Bubble formation at an orifice

Thus bubble formation at an orifice is a surprisingly complex phenomenon. For intermediate conditions and a perfectly wetted orifice, the volume of the bubble formed may be written" ... 

The analysis also explains why jets are not normally observed for bubble formation at an orifice. When a gas is injected into a liquid, unstable disturbances amplify to the radius of the orifice within a very short distance (MIO). Some data on jet lengths for gas flow into liquids have been published (P4). 

Davidson JF. Harrison D. Fluidization. New York Academic Press. 1971 Chapters 2,4. Harrison D. Leung L. Bubble formation at an orifice in a fluidized bed. Trans Inst Chem Engrs 1961 39 409. 

Davidson JF, Schueler BOG. (1960) Bubble formation at an orifice in a viscous hquid. Trans. Inst. Chem. Eng., 38 144—154. 

Wilkinson PM, van Dierendonck LL. A theoretical model for the influence of gas properties and pressure on single-bubble formation at an orifice. Chem Eng Sci 49 1429-1438, 1994. 

In bubbling, the control of the bubble diameter is a little easier. In these methods bubbles are made at an orifice or a multitude of orifices. If there is only one orifice, of radius r, and if bubble formation is slow and undisturbed, the greatest possible bubble volume is 27rry/gp] y is the surface tension of the liquid, p the difference between the densities of liquid and gas (practically equal to the density of the liquid), and g is acceleration due to gravity. Every type of agitation lowers the real bubble size. On the other hand, if there are many orifices near enough to each other, the actual bubble may be much larger than predicted by the above expression. 

Harrison and Leung1561 have shown that the frequency of formation of bubbles at an orifice (size range 1.2-25 mm) is independent of the bed depth, the flowrate of gas and the properties of the particles constituting the continuous phase, although the frequency of formation depends on the injection rate of gas, tending to a frequency of 18-21 s 1 at high flowrates. 

Mass transfer during formation of drops or bubbles at an orifice can be a very significant fraction of the total mass transfer in industrial extraction or absorption operations. Transfer tends to be particularly favorable because of the exposure of fresh surface and because of vigorous internal circulation during the formation period. In discussing mass transfer in extraction, it has become conventional (H12) to distinguish four steps (1) formation, (2) release, (3) free rise or fall, (4) coalescence. Free rise or fall has been treated in previous chapters. Steps 1 and 2 are considered here. 

Correlation of Experimental Data - Formation of Gas Bubbles at an Orifice... 

A major factor in fluidized bed behavior is the interaction between the gas flow from individual orifices and the particle and gas mixture within the bed. The jet penetration and the subsequent bubble formation have an important influence upon solids and gas mixing and, ultimately, upon the usefulness of the bed for reactor purposes. While flow visualization data are available at ambient pressures and temperatures, the natures of jet penetration and bubble development at high pressures and temperatures are not easily measured. Typical data on bubble size and bubble velocity at ambient conditions are shown, represented by the small size symbols, in Figure 2. It is well known that bubble volume can be correlated as a function of gas volumetric flow rate ( ) and that bubble velocity is related to the size of the bubble radius ( ). Such semi-empirical correlations are indicated as solid lines in that figure. 

The bubble size at formation varied with particle characteristics. It was further observed that the bubble size decreased with increasing fluidization intensity (i.e., with increasing liquid velocity). The rate of coalescence likewise decreased with increasing fluidization intensity the net rate of coalescence had a positive value at distances from 1 to 2 ft above the orifice, whereas at larger distances from the orifice the rate approached zero. The bubble rise-velocity increased steadily with bubble size in a manner similar to that observed for viscous fluids, but different to that observed for water. An attempt was made to explain the dependence of the rate of coalescence on fluidization intensity in terms of a relatively high viscosity of the liquid fluidized bed. 

A common dimensionless number used to characterize the bubble formation from orifices through a gas chamber is the capacitance number defined as Nc — 4VcgpilnDoPs. For the bubble-formation system with inlet gas provided by nozzle tubes connected to an air compressor, the volume of the gas chamber is negligible, and thus, the dimensionless capacitance number is close to zero. The gas-flow rate through the nozzle would be near constant. For bubble formation under the constant flow rate condition, an increasing flow rate significantly increases the frequency of bubble formation. The initial bubble size also increases with an increase in the flow rate. Experimental results are shown in Fig. 6. Three different nozzle-inlet velocities are used in the air-water experiments. It is clearly seen that at all velocities used for nozzle air injection, bubbles rise in a zigzag path and a spiral motion of the bubbles prevails in air-water experiments. The simulation results on bubble formation and rise behavior conducted in this study closely resemble the experimental results. 

Krishnamurthi, Kumar, and Datta (K7) employed a circular orifice of arbitrarily chosen dimensions as the standard, and constructed two sets of noncircular orifices having either the perimeter or the area equal to that of the standard orifice. The configurations chosen were an equilateral triangle, a square, and a rectangle. The system used by these authors was air-water, and their studies were confined to extremely small flow rates (<0.5 cm3/sec). Their results indicate that noncircular orifices do not utilize their entire perimeter for bubble formation, and, for equi-sided orifices at low frequencies of formation, the bubble is formed as if from a circle inscribed in the noncircular orifice. In this range, the perimeter and the area are important in determining the final bubble size. 

The first quantitative attempt (K12) in this direction was made with vertical orifices, under constant flow conditions. Here, the bubble formation is considered to be occurring in two distinct steps. In the first stage, the bubble is assumed to expand at the tip, moving vertically at the same time. As the bubble is formed at an angle to the vertical, a vertical component of the surface tension force will be operative during this stage. The first stage is... 

The formation of bubbles at orifices in a fluidised bed, including measurement of their size, the conditions under which they will coalesce with one another, and their rate of rise in the bed has been investigated. Davidson el alP4) injected air from an orifice into a fluidised bed composed of particles of sand (0.3-0.5 mm) and glass ballotini (0.15 mm) fluidised by air at a velocity just above the minimum required for fluidisation. By varying the depth of the injection point from the free surface, it was shown that the injected bubble rises through the bed with a constant velocity, which is dependent only on the volume of the bubble. In addition, this velocity of rise corresponds with that of a spherical cap bubble in an inviscid liquid of zero surface tension, as determined from the equation of Davies and Taylor ... 

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