j8 is... 

One of the best-known physical ordering phenomena is the Benard cells, which occur during the heating a fluid held between two parallel horizontal plates separated by a small distance. The lower plate is heated, and the temperature is controlled. The upper plate is kept at a constant temperature. When the temperature difference between the two plates reaches a certain critical value, the elevating effect of expansion predominates, and the fluid starts to move in a structured way the fluid is divided into horizontal cylindrical convection cells, in which the fluid rotates in a vertical plane. At the lower hot plate, the hot fluid rises later, it is cooled at the upper plate, and its density increases again this induces a movement downward, as seen in Figure 13.2. The Benard cells are one of the best-known physical examples of spontaneous structurization as a result of sufficient distance from equilibrium, which is the large temperature difference between the plates. The critical temperature difference ( A 7 )c can be determined from the... 

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