Liquid velocity experimental approach

Grimley (G10, Gil) used an ultramicroscope technique to determine the velocities of colloidal particles suspended in a falling film of tap water. It was assumed that the particles moved with the local liquid velocity, so that, by observing the velocities of particles at different distances from the wall, a complete velocity profile could be obtained. These results indicated that the velocity did not follow the semiparabolic pattern predicted by Eq. (11) instead, the maximum velocity occurred a short distance below the free surface, while nearer the wall the experimental results were lower than those given by Eq. (11). It was found, however, that the velocity profile approached the theoretical shape when surface-active material was added and the waves were damped out, and, in the light of later results, it seems probable that the discrepancies in the presence of wavy flow are due to the inclusion of the fluctuating wavy velocities near the free surface. 

To estimate the superficial liquid velocity in the riser, this correlation must be combined with the Fanning friction factors in the riser and downcomer, f and f, the frictional loss coefficients at the top and bottom of the airlift, and and the gas hold-up in the riser, This approach predicted their experimental data in a pilot-plant scale external-loop airlift column for a carboxymethyl cellulose solution, with an error of 20%. 

Distinct characters of the static structure enter the specification of this more complex motion. Same as for librational oscillations, the symmetry of tumbling reorientations proceeds from both the symmetry of the intermolecular torques and the symmetry of the molecules themselves through the values of their distinct molecular moments of inertia. The most prominent role of inertial factors, and more recently that of torques too, have been made especially clear by W.A. Steele (1). Apart from these molecular and local factors, collective properties of the liquid enter the dynamics through the rate of reorientation. This rate itself is a combination of two factors, generally undistin-guishable in the observed mean value these are the velocity of the angular rotation and the rate of occurence of elementary rotations. Hereafter in section V we will come back to experimental approaches specifying the rate of occurence dependence upon the liquid equation of state (i.e. its temperature and density dependence). ... 

The flow of a long bubble in a capillary is a classical problem in fluid mechanics. Bubbles have been used as tracers in capillaries filled with liquid in order to determine liquid velocity. This application led to the discovery that when a wetting viscous liquid is displaced by a gas bubble in a capillary a liquid film is deposited on the wall. Initial experimental findings that the thickness of the film was proportional to Ca / were confirmed and extended to Ca= 10 [3]. In his pioneering approach, Brether-ton [1] assumed creeping flow in the liquid and used lubrication theory for the region of the film between the end of the spherical bubble cap and the flat film behind it to calculate the thickness of the film, the pressure drop and... 

The models based on superficial liquid velocity have been extensively used by various researchers to simulate three-phase experimental reactors (Korsten and Hoffmann, 1996 Chowdhuri et al., 2002 Rodriguez and Ancheyta, 2004 Mederos et al., 2006). The same approach has been followed in this work in order to simulate hydrodesulfurization and hydrodemetallization of heavy crude oil. 

Fig. 3a indicates that the bubble-rise velocity measured based on the displacement of the top surface of the bubble ( C/bt) quickly increases and approaches the terminal bubble rise velocity in 0.02 s. The small fluctuation of Ubt is caused by numerical instability. The bubble-rise velocity measured based on the displacement of the bottom surface of the bubble (Ubb) fluctuates significantly with time initially and converges to Ubt after 0.25 s. The overshooting of Ubb can reach 45-50 cm/s in Fig. 3a. The fluctuation of Ubb reflects the unsteady oscillation of the bubble due to the wake flow and shedding at the base of the bubble. Although the relative deviation between the simulation results of the 40 X 40 x 80 mesh and 100 x 100 x 200 mesh is notable, the deviation is insignificant between the results of the 80 x 80 x 160 mesh and those of the 100 X 100 x 200 mesh. The agreement with experiments at all resolutions is generally reasonable, although the simulated terminal bubble rise velocities ( 20 cm/s) are slightly lower than the experimental results (21 25 cm/s). A lower bubble-rise velocity obtained from the simulation is expected due to the no-slip condition imposed at the gas-liquid interface, and the finite thickness for the gas-liquid interface employed in the computational scheme.

The principal feature of this relationship is that F values are derived solely from molecular formulae and chemical structures and require no prior knowledge of any physical, chemical or thermochemical properties other than the physical state of the explosive that is, explosive is a solid or a liquid [72]. Another parameter related to the molecular formulae of explosives is OB which has been used in some predictive schemes related to detonation velocity similar to the prediction of bri-sance, power and sensitivity of explosives [35, 73, 74]. Since OB is connected with both, energy available and potential end products, it is expected that detonation velocity is a function of OB. As a result of an exhaustive study, Martin etal. established a general relation that VOD increases as OB approaches to zero. The values of VOD calculated with the use of these equations for some explosives are given in the literature [75] and deviations between the calculated and experimental values are in the range of 0.46-4.0%. 

The velocity distribution equation (27) indicates that in the absence of surface tension effects the maximum velocity in a film flowing in a flat channel of finite width should occur at the free surface of the film at the center of the channel. The surface velocity should then fall off to zero at the side walls. However, experimental observations have shown (BIO, H18, H19, F7) that the surface velocity does not follow this pattern but shows a marked increase as the wall is approached, falling to zero only within a very narrow zone immediately adjacent to the walls. The explanation of this behavior is simple because of surface tension forces, the liquid forms a meniscus near the side walls. Equation (12) shows that the surface velocity increases with the square of the local liquid depth, so the surface velocity increases sharply in the meniscus region until the side wall is approached so closely that the opposing viscous edge effect becomes dominant. 

The microstructural models described here represent theoretical milestones in gasless combustion. Using similar approaches, other models have also been developed. For example, Makino and Law (1994) used the solid-liquid model (Fig. 20c) to determine the combustion velocity as a function of stoichiometry, degree of dilution, and initial particle size. Calculations for a variety of systems compared favorably with experimental data. In addition, an analytical solution was developed for diffusion-controlled reactions, which accounted for changes in X, p, and Cp within the combustion wave, and led to the conclusion that U< Ud(Lak-shmikantha and Sekhar, 1993). 

There is a great deal of theoretical and experimental information from micrometeorological research on the transfer of momentum, heat, and mass at solid and liquid surfaces and across their associated air boundary layers (hence the term boundary layer models for relationships arising from this approach). Based on the analogy between transfer of momentum and mass, it has been shown that k is proportional to the friction velocity in air (u ) and that k is also proportional to Sc. Apart from an assumption that the surface was smooth and rigid, it was also necessary to assume continuity of stress across the interface in order to convert the velocity profile in air to the equivalent profile in the water (Deacon, 1977). The relationship developed by Deacon is as follows ... 

In order to determine the mean turbulent approach velocity of bubbles causing bubble-bubble collisions, a series of questionable assumptions were made by Luo and Svendsen [74]. First, in accordance with earlier work on fluid particle coalescence the colliding bubbles were assumed to take the velocity of the turbulent fluid eddies having the same size as the bubbles [16, 92]. Luo and Svendsen [74] further assumed that the turbulent eddies in liquid flows may have approximately the same velocity as neutrally buoyant droplets in the same flow. Utilizing the experimental results obtained in an investigation on turbulent motion of neutrally buoyant droplets in stirred tanks reported by Kuboi et al [53, 54], the mean square droplet velocity was expressed by ... 

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