Convective motion

For a chemical reaction such as combustion to proceed, mixing of the reactants on a molecular scale is necessary. However, molecular diffusion is a very slow process. Dilution of a 10-m diameter sphere of pure hydrocarbons, for instance, down to a flammable composition in its center by molecular diffusion alone takes more than a year. On the other hand, only a few seconds are required for a similar dilution by molecular diffusion of a 1-cm sphere. Thus, dilution by molecular diffusion is most effective on small-scale fluctuations in the composition. These fluctuations are continuously generated by turbulent convective motion. 

The flow in a heated capillary depends on a number of parameters including the channel geometry, physical properties of the liquid and the heat flux. An immediate consequence of the liquid heating and evaporation is convective motion of both phases. The latter leads to a velocity and temperature field fransformation and a change in fhe meniscus shape. 

Another area of rapid growth for particle separation has been that of Field-Flow Fractionation (FFF) originally developed by Giddings (12,13>1 1 ) (see also papers in this symposium series). Like HDC, the separation in field-flow fractionation (FFF) results from the combination of force field interactions and the convected motion of the particles, rather than a partitioning between phases. In FFF the force field is applied externally while in HDC it results from internal, interactions. 

The electroosmotic pumping is executed when an electric field is applied across the channel. The moving force comes from the ion moves in the double layer at the wall towards the electrode of opposite polarity, which creates motion of the fluid near the walls and transfer of the bulk fluid in convection motion via viscous forces. The potential at the shear plane between the fixed Stem layer and Gouy-Champmon layer is called zeta potential, which is strongly dependent on the chemistry of the two phase system, i.e. the chemical composition of both solution and wall surface. The electroosmotic mobility, xeo, can be defined as follow,... 

Wall-jet design is based on flow rate acceleration, perpendicular to the working electrode to create strong convective motion of the analyte towards the working electrode (see Figure 3-2). 

Porous electrodes may be regarded as a combination of thin-layer and wall-jet design short diffusion path length, strong convective motion due to high liquid velocities in narrow pores. 

A rheological measurement is a useful tool for probing the microstructural properties of a sample. If we are able to perform experiments at low stresses or strains the spatial arrangement of the particles and molecules that make up the system are only slightly perturbed by the measurement. We can assume that the response is characteristic of the microstructure in quiescent conditions. Here our convective motion due to the applied deformation is less than that of Brownian diffusion. The ratio of these terms is the Peclet number and is much less than unity. In Equation (5.1) we have written the Peclet number in terms of stresses ... 

It is generally agreed that mass transfer coefficients are only correlated for negligibly small convectional motion of the transitional component, which is vertical to the interface. However, when the mass transfer is mutual and equimolar, no such convections normal to the interface result otherwise the transfer coefficient and the driving force must be corrected with the aid of theories of mass transfer [18]. The transitional rates and, accordingly, convectional flow rates normal to the interface are only low for the extraction process, so that the uncorrected Eq. (9.31) may be used. 

The purpose of this paper Is to present a brief overview and description of a modelling approach we are taking which Is aimed at developing a quantitative understanding of the mechanisms and separation capabilities of particle column chromatography. The main emphasis has been on the application of fundamental treatments of the convected motion and porous phase partitioning behavior of charged Brownian particles to the development of a mechanistic rate theory which can account for the unique size and electrochemical dependent separation behavior exhibited by such systems. 

Rapid polymer transport and associated structured flow formation are multistep processes. These processes may include 1) initial diffusion of components across the boundary 2) inversion of density, 3) convective motions occurring in regions that are unstable with respect to density, 4) birth and nucleation of structured flows, 5) development of visible structured flows, and 6) movement and maintenance of structured flows over longer periods. A clear delineation of any of these steps has not been achieved so far. Future work will be concerned with the development of systems in which these individual steps may be studied in more detail. 

This characterizes the time taken for the restoration of the equilibrium microstructure after a disturbance caused, for example, by convective motion, i.e., this is the relaxation time of the microstructure. The time scale of shear flow is given by the reciprocal of the shear rate, 7. The dimensionless group formed by the ratio (tD ff/tShear) is the Peclet number... 

The physical reason behind the modification at low wind speed as suggested by field data remains unclear. Yet, we should not forget that at low wind speed, the instantaneous wind is not the only significant source of motion at the water surface. Water motions caused by wind do not stop as soon as the wind ceases. Furthermore, thermal processes lead to density instabilities and convective motion, even if there is absolutely no wind. In fact, natural surface water bodies are hardly ever at rest. 

In early type stars, the bottom boundary penetrates into convective core (Osaki 1975). Accordingly, convective motion of eddies excites sound waves, as in the case of acoustic noise emmision from incompressible turbulence, shown by Lighthill (1978). Since the frequency of excited waves is higher than the Brunt-Vaisala frequency at the photosphere, the waves are not trapped, but running outward (cf. Unno et al 1979). 

