Apparent velocity

The conseqnence is that the rate of prodnction of volnme of hnrned prodncts is greater dne to the density decrease resnlting from the reaction. As the prodncts expand this canses the nnhnrned mixtnre to move as well. The flame is then seen to move forward with a higher apparent velocity, Vf, the snm of the mean nnhnrned gas velocity, u, and the tnrhnlent hnrning velocity, S. Vf is called the flame velocity (flame speed). 

This further assumption concerning velocity and the volumetric rate of flow restricts flow to the pores and not the full area. Therefore, v is an apparent velocity. The actual velocity, assuming a uniform medium, is... 

FIG. 1. Phenylephrine (PE)-mediated asynchronous wave-like [Ca2+] oscillations and contraction in the rabbit inferior vena cava. (A) [Ca2+] oscillations recorded in neighbouring smooth muscle cells within the intact vessel are not synchronized between cells as they each display different frequency of oscillations. (B) Individual Ca2+ spike in PE-mediated [Ca2+]j oscillations are wave-like as different regions (1, 2 and 3) in the same ribbon-shaped VSMC experience sequential rise of [Ca2+] in time. (C) The [PE]-dependence in force generation is compared to the [PE]-dependence in the percentage recruitment of cells, the amplitude of the [Ca2+]j oscillations, the frequency of the [Ca2+]j oscillations and the apparent velocity of the recurring Ca2+ waves. (Experimental traces reproduced, with permission from Lee et al 2001.)... 

Substituting Eq. 7.18 into Eq. 7.3 and solving Eqs. 7.1 and 7.3 for V, 14, and Vp, the solution for the transformed boundary condition problem Is obtained, and the equations are shown by Eqs. 7.21, 7.23, and 7.26. These equations physically represent the flow due to rotation and pressure in the transformed frame of reference in Fig. 7.10. Equation 7.21 is the velocity equation for the x-direction recirculatory cross-channel flow for the observer attached to the screw, and Eq. 7.23 is the apparent velocity in the z direction for the observer attached to the moving screw. 

EXAMPLE 12.4 Electrophoretic Mobility of Bacteria. It is proposed to evaluate the electrophoretic mobility of the bacteria cells shown in Figure 12.10a by multiplying the appropriate value of time-1 by the distance of particle displacement and then dividing by E. Criticize or defend the following proposition It is appropriate to use the maximum apparent velocity since this is measured at the center of the cell and is therefore subject to the least interference by wall effects. 

It is, perhaps, less known that the concepts of complementarity and indeterminacy also arise naturally in the theory of Brownian motion. In fact, position and apparent velocity of a Brownian particle are complementary in the sense of Bohr they are subject to an indeterminacy relation formally similar to that of quantum mechanics, but physically of a different origin. Position and apparent velocity are not conjugate variables in the sense of mechanics. The indeterminacy is due to the statistical character of the apparent velocity, which, incidentally, obeys a non-linear (Burgers ) equation. This is discussed in part I. 

Here n designates the density or distribution function j the diffusion current vd the apparent velocity, namely, the drift velocity, of a Brownian particle and D the diffusion constant. Equation (1) is a continuity equation while Eq. (2) is simply Fick s law augmented by a definition of vd. 

Here, tr, is the liquid-to-surface interfacial tension l , u the vapor apparent velocity directing the droplets and S characterizes the wire mesh By ignoring the secondary effects, a simplified force balance can be written for the disengaging droplet size ... 

The apparent velocity, t 4, is related to the fraction of area covered by liquid, t. The liquid-free surface for vapor flow is, therefore, 1 —<), with. 4, being the total surface area of the impingement pad. And the apparent velocity becomes ... 

Thus, for a vapor of p,.-0.2 Ibn/Tt at an apparent velocity of l, 3 ft/s carrying an entrained liquid of density p,>45 Ibm/fl, with the interfacial tension 0.066 Ibm/s, the minimum size at which coalesced droplets will start to disengage is D >0.0I7 ft (5.000 Sim). The actual disengagement size may be smaller, due to the droplets smaller wetted perimeter (smaller surface-tension force) and droplet deformation (smaller projected area receiving the vapor momentum). 

At the reaction temperature, the concentration of methane obeys the following equation (apparent velocity increase kv given in [38] ss) ... 

The apparent diffusion coefficient D is determined by minimizing the difference between the experimental and the calculated apparent velocity versus dp 16. Then we have to determine two parameters Km and Vmax. V, does not depend on the particule size so these two parameters are determined by studying the influence of myristic acid concentration on apparent velocity. 

Shen, T. Influence of Apparent Velocity upon the Regenerator Performance of a FCC Unit, Petroleum Processing (Chinese), No. 9, pp. 1-8 (1988). 

FIGURE 2.2 Electro-osmotic velocity of liquid (dashed parabola) and apparent velocity of particles (circles) in a flat cell. Zero velocity is represented by the horizontal solid line. 

Vf = the reaction velocity after the transition k = apparent velocity constant of the transition t = time (8,13). 

The simulations were performed for a 1 m thick wall. The apparent velocity and... 

Micellar electrokinetic chromatography (MEKC) is a particular EKC mode where the secondary phase is composed by micellized surfactant (MEKC is discussed in detail in Chapter 3 by Terabe). Solute differential retention occurs as a result of a partition mechanism between a dispersed phase defined by the total volume of micelles and the remaining aqueous phase. MEKC modes of elution comprise normal, restricted, and reversed MEKC, based on the relative migration of the analyte and secondary phase apparent velocity. 

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