Orifice, bubble formation

There are two types of impulse printers (Eig. 19). A piezoelectric ink jet propels a drop by flexing one or more walls of the firing chamber to decrease rapidly the volume of the firing chamber. This causes a pressure pulse and forces out a drop of ink. The flexing wall is either a piezoelectric crystal or a diaphragm driven by a piezoelectric incorporated into the firing chamber (Eig. 19a). Thermal impulse ink jets also propel one drop at a time, but these use rapid bubble formation to force part of the ink in a firing chamber out the orifice (Eig. 19b). 

As gas flows with fixed volumetric flow rate through an orifice gas sparger, bubbles are formed with diameter Analysis of bubble formation is based on the balance of buoyant force, as the bubbles leave the orifice and rise through the media (irApgDl)/6 with rest of the forces resulting from the surface tension, Trad. 

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. 

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. 

The chamber volume can be varied by varying either the diameter or the height of the chamber. It is of interest to know whether the geometrical proportions of the chamber have any influence on the bubble volumes obtained. Hayes et al. (H4) studied this aspect of the problem and found that the effect of the diameter of the gas chamber is insignificant in the formation of the bubbles, provided that the ratio of internal diameter of the gas chamber to that of the orifice is equal to or greater than 4.5. When the diameter of the gas chamber approaches that of the orifice, the bubble formation occurs as if at zero gas chamber volume. The bubble formation is further found to be independent of the chamber volume, provided that the latter is larger than about 800 cm3. 

Similarly, if conditions are such that on the air-supply side of the orifice the pressure is maintained constant during bubble formation, as the bubble size increases, the pressure inside it decreases, resulting in a higher flow rate... 

Schurmann (S6) and Davidson and Schuler (D8) used extremely small orifices, so that the downward surface-tension force was negligible, and viscosity was the controlling factor in bubble formation Hence these investigators concluded that viscosity has a great influence on the bubble formation. 

The bubble is now assumed to detach when its center has covered a distance equal to the sum of the radius of the final bubble arid the radius of the orifice. If the radius of the orifice is R and if it is assumed that V0 = (4tt/ 03/3), then the time of bubble formation can be obtained by plotting on the same axes Eq. (9) and (r + K) as a function of time from Eq. (8). 

The above equation is applicable when the bubble detaches at s = rF. But if the orifice diameter is large, the authors recommend the use of the relation s = (rF + 2 ) to obtain a better value of the time of bubble formation. Then Eq. (39) is modified to... 

Q is not a constant in this case it depends on the stage of bubble formation. It can be determined from orifice equation, as... 

From Eq. (89), the surface tension is seen to influence the bubble volume in two ways, viz. by varying the flow rate in the expanding bubble, and by causing a downward force at the periphery of the orifice. Even if the effect of the surface tension becomes negligible at the orifice tip due to either the small size of the orifice or the nonwettable character of the system, it still influences the bubble volume because of the variations in flow during the bubble formation. 

This model is a modification of the model developed by Kumar and Kuloor (K18) for bubble formation in inviscid fluids in the absence of surface-tension effects. The need for modification arises because the bubble forming nozzles actually used to collect data on bubble formation in fluidized beds differ from the orifice plates in that they do not have a flat base. Under such conditions the bubble must be assumed to be moving in an infinite medium and the value of 1/2 is more justified than the value 11/16. 

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. 

Fig. 18. Effect of orifice geometry on bubble formation for orifices based on area equivalence.

IX. The Influence of Orifice Orientation on Bubble Formation A. Introduction... 

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... 

Fig. 20. Effect of orientation of orifice on bubble formation under constant flow conditions.

Fig. 21(a). Bubble formation at oriented orifices in viscous systems. 

Fig. 21(c). Idealized sequence of bubble formation at inclined orifices. 

In the absence of surface tension influences, the drop formation at vertical orifices is expressed by the equation given for bubble formation. The force due to kinetic energy of the liquid is neglected as its component is zero in the vertical direction. The drop ascends right from the beginning according to the equation of motion and detaches when it has covered a distance equal to the diameter of the nozzle. 

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" ... 

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