Hemispherical bubbles

If the contact angle is zero, as in Fig. XIII-8e, there should be no tendency to adhere to a flat surface. Leja and Poling [63] point out, however, that, as shown in Fig. XIII-8/, if the surface is formed in a hemispherical cup of the same radius as the bubble, then for step la, the free energy change of attachment is... 

Two complementai y reviews of this subject are by Shah et al. AIChE Journal, 28, 353-379 [1982]) and Deckwer (in de Lasa, ed.. Chemical Reactor Design andTechnology, Martinus Nijhoff, 1985, pp. 411-461). Useful comments are made by Doraiswamy and Sharma (Heterogeneous Reactions, Wiley, 1984). Charpentier (in Gianetto and Silveston, eds.. Multiphase Chemical Reactors, Hemisphere, 1986, pp. 104—151) emphasizes parameters of trickle bed and stirred tank reactors. Recommendations based on the literature are made for several design parameters namely, bubble diameter and velocity of rise, gas holdup, interfacial area, mass-transfer coefficients k a and /cl but not /cg, axial liquid-phase dispersion coefficient, and heat-transfer coefficient to the wall. The effect of vessel diameter on these parameters is insignificant when D > 0.15 m (0.49 ft), except for the dispersion coefficient. Application of these correlations is to (1) chlorination of toluene in the presence of FeCl,3 catalyst, (2) absorption of SO9 in aqueous potassium carbonate with arsenite catalyst, and (3) reaction of butene with sulfuric acid to butanol. 

Single gas bubbles in an inviscid liquid have hemispherical leading surfaces and somewhat flattened wakes. Their rise velocity is governed by Bernoulli s theory for potential flow of fluid around the nose of the bubble. This was first solved by G. I. Taylor to give a rise velocity Ug of ... 

Fuel-pair mixtures, in soap bubbles ranging from 4 to 40 cm diameter and with no internal obstacles, produced flame speeds very close to laminar flame speeds. Cylindrical bubbles of various aspect ratios produced even lower flame speeds. For example, maximum flame speeds for ethylene of 4.2 m/s and 5.5 m/s were found in cylindrical and hemispherical bubbles, respectively (Table 4.1a). This phenomenon is attributed to reduced driving forces due to the top relief of combustion products. 

Lihou and Maund (1982) used soap bubbles filled with flammable gas which were blown on the bottom of a fireball chamber to form fireballs. A hemispherical bubble was formed on a wire mesh 200 mm above the base of the measuring chamber in order to permit study of elevated sources. The gas bubble was ignited by direct contact with a candle flame, and the combustion process was filmed at a speed of 64 frames per second. The fireball s color temperature was measured. 

ASME JSME Thermal Eng loint Conf Proc 5 455 62 Nigmatulin IR (1991) Dynamics of multiphase media and 2. Hemisphere, London Ory E, Yuan H, Prosperetti A, Popinet S, Zaleski S (2000) Growth and coUapse of vapor bubble in a narrow tube. Phys Fluids 12 1268-1277... 

Figure 2.2 Bubble activation (a) change of radius of curvature of a bubble as it grows out from a cavity (b) criterion for activation of ebullition site. (From Hsu and Graham, 1976. Copyright 1976 by Hemisphere Publishing Corp., New York. Reprinted with permission.)...

For liquid metals the superiority of nucleate boiling heat transfer coefficients over those for forced-convection liquid-phase heat transfer is not as great as for ordinary liquids, primarily because the liquid-phase coefficients for liquid metals are already high, and the bubble growth period for liquid metals is a relatively short fraction of the total ebullition cycle compared with that for ordinary fluids. In the case of liquid metals, the initial shape of the bubbles is hemispheric, and it becomes spherical before leaving the heating surface. This is because of very rapid... 

Dwyer, O. E., and C. J. Hsu, 1976, Evaporation of the Microlayer in Hemispherical Bubble Growth in Nucleate Boiling of Liquid Metals, Int. J. Heat Mass Transfer 79 185. (2)... 

Sekoguchi, K., H. Fukui, and Y. Sato, 1981, Flow Characteristics and Heat Transfer in Vertical Bubble Flow, in Two-Phase Flow Dynamics Japan-US Seminar, A. E. Bergles and S. Ishigai, Eds., Hemisphere, New York. (3)... 

Zun, I., 1988, Transition from Wall Void Peaking to Core Void Peaking in Turbulent Bubbly Flow, in Transient Phenomena in Multiphase Flow, ICHMT Int. Seminar, N. H. Afgan, Ed., pp. 225-245, Hemisphere, Washington, DC. (3)... 

Chhabra RP, D De Kee. Transport Processes in Bubbles, Drops, and Particles. Washington, DCP Hemisphere, 1992. 

A model was developed to describe this phenomenon by assuming that the gas leaks out through the bubble boundary at a superficial velocity equivalent to the superficial minimum fluidization velocity. For a hemispherical bubble in a semicircular bed, the rate of change of bubble volume can be expressed as ... 

