Buoyancy theory

The good agreement obtained for all data using the modified Froude number signifies the physical significance of the parameter. In fact, the dependence of jet penetration on the two-phase Froude number can be derived theoretically from the buoyancy theory following that of Turner (1973). 

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. 

A theory of two-phase bubble flow has been developed by Nicklin (N1), who shows that the motion of bubbles arises partly from buoyancy and partly from the nominal velocity caused by the entry of the two phases into the tube. Theoretical and semiempirical studies of bubble flow have also been presented by Azbel (A2) and by Azizyan and Smirnov (A3), and further experimental data on holdup have been recently reported by Yoshida and Akita (Yl), by Braulick et al. (B9) and by Towell et al. (T3). 

The hydrodynamic region has received considerable attention over the years. Equations (2-63) and (2-64) follow the buoyancy-drag force balance theory. If we... 

U-shaped curve, we have mixtures that can be ignited for a sufficiently high spark energy. From Equation (4.25) and the dependence of the kinetics on both temperatures and reactant concentrations, it is possible to see why the experimental curve may have this shape. The lowest spark energy occurs near the stoichiometric mixture of XCUi =9.5%. In principle, it should be possible to use Equation (4.25) and data from Table 4.1 to compute these ignitability limits, but the complexities of temperature gradients and induced flows due to buoyancy tend to make such analysis only qualitative. From the theory described, it is possible to illustrate the process as a quasi-steady state (dT/dt = 0). From Equation (4.21) the energy release term represented as... 

In well-developed fires, the convective heat fraction is typically measured at more than about 65% of the total heat release rate (Heskestad, 2002). This heat is carried away by the plume above the flames. Prediction of plume velocity and temperatures above the flames serve as the basis for convective heat transfer calculations where overhead equipment exists. Widely used fire plume theory assumes a point source origin, and uniformity throughout the plume relative to air density, air entrainment, velocity profile, and buoyancy. 

If the liquid laminae of a foam system can be converted to impermeable solid membranes, the film viscosity can be regarded as having become infinite, and the resulting solid foam will be permanent. Likewise, if the laminae are composed of a gingham plastic or a thixotrope, the foam will be permanently stable for bubbles whose buoyancy does not permit exceeding the yield stress. For other non-newtonian fluids, however, and for all newtonian ones, no matter how viscous, the viscosity can only delay but never prevent foam disappearance. The popular theory, held since the days of Plateau, that foam life is proportional to surface viscosity and inversely proportional to interfacial tension, is not correct, according to Biker-man (op. cit., p. 161), who points out that it is contradicted by experiment. 

The value of Km depends on the properties of the mean flow at a particular location and time. To account for the contribution of thermal stratification (buoyancy) to the production or suppression of turbulent energy. Km is taken to be a function of the local value of the flux Richardson number, which expresses the ratio of the rate of generation of energy by buoyancy forces to the rate of generation of energy by the turbulent momentum fluxes. In this approach the influence of the past history of the turbulence on velocity field is not considered the approach is termed a local theory. 

This paper aims at presenting the results of the potential theory applied to high pressure and high temperature adsorption data for both sub and supercritical fluids. We used two different procedures for the calculation of the reference characteristic curve The first one is based on the works by Ozawa, Agarwal and Dubinin The second one is based on the works by Dhima and Neimark. The second method leads to satisfactory results as it is possible to obtain a unique characteristic curve but it requires the revision of the classical laws relating the characteristic curve to the structural properties of the adsorbent Using this procedure, it has been possible to point out the influence of the buoyancy effect on the adsorbed phase for the high pressure data and to propose a method to correct it... 

Because of the fact that the capsules in HCP have no wheels and are strongly affected by the buoyancy and hydrodynamic lift, the fluid mechanics of HCP is far more complicated than that of PCP. However, extensive research has been conducted in HCP since 1960 by more than 30 researchers in about 10 nations to understand the basic nature of HCP flow and to derive the necessary equations for the design of HCP. In what follows, only the most pertinent theories and equations needed for the design of commercial HCPs are discussed. Readers interested in knowing more about the theory of HCP should read the vast body of papers and reports published they total well over 100. 

The governing equations for the linear stability theory are the same as for the Rayleigh-Benard problem, namely (12-215), except that it is customary to drop the buoyancy terms because these are of secondary importance for very thin fluid layers where Marangoni instabilities are present but Ra <neutral state. Assuming that... 

V. S. Arpaci and J. E. Dec, A theory for buoyancy-driven turbulent flows, The24th ASME National Heat Transfer Conference, ASME 87-HT, vol. 5, p. 1, Pittsburgh, Pennsylvania, 1987. 

DAL influences practically all stages of the elementary flotation act. Buoyancy velocity of bubbles of definite size with retarded and non-retarded surfaces can differ from each another by a factor of about 2 (see Fig. 8.2). According to the theory of quasi-elastic (Section 10.1) and inelastic (Section 10.2) collisions, a smaller film thickness h corresponding to the beginning... 

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