Bubble contracting

Objectives and Assumptions. In an effort to complement developments from earlier sections, mass transfer across a gas-liquid interface into a quiescent liquid is considered here. This problem differs slightly from the classic unsteady-state penetration theory analysis because the bubble radius R(t) depends on time, for example, due to the fact that the bubble contracts or expands. The overall objectives are to predict the following quantities ... 

The microjet formation process proceeds while the bubble contracts and re-expands. Its driving force is the abovementioned peak pressure. The microjet penetrates the other side of the bubble in a few ysec after re-expansion of the bubble. 

The halothane contraction test involves exposing viable muscle fibers to nonincremental 3% halothane, bubbled through the tissue bath for 10 min. A positive halothane contraction test is defined as a > 0.2-0.7 g contraction after exposure to 3% halothane for 10 min. 

Scuba divers experience similar pressure changes. The amount of air dissolved in the blood increases significantly as the diver descends. If a diver returns to the surface too quickly, nitrogen gas dissolved in the blood forms bubbles in the same way as the CO2 in a freshly opened carbonated drink. These bubbles interfere with the transmission of nerve impulses and restrict the flow of blood. The effect is extremely painful and can cause paralysis or death. The bubbles tend to collect in the joints, where they cause severe contractions. This is the source of the name of this dangerous condition—the bends . 

In diffusing aerated confections under heating conditions, if the material can be processed at a high temperature, the bubble structure, after emerging from the diffusion chamber, will contract the air cell upon cooling, and thus become even smaller. 

Tension in the free surface of a liquid is the cause of the tendency of a liquid surface to assume the form having a minimum area, as manifested in the shape of a bubble or a drop of liquid.25 The tendency to contract is a special case of the general principle that potential energy tends toward a minimum value. 

Let us assume that the bubble on expansion (or contraction) increases (or decreases) its radius by an amount r, such that R, the bubble radius at any time is given by R = R,. + r. Then provided r << R, substitution into Eq. 2.29, followed by expanding in powers of 1 /R (and retaining only the first order terms) gives Eq. 2.30. 

If a bubble of radius R, present in a liquid is to remain in equilibrium (i. e. neither contracting nor expanding), then the forces (or pressure) acting on the bubble walls attempting to collapse the bubble must equal those forces responsible for attempting to expand the bubble. In the case of expansion this pressure, will be due to the trapped gas and vapour in the bubble, so that... 

As is known, if one blows air bubbles in pure water, no foam is formed. On the other hand, if a detergent or protein (amphiphile) is present in the system, adsorbed surfactant molecules at the interface produce foam or soap bubble. Foam can be characterized as a coarse dispersion of a gas in a liquid, where the gas is the major phase volume. The foam, or the lamina of liquid, will tend to contract due to its surface tension, and a low surface tension would thus be expected to be a necessary requirement for good foam-forming property. Furthermore, in order to be able to stabilize the lamina, it should be able to maintain slight differences of tension in its different regions. Therefore, it is also clear that a pure liquid, which has constant surface tension, cannot meet this requirement. The stability of such foams or bubbles has been related to monomolecular film structures and stability. For instance, foam stability has been shown to be related to surface elasticity or surface viscosity, qs, besides other interfacial forces. 

The oil formation volume factor at pressures above the bubble-point pressure is less than the formation volume factor at bubble-point pressure because of the contraction of the oil as reservoir pressure is increased. This compression due to increased reservoir pressure is the only factor which affects formation volume factor at pressures above the bubble point. 

Recovery is a measure of the degree of pressure recovery at the valve outlet from the low pressure at the vena contracts. When flashing occurs at the vena contracts and the pressure recovery is high, the bubbles collapse with resulting cavitation and noise. The more streamlined the valve, the more complete the pressure recovery thus, from this point of view streamlining seems to be an undesirable quality. A table of recovery factors of a number of valve types is given by Chaffin (1980) such data usually are provided by manufacturers. 

Flotation. This is a means of separating a relatively small particle from a Liquid medium. The particle may have a specific gravity greater than, less than, or the same as the liquid from which it is floated. There are two fundamental requirements (1) a gas bubble and particle must come in contract with each other and (2) the particle should have an affinity for attaching itself to the bubhle. 

SURFACE TENSION. Fluid surfaces exhibit certain features resembhng the properties of a stretched elastic membrane hence the term surface tension. Thus, one may lay a needle or a safety-razor blade upon the surface of water, and it will lie at rest in a shallow depression caused by its weight, much as if it were on a rubber air-cushion. A soap bubble, likewise, tends to contract, and actually creates a pressure inside, somewhat after the manner of a rubber balloon. The analogy is imperfect, however, since the tension in the rubber increases with the radius of the balloon, and the pressure inside, which would otherwise decrease, remains approximately constant while the liquid film tension remains constant and the pressure in the bubble falls off as the bubble is blown. 

A number of such compds were prepd and then converted to the corresponding nitric esters by Wolfram et al of Ohio State Univ while working under a US Ordnance Corps contract(Ref 5 6). They found that all the pentanitrates prepd by them could be detonated by gentle heat or by a hammer blow on steel. Thermal stability tests have shown that the aldonamide pentanitrates are more stable than aldonic acid pentanitrates or their methyl esters and that the esters were less stable than the corresponding acids. All of their purified nitrates underwent rapid decompn at their mp s, accompanied by violent bubbling and evolution of nitrogen oxides. No residue was visible after decompn... 

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