Characteristic Bubble Ratios

To properly describe and control the bubble-forming process, certain quantities have been developed to characterize the process conditions that influence bubble geometry. These quantities are the take-up ratio (TUR), the blow-up ratio (BUR), and the forming ratio (FR). 

The TUR is the ratio of him velocity (Vf) to melt velocity (Vj ), i.e., TUR = V IV. This quantity provides an indication of the amount of stretching, hence molecular orientation, in MD. The him velocity is the upward speed of the him above the frost line and is established by the control system. It is equivalent to the nip speed. The melt velocity is the upward speed of the molten polymer as it exits from the die lips. It is related to, but is not equal to, the screw speed. The melt velocity can be determined experimentally by marking the him and tracking the mark, but an easier method is to employ the principle of conservation of mass. 

The conservation of mass states that the mass how rate (pounds/hour) at all points along the bubble is equal. Mathematically, 

The area of an annulus (Fig. 4.1) can be calculated from the following equation  

Since the nip speed is always greater than the melt speed, the TUR is always greater than one. 

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A colloid is a material that exists ia a finely dispersed state. It is usually a solid particle, but it may be a Hquid droplet or a gas bubble. Typically, coUoids have high surface-area-to-volume ratios, characteristic of matter ia the submicrometer-size range. Matter of this size, from approximately 100 nm to 5 nm, just above atomic dimensions, exhibits physicochemical properties that differ from those of both the constituent atoms or molecules and the macroscopic material. The differences ia composition, stmcture, and iateractions between the surface atoms or molecules and those on the iaterior of the colloidal particle lead to the unique character of finely divided material, specifics of which can be quite diverse (see Flocculating agents). 

Characteristic length [Eq. (121)] L Impeller diameter also characteristic distance from the interface where the concentration remains constant at cL Li Impeller blade length N Impeller rotational speed also number of bubbles [Eq, (246)]. N Ratio of absorption rate in presence of chemical reaction to rate of physical absorption when tank contains no dissolved gas Na Instantaneous mass-transfer rate per unit bubble-surface area Na Local rate of mass-transfer per unit bubble-surface area Na..Average mass-transfer rate per unit bubble-surface area Nb Number of bubbles in the vessel at any instant at constant operating conditions N Number of bubbles per unit volume of dispersion [Eq. (24)] Nb Defined in Eq. (134)... 

Glicksman and Farrell (1995) constructed a scale model of the Tidd 70 MWe pressurized fluidized bed combustor. The scale model was fluidized with air at atmospheric pressure and temperature. They used the simplified set of scaling relationships to construct a one-quarter length scale model of a section of the Tidd combustor shown in Fig. 34. Based on the results of Glicksman and McAndrews (1985), the bubble characteristics within a bank of horizontal tubes should be independent of wall effects at locations at least three to five bubble diameters away from the wall. Low density polyurethane beads were used to obtain a close fit with the solid-to-gas density ratio for the combustor as well as the particle sphericity and particle size distribution (Table 6). 

The ultimate cause of bubble formation is the universal tendency of gas-solid flows to segregate. Many studies on the theory of stability [3, 4] have shown that disturbances induced in an initially homogeneous gas-solid suspension do not decay but always lead to the formation of voids. The bubbles formed in this way exhibit a characteristic flow pattern whose basic properties can be calculated with the model of Davidson and Harrison [30], Figure 5 shows the streamlines of the gas flow relative to a bubble rising in a fluidized bed at minimum fluidization conditions (e = rmf). The characteristic parameter is the ratio a of the bubble s upward velocity u, to the interstitial velocity of the gas in the suspension surrounding the bubble ... 

To test the viability of in quantifying fluidizing characteristics, it is plotted against the ratio of incipient bubbling velocity to incipient fluidization velocity, the latter being calculated after Geldart. Figure 69 shows... 

Figure 20 presents mesophase rods produced by extrusion alone and by a light draw after extrusion. As Jenkins and Jenkins observed (34), the strong preferred orientation induced by extrusion was easily disturbed by pyrolysis bubbles or even by small flow irregularities. However, modest draws (e.g., draw ratio = 2) after extrusion produced fibrous morphologies with good uniformity. At these draw levels, the nodes and crosses characteristic of wedge disclinations could be resolved on transverse sections. 

The growth of bubbles is controlled by the rates at which volatiles in the melt can diffuse towards the bubbles, and the opposing viscous forces. Near a bubble, volatiles are depleted such that melt viscosity increases dramatically, and diffusivities drop, making it harder for volatiles to diffuse through and grow the bubble. These opposing factors are described by the nondimensional Peclet number (Pe), which is the ratio of the characteristic timescales of volatile diffusion (T(1 = r lD, where r is the bubble radius and D the diffusion coefficient of the volatile in the melt) and of viscous relaxation (t = 17/AP where 17 is the melt dynamic viscosity and AP the oversaturation pressure, i.e., Pe = Dingwell... 

To explain why the boiling number seems to govern the transition between heat flux increasing a and vapour quality increasing a, the following interpretation is proposed, based on macroscale boiling mechanisms. From the Rohsenow (1952) and Kew and Cornwell (1997) analysis, an inertial characteristic time "Ccv for the liquid layer and a characteristic time Xb for bubbles leaving the wall can be defined. Then, from the Kutaleladze (1981) and Rohsenow (1952) analysis it can be shown that the ratio of these two characteristic times can be written ... 

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