Buoyant velocity

The Rear Stagnant Cap and Bubble Buoyant Velocity at Small Re... 

The rising time t, results simply from the height of cell 1 and buoyant velocity v, 1... 

Ig grows with buoyant velocity v and Re. Even at Re 10 when the bubble behaviour is complicated due to the variation of its form by surface oscillations etc., 1 attains a values of the order of 10 cm, again at very high surface activity (F / c 10 cm). 

The stagnant cap theory permits a quantitative evaluation of the variation of the total amount of surfactant adsorbed at the bubble as a function of its buoyant velocity. The discussion of these results are avoided since they are restricted to Re 1 and experimental data about the mobility of the bubble surface at small Reynolds numbers do not exist. 

The theory of weak retardation of surface motion allows relations to be obtained to give an estimate of the minimum surfactant concentration for the appearance of a stagnant cap which exerts and effects the buoyant velocity. The theory of strong retardation yields a maximum surfactant concentration which separates the transient state from a complete retardation of the bubble surface. Thereby, the transition between the theory of limiting states of the dynamic adsorption layer and the theory of the transient state is obtained, which is important for two reasons. First of all, the theories were developed by different teams of scientists independently. Secondly, it allows to conclude the appropriateness of the approximate methods employed which gives a complete picture of different states of the dynamic adsorption layer. This is possible without huge efforts necessary for numerical solutions. 

Head meters with density compensation. Head meters such as orifices, venturis, or nozzles can be used with one of a variety of densitometers [e.g., based on (a) buoyant force on a float, (b) hydrauhc couphug, (c) voltage output from a piezoelectric ciystal, or (d) radiation absolution]. The signal from the head meter, which is proportional to pV" (where p = fluid density aud V = fluid velocity), is multiphed by p given by the densitometer. The square root of the produc t is proportional to the mass flow rate. 

Forveiy thin hquids, Eqs. (14-206) and (14-207) are expected to be vahd up to a gas-flow Reynolds number of 200 (Valentin, op. cit., p. 8). For liquid viscosities up to 100 cP, Datta, Napier, and Newitt [Trans. In.st. Chem. Eng., 28, 14 (1950)] and Siems and Kauffman [Chem. Eng. Sci, 5, 127 (1956)] have shown that liquid viscosity has veiy little effec t on the bubble volume, but Davidson and Schuler [Trans. Instn. Chem. Eng., 38, 144 (I960)] and Krishnamiirthi et al. [Ind. Eng. Chem. Fundam., 7, 549 (1968)] have shown that bubble size increases considerably over that predic ted by Eq. (14-206) for hquid viscosities above 1000 cP. In fac t, Davidson et al. (op. cit.) found that their data agreed veiy well with a theoretical equation obtained by equating the buoyant force to drag based on Stokes law and the velocity of the bubble equator at break-off ... 

A particularly difficult aspect of the problem of diffusion of atmospheric pollution is the determination of the height to which a buoyant plume with an initial exit velocity will rise. Plume rise, which is defined as the distance between the top of the stack and the axis of the centroid of the pollutant distribution, has been found to depend on ... 

Airborne contaminant movement in the building depends upon the type of heat and contaminant sources, which can be classified as (1) buoyant (e.g., heat) sources, (2) nonbuoyant (diffusion) sources, and (d) dynamic sources.- With the first type of sources, contaminants move in the space primarily due to the heat energy as buoyant plumes over the heated surfaces. The second type of sources is characterized by cimtaminant diffusion in the room in all directions due to the concentration gradient in all directions (e.g., in the case of emission from painted surfaces). The emission rare in this case is significantly affected by the intensity of the ambient air turbulence and air velocity, dhe third type of sources is characterized by contaminant movement in the space with an air jet (e.g., linear jet over the tank with a push-pull ventilation), or particle flow (e.g., from a grinding wheel). In some cases, the above factors influencing contaminant distribution in the room are combined. 

Buoyant jets when the buoyant force acts in the direction of the jet supply velocity at the origin, i.e., upward-projected heated air jet or downward-projected cooled air jet... 