A bubble of air in a liquid is, as we know, spherical, and it is obvious that this spherical shape can only be maintained if the pressure on the inside is greater than that outside. Let P be the excess of pressure inside per unit surface, and a the radius of the sphere the pressure tending to force the two hemispheres apart is then evidently P x area of largest circle, i.e., P naa. This pressure is balanced by the pull arising from surface tension, which acts round the circumference of the same circle, and is, accordingly, 2ira[Pg.17]

Consider the vacuum forming of a polymer sheet into a conical mold as shown in Figure 7.84. We want to derive an expression for the thickness distribution of the final, conical-shaped product. The sheet has an initial uniform thickness of ho and is isothermal. It is assumed that the polymer is incompressible, and it deforms as an elastic solid (rather than a viscous liquid as in previous analyses) the free bubble is uniform in thickness and has a spherical shape the free bubble remains isothermal, but the sheet solidifies upon confacf wifh fhe mold wall fhere is no slip on fhe walls, and fhe bubble fhickness is very small compared fo ifs size. The presenf analysis holds for fhermoforming processes when fhe free bubble is less than hemispherical, since beyond this point the thickness cannot be assumed as constant. 

Focusing on the bubbles, it should be mentioned that they are not exactly spherical. They contain very small amounts of solids and have an approximately hemispherical top and a pushed-in bottom. Each bubble of gas has a wake that contains a significant amount of solids. These characteristics are illustrated in Figure 3.58. Consequently, during their journey in the reactor, the bubbles carry an amount of solids. The net flow of the solids in the emulsion phase must therefore be downward. The gas within a particular bubble remains largely within that bubble and only a small part of it penetrates a short distance into the surrounding emulsion phase, forming the so-called cloud. 

Support an hemispherical iron dish of 10 cm. diameter (or an iron crucible) on a ring stand and place in it about 75 g. of sodium nitrate. Heat the nitrate until it melts and just begins to evolve bubbles of oxygen. While maintaining a steady temperature, drop in pieces of granulated lead or chopped-up lead pipe, stirring well with an iron rod (old round file) after each addition. A little more than the equivalent of lead should be added, since some of it will be oxidized by the air. For this reason, a flat iron sand-bath dish is not suitable for the experiment. The reduction of the nitrate is rapid, and if much lead is added at a time, the mass may become incandescent. 

Besides the RDE and DME, other uniformly accessible electrodes under laminar flow have been described. They include the rotating hemispherical and rotating cone electrodes, which were developed to obviate the problem of trapped gas bubbles at the centre of an RDE their use is not widespread. 

Bell cap a hemispherical or triangular cover placed over the riser in a (distillation) tower to direct the vapors through the liquid layer on the tray see Bubble cap. 

Table 13.3 indicates the tissue distribution of LCM in rats at different time points after intravenous injection (ref. 532). No microbubbles were detected in brain within the left hemisphere (i.e., opposite the tumor), spleen, muscle, testes, or intestine at any time after intravenous injection of LCM. Microbubble aggregation in liver increased significantly 3 hours after injection, and by 24 hours, patches of bubbles could be detected. In the kidney, the... 

Additional information on hydrodynamics of bubble columns and slurry bubble columns can be obtained from Deckwer (Bubble Column Reactors, Wiley, 1992), Nigam and Schumpe (Three-Phase Sparged Reactors, Gordon and Breach, 1996), Ramachandran and Chaudhari (Three-Phase Catalytic Reactors, Gordon and Breach, 1983), and Gianetto and Silveston (Multiphase Chemical Reactors, Hemisphere, 1986). Computational fluid mechanics approaches have also been recently used to estimate mixing and mass-transfer parameters [e.g., see Gupta et al., Chem. Eng. Sci. 56(3) 1117-1125 (2001)]. 

Fig. 5 shows a vertical tube of internal radius r dipping into a liquid. If a bubble is blown at the end of this tube it will have the form of a segment of a sphere, if the radius of the tube is small. The radius of this sphere will first decrease, until the bubble becomes hemispherical. Further growth of the bubble will increase the radius. By equation (3) the pressure in the bubble will be a maximum when the radius is a minimum, that is, when the radius of the bubble is equal to that of the tube. The bubble will be unstable when it has grown beyond the hemispherical shape, because the pressure decreases as more air passes into it. Hence the maximum pressure attainable in a bubble blown on a small tube is... 

The maximum bubble pressure method. If a bubble is blown at the bottom of a tube dipping vertically into a liquid, the pressure in the bubble increases at first, as the bubble grows and the radius of curvature diminishes. It was shown in Chap. I, 13, that when the bubble is small enough to be taken as spherical, the smallest radius of curvature and the maximum pressure occurs when the bubble is a hemisphere further growth causes diminution of pressure, so that air rushes in and bursts the bubble. At this point the pressure in the bubble is... 

The main stages of foam formation can be established through observing the behaviour of a certain number of rising bubbles. When bubbles are formed or created in a surfactant solution, an absorption of the surfactant starts at their interface. Reaching the liquid surface each bubble forms a hemispherical liquid film which consists of two surfactant adsorption... 

The spherical foam films can be obtained by blowing a bubble from a vertical capillary tube. The principle of formation of such a bubble is illustrated in Fig. 2.22. A vertical capillary tube is placed in a vessel with the surfactant solution so that its upper orifice is close to the solution surface. When a gas (air) with a definite pressure is introduced into the tube over the solution surface a foam film is formed acquiring the shape of a hemisphere. 

The device, presented in Fig. 2.25 (without electrodes 1 and 6) has been used in [136] for the determination of K by the so-called stationary bubble method . A foam film forms on the porous plate acquiring the shape of a hemisphere. The radius of curvature R is practically equal to the radius of the perimeter at the base of the hemispherical bubble. Because of the gas passing from the bubble through the foam film into the atmosphere, R decreases with time t. The values of r are measured and K is calculated from... 

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