Microturbulence seldom occurs alone it is generally driven by larger-scale motions microturbulence is the high-wavenumber part of the atmospheric spectrum of turbulence. For the stars discussed here the origin of the motion field may be found in pulsations or in convective motions. Such motions have been discovered in a Cyg (Boer et al., 1987 ) they have up- and downward velocities of 14 km s-1 and the... 

Numerous electroanalytical techniques are performed on quiet or stationary solutions. The ideal stationary solution has no convective motion due to vibrations, mechanical stirring, motion of the electrode(s), temperature gradients, or density gradients. At long times only natural convection effects arising from the electrode reaction itself will contribute to nonideality. 

Laws were found for the combustion of gases in laminar or turbulent flow. Similarity laws were formulated for flame propagation under conditions in which the difference in density of a substance before and after combustion causes convective motion of the gas and flame.1... 

As the heat transfer increases, the flame velocity decreases, but before the decrease becomes significant propagation stops. Quantitative verification is hampered by complicating factors convective motion of the gas, which bends the flame front, causes a difference between the theoretical rate of flame motion with respect to the gas and the measured rate of flame motion with respect to the walls. 

In a mixture at rest, a diffusive flame would take the form of a sphere convective motion of the gas leads to the flame taking the form of a bent cap. When a lean mixture is ignited with an electric spark, one or several such caps form and rise slowly upward to the end of the tube. An elementary calculation of diffusive combustion in a gas at rest yields a combustion temperature which depends only on the ratio i9/k, and not on the radius... 

Thus, it is not the absolute value of D, but its ratio with k that determines the character of the phenomena. Convection blurs the effect in convective motion the particles of gas which carry quantities of material and heat are in the ratio of the concentration to the product of the specific heat and temperature, which corresponds to equality of the effective (related to the gas motion) coefficients of diffusion and thermal diffusivity. In all cases radiation from the surface of the catalyst lowers its temperature Tr. 

P 11] Simulations were carried with a simplified chamber and air-bubble pocket geometry. Details on this geometry and the several assumptions taken for describing the fluid dynamics can be found in [23] and are not described further here. Generally, the experimental known fluid dynamic features were taken into account, e.g. the convective motion based on vortices was assumed also in the model. 

Ribbon blenders consist of some moving elements, such as a spiral element, that induce convective motion. They are good for cohesive particulate mixtures, but they require more power than tumbling blenders and are more difficult to clean. In ribbon-type blenders, as well as some other types, PVC dry blend can be prepared by slowly spraying small amounts of liquid additives into the mixture. Such additives may sometimes generate the formation of small, soft balls, which should be avoided if a free-flowing dry blend is desired. Ribbon blenders generate considerable static electricity. 

Closed vessel One in which the rate of diffusion across the vessel entrance and exit boundaries is negligible compared to the rate of convective motion across the boundaries. 

The RTD concept is now well established and widely used for designing, scaling-up and optimizing chemical reactors. This subject was recently reviewed by Nauman (1). Most classical textbooks (55) mainly deal with the simple case of steady state incompressible flow, single inlet and outlet, and purely convective motion... 

This term varies significantly with the nature of the fuel. Liquid fuels are characterized by the presence of recirculation currents induced by buoyancy. These currents homogenize the temperature distributions, reducing in-depth conduction. Nevertheless, convective motion transfers heat to the interior of the pool leading to an additional term of in-depth convection. Convective heat transfer in polymer melts has a similar behavior and could potentially have an important effect on burning rates nevertheless, the impact of polymer melt rheology on the flammability of materials is still a matter of great controversy. 

Convective motion then begins fluid near the hot wall rises and the cooled fluid descends. Meanwhile, thermal diffusion enriches different components in either the hot or cooled regions, and the different flow direction in the two regions leads to component separation. 

It will be assumed here that the convective heat transfer rates are high enough to allow the effects of radiation on the convective motion to be ignored, i.e., to assume that the convection and the radiation can be considered separately and that the total heat transfer rate will be the sum of the separately evaluated convective and radiant heat transfer rates. 

As mentioned before, there are analytical solutions for the heat transfer that apply under certain limiting conditions. For example, if the Rayleigh number is very low, the convective motion will be so weak that it has no influence on the heat transfer rate and the heat transfer will effectively be by pure conduction. In this case the heat transfer rate is uniform on the hot and cold walls and is given by ... 

Solution. Convective motion will be assumed to begin when ... 

At this temperature, air at standard ambient pressure, has the following properties 0 = 0.0033K 1, v = 16 x 10 6 m2/s, Pr = 0.7 Hence, convective motion will be assumed to begin when ... 

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