FIGURE 7.80 CDF-predicted values of maximum velocity V, temperature differential, ( C), and airflow, q (Us), in the horizontal cross-section of the buoyant plume above the heated cube (0.66 m x 0.66 m X 0.66 m, 22SW).i ... 

In aerosol theory, is the velocity of free fall of a particle, and by extension in the current work is an empirical velocity related to the buoyancy of the contaminant in air. We further assume that the overall fluid flow pattern is unaffected by the minor quantity of the buoyant contaminant. 

The model is a straightforward extension of a pool-fire model developed by Steward (1964), and is, of course, a drastic simplification of reality. Figure 5.4 illustrates the model, consisting of a two-dimensional, turbulent-flame front propagating at a given, constant velocity S into a stagnant mixture of depth d. The flame base of width W is dependent on the combustion process in the buoyant plume above the flame base. This fire plume is fed by an unbumt mixture that flows in with velocity Mq. The model assumes that the combustion process is fully convection-controlled, and therefore, fully determined by entrainment of air into the buoyant fire plume. 

This angle plate gravity separator removes suspensions of solids from a dilute liquid. The unit is more compact than a box-type settler due to the increased capacity achiev ed by the multiple parallel plates. The concept is fairly standard (U.S. Patent 1,458.805—year 1923) but there are variations in some details. For effective operation, the unit must receive the mixture with definite particles having a settling velocity. The units are not totally effective for flocculants or coagulated masses that may have a tendency to be buoyant. 

The flow patterns for single phase, Newtonian and non-Newtonian liquids in tanks agitated by various types of impeller have been repotted in the literature.1 3 27 38 39) The experimental techniques which have been employed include the introduction of tracer liquids, neutrally buoyant particles or hydrogen bubbles, and measurement of local velocities by means of Pitot tubes, laser-doppler anemometers, and so on. The salient features of the flow patterns encountered with propellers and disc turbines are shown in Figures 7.9 and 7.10. 

Even though upward motion causes cooling of a parcel of air, the condensation of water vapor can maintain the temperature of a parcel of air above that of the surrounding air. When this happens, the parcel is buoyant and may accelerate further upwards. Indeed, this is an unstable situation which can result in violent updrafts at velocities of meters per second. Cumulus clouds are produced in this fashion, with other phenomena such as lightning, heavy precipitation and locally strong horizontal winds below the cloud (which provide the air needed to support the vertical motion). 

This technique is invasive however, the particle can be designed to be neutrally buoyant so that it well represents the flow of the phase of interest. An array of detectors is positioned around the reactor vessel. Calibration must be performed by positioning the particle in the vessel at a number of known locations and recording each of the detector counts. During actual measurements, the y-ray emissions from the particle are monitored over many hours as it moves freely in the system maintained at steady state. Least-squares regression methods can be applied to evaluate the temporal position of the particle and thus velocity field [13, 14]. This technique offers modest spatial resolutions of 2-5 mm and sampling frequencies up to 25 Hz. 

Thus as pointed out above, further treatment on the mechanics of particle motion remains confined only to one-dimensional motion of particle through fluid. A particle of mass m moving through a fluid under the action of an external force Fe is considered. The velocity of the particle relative to the fluid is taken to be v. The buoyant force on the particle is taken to be Fb, and the drag force be FD. Then, the resultant force on the particle is Fe - Fb - Fd, the acceleration of the particle is dv/dt, and the resulting equation of motion is given by... 

Flow effects on non-neutrally buoyant emulsions and suspensions can be studied in various geometries. For example, flow in rotating cylinder and narrow gap concentric cylinder geometries in both horizontal and vertical orientations can be studied. Flow instabilities in settling suspensions in a horizontal rotating cylinder have recently been reported [84], Measurements of velocity fields have not been reported in the literature, but can be performed by using the methods presented in this work. 

Under the influence of a gravitational (centrifugal) field, a solute particle of mass m — M/Ni immersed in a solvent of density p at a distance r from the rotor axis experiences three forces. Within the frame of reference of the rotor, spinning with angular velocity co, these are the centrifugal force Fc, the buoyant force Fb, and the frictional force Ff. 

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