Buoyancy processes

Coalescence probability due to buoyancy processes (—) Coalescence probability due to turbulence processes (—) Advance particle distribution function with multiple inner coordinates... 

Separations. Foams have important uses in separations, both physical and chemical (51,52). These processes take advantage of several different properties of foams. The buoyancy and mechanical rigidity of foam is exploited to physically separate some materials. The large volume of vapor in a foam can be exploited to filter gases. The large surface area of a foam can also be exploited in the separation of chemicals with different surface activities. 

The sequence, flocculation — coalescence — separation, is compHcated by the fact that creaming or sedimentation occurs and that this process is determined by the droplet size. The sedimentation velocity is monitored by the oppositely directed forces which form the buoyancy and the viscous drag of the continuous phase on the droplet ... 

In this section the correlations used to determine the heat and mass transfer rates are presented. The convection process may be either free or forced convection. In free convection fluid motion is created by buoyancy forces within the fluid. In most industrial processes, forced convection is necessary in order to achieve the most economic heat exchange. The heat transfer correlations for forced convection in external and internal flows are given in Tables 4.8 and 4.9, respectively, for different conditions and geometries. 

Use of warm processes on a downdraft table should be avoided since the air velocity created by the exhaust is often lower than the velocity due to buoyancy effects. Effective use of a downdraft table for welding requires velocities high enough to counteract the buoyancy, which could result in disturbances of the welding process. 

The stopwatch technique for determining emission volume flow rate is based on measuring with a stopwatch the elapsed time for fume to rise between two known levels (e.g., Zj, Z,). For this test procedure to be valid, the test must be carried out in a region where the rising fume clearly exhibits buoyancy-dominated plume behavior. The calculation procedure depends on a good estimate of the location of the virtual origin of the plume and the heat release for the process. 

The factors affecting the performance of a local exhaust system are well known. For fume control, an added factor is the effect of heat release or buoyancy. Important design parameters are process heat release and the size and geometry of air-supply openings and their location relative to major surfaces of the enclosure, lire kxation of the fume off-take is usually only of secondary importance. 

In the set of conservation equations described earlier, the Reynolds number and the Froude number must be the same for the model and the prototype. Since most industrial operations involve turbulent flow for which the Reynolds number dependence is insignificant, part of the dynamic similarity criteria can be achieved simply by ensuring that the flow in the model is also turbulent. For processes involving hot gases (i.e., buoyancy driving forces), the Froude number similarit) yields the required prototype exhaust rate as follows. 

Sub-ground pits may be required for access, service distribution or process requirements. Depending on pit dimensions and water table levels, problems that may have to be considered at the design stage include heave due to relief of overburden, buoyancy from water pressure and waterproofing. 

For these processes which depend on buoyancy effects, the rate of heat transfer might be expected to follow a relation of the form ... 

In Og (Figure 8.1.5b), xmlike in the Ig case, the fuel jet momentum dispersed and the centerline velocity decayed rapidly owing to the lack of buoyancy. As a result, the fuel molecules diffused in every direction and formed a quasi-spherical flame. The slow diffusion processes (1) limited the transport rates of the fuel and oxygen into the flame zone and (2) decreased... 

We use computational solution of the steady Navier-Stokes equations in cylindrical coordinates to determine the optimal operating conditions.Fortunately in most CVD processes the active gases that lead to deposition are present in only trace amounts in a carrier gas. Since the active gases are present in such small amounts, their presence has a negligible effect on the flow of the carrier. Thus, for the purposes of determining the effects of buoyancy and confinement, the simulations can model the carrier gas alone (or with simplified chemical reaction models) - an enormous reduction in the problem size. This approach to CVD modeling has been used extensively by Jensen and his coworkers (cf. Houtman, et al.) ... 

Boundary layer similarity solution treatments have been used extensively to develop analytical models for CVD processes (2fl.). These have been useful In correlating experimental observations (e.g. fi.). However, because of the oversimplified fiow description they cannot be used to extrapolate to new process conditions or for reactor design. Moreover, they cannot predict transverse variations In film thickness which may occur even In the absence of secondary fiows because of the presence of side walls. Two-dimensional fully parabolized transport equations have been used to predict velocity, concentration and temperature profiles along the length of horizontal reactors for SI CVD (17,30- 32). Although these models are detailed, they can neither capture the effect of buoyancy driven secondary fiows or transverse thickness variations caused by the side walls. Thus, large scale simulation of 3D models are needed to obtain a realistic picture of horizontal reactor performance. 

The physical process of melt ascent during two-phase flow models is typically based on the separation of melt and solid described by Darcy s Law modified for a buoyancy driving force. The melt velocity depends on the permeability and pressure gradients but the actual microscopic distribution of the melt (on grain boundaries or in veins) is left unspecified. The creation of disequilibria only requires movement of the fluid relative to the solid. 

Aggregation of particles may occur, in general, due to Brownian motion, buoyancy-induced motion (creaming), and relative motion between particles due to an applied flow. Flow-induced aggregation dominates in polymer processing applications because of the high viscosities of polymer melts. Controlled studies—the conterpart of the fragmentation studies described in the previous section—may be carried out in simple flows, such as in the shear field produced in a cone and plate device (Chimmili, 1996). The number of such studies appears to be small. 

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