Velocity and concentration

It is important to recognize the approximations made here the electric field is supposed to be sulficiently small so that the equilibrium distribution of velocities of the ions is essentially undisturbed. We are also assuming that the we can use the relaxation approximation, and that the relaxation time r is independent of the ionic concentration and velocity. We shall see below that these approximations break down at higher ionic concentrations a primary reason for this is that ion-ion interactions begin to affect both x and F, as we shall see in more detail below. However, in very dilute solutions, the ion scattering will be dominated by solvent molecules, and in this limiting region A2.4.31 will be an adequate description. 

G. Laminar, fully developed concentration and velocity profile... 

The difficulty with Eq, (26-58) is that it is impossible to determine the velocity at every point, since an adequate turbulence model does not currently exist, The solution is to rewrite the concentration and velocity in terms of an average and stochastic quantity C = (C) -t- C Uj = (uj) + Uj, where the brackets denote the average value and the prime denotes the stochastic, or deviation variable. It is also helpful to define an eddy diffusivity Kj (with units of area/time) as... 

The constant, K, depends on the target material, particle abrasiveness, and size distribution of the particles. The kinetic energy of the particles is Mp x Vp + 2. This parameter includes the solids loading, or concentration, and velocity of the particle. Alpha is the angle of impingement of the particle on the blade surface. 

For this safety criterion, we consider the fact that as the velocity decreases with increasing distance from the surface of the tank, it will reach some critical velocity, at which the induced movement of air will be insufficient to overcome the effects of crossdrafts or the buoyancy velocity At this point, we must ensure that the concentration is at, or below, some critical allowable concentration, Qfj,. The values of the critical concentration and velocity will depend (tn particular circumstances, but it is worth noting that must be at least equal to I g in order to overcome the effects of buoyancy, and the appropriate value will depend on the crossdrafts, which typically vary between 0.05 m to 0.5 in s F For the sake of providing examples, we have chosen to be the maximum of the buoyancy velocity and the typical cross-draft velocity. For the critical concentration we have chosen two values, C = 0.05 and C = 0.10. The actual value used by a designer would depend on the toxicity of the contaminant in question. 

Ideally the design engineer requires an equation which condenses all this information and from which he can calculate the effect of a particular chemical upon a range of materials, and the limiting conditions of say temperature, concentration and velocity. To achieve this objective he needs to know which of the properties of the chemical and the material are the most important in determining the interaction leading to corrosion. 

J.B. Moss 1980, Simultaneous measurements of concentration and velocity in an open premixed turbulent flame. Combust. Sci. Tech. 22 119-129. 

A. M. Corbett, R. J. Phillips, R. J. Kauten, K. L. McCarthy 1995, Magnetic resonance imaging of concentration and velocity profiles of pure fluids and solid suspensions in rotating geometries),/. Rheol. 39, 907. 

Dispersion is another reactor mixing topic that will be discussed in Chapter 6. Dispersion normally is used when cross-sectional mean concentrations and velocities are being computed. A cross-sectional mean concentration is useful for a pipe, stripping tower, river, or groundwater transport. 

The turbulent transport equations are obtained in the traditional treatment of turbulence by time averaging the unsteady-state transport equations, after substituting the concentration and velocity components by the sum of their mean values and the corresponding time-dependent fluctuations. The following expression is thus obtained for the (time) average of the number of moles N that are transferred per unit time through unit area, in the direction y normal to the wall ... 

In most applications, the axial dispersion in both phases can be considered to be negligible (Smith, 1981). Moreover, no radial gradients of concentration and velocity exist for the gas or liquid. 

But the answer to this, and to similar questions arising out of analogous instances, is not forthcoming. The reason is partly that thorough investigations of the relation between concentration and velocity of reaction have seldom been made in suitable cases, and partly because, even when they have been made, the interpretation of the results is not easy. 

Species concentration and velocity fields along the flow passage at Dean numbers above and below the threshold value... 

M 69] [P 61 ] For a curved channel design, species concentration and velocity fields of the secondary flow were given (see Figure 1.146) [152], These fields each were... 

In conclusion, droplet size measurements in the range 10 to 100 m can be performed, also in hostile environments, from the visibility of individual scattered signal. Advantages of this method are simultaneous measurement of particle size, concentration and velocity no calibration is necessary good spatial resolution up to less than 1 mm-3 the visibility is independent on particle trajectory. Limitations are individual scattered signal can be obtained only with moderate particle concentration it is difficult to automatically process scattered signals to extract the visibility value and to check validation conditions it seems very difficult to extend the technique to cover the entire spray distribution the lower limit in the small particle end of the distribution curve depends upon experimental sensitivities and V(d) curve flatness... 

The appropriate boundary conditions for flow over the flat plate are ux=Uy=0 at y=0 and ux=m, at y=°°. Given these, Eqs. (96) and (98) can be solved to determine the steady state velocity profile adjacent to the flat plate. If we assume that the concentration and velocity profiles have similar shape, the mass flux per unit area from the surface of the plate is defined as follows [50] ... 

The neutron flux (the product of neutron concentration and velocity) is a strong function of neutron energy, position in the target island, and the reactor operating conditions. The means by which these variations are handled is discussed below. 

Hartge, E. U., Rensner, D., and Werther, J. Solids concentration and velocity patterns in circulating fluidized beds, in Circulating Fluidized Bed Technology II (P. Basu and J. F. Large, eds.), p. 165. Pergamon Press, 1988. 

The above equations assume that the liquid-phase reactant C, the product of the reaction, and the solvent are nonvolatile. The effective interfacial area for mass transfer (nL) and the fractional gas holdup (ii0o) arc independent of the position of the column. The Peclet number takes into account any variations of concentration and velocity in the radial direction. We assume that Peclet numbers for both species A and C in the liquid phase are equal. For constant, 4 , Eq. (4-73) assumes that the gas-phase concentration of species A remains essentially constant throughout the reactor. This assumption is reasonable in many instances. If the gas-phase concentration does vary, a mass balance for species A in the gas phase is needed. If the gas phase is assumed to move in plug flow, a relevant equation would be... 

Lemoine, F Wolff, M., and Lebouche, M., Simultaneous concentration and velocity measurement using combined laser-induced fluorescence and laser Doppler velocimetry Application to turbulent transport. Exp Fluids 20,319 (1996). 

Temperature, Concentration, and Velocity Measurements in Fuel Spray Free Flames... 

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