Collapsing the Bubble

Obviously, if the pressure within the bubble (P + Pg) exceeds those trying to collapse the bubble (Pj + 2a/Ro), the bubble will expand (and vice-versa). In other words a bubble will grow (expand) when (P + Pg) is greater than (Pj + 20/Rq) (Eqs. 2.20 and 2.21). 

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... 

The time to collapse the bubble can now be obtained by integrating the right hand side of Eq. A.19 from R to zero to give... 

It is also possible to collapse the bubble and heat it in order to seal the two halves of the tube together, producing a multilayer film of double the thickness. 

A visible exudation or efflorescence on the surface of a plastic - it may be caused by lubricant, plasticizer, etc. Techniques for making film by extruding the plastic through a circular die, followed by expansion (by the pressure of internal air admitted though the center of the mandrel), cooling, and collapsing the bubble. 

The take-off tower consists of guide rolls, a steel nip (pinch) roll, and a rubber nip (pinch) roll. The guide rolls (or forming tent) collapse the bubble and guide the flattened film tube into the nip rolls. The steel roll is a driven roll which pulls the collapsed tube away from the die. The rubber rotates with the steel nip roll. Typical line speeds are 10 to 90 m/min (35 to 300 ft/min.). ... 

Heaters will soften the tube and the tube is inflated with air. The initial filling of the tube with air requires good timing by the operator. As air is pumped into the expanding tube, the operator pulls the tube away faster than the top nip supplies cast tube. Once the inflated bubble reaches the bottom of the stretch tower, a second nip closes. This second nip seals the air in the tube. The second nip runs at a speed greater than the first and provides the machine direction orientation. The amount of air pumped into the tube before the second nip closes is one of the primary factors in the transverse direction stretch ratio. Other process variables that contribute to the transverse stretch ratio are the web temperature and machine direction stretch ratio. Pressure in the tube may be increased by narrowing the frame used to collapse the bubble. 

Fig. 3. Liquid jet produced during collapse of a cavitation bubble near a solid surface. The width of the bubble is about 1 mm.

The film tube is collapsed within a V-shaped frame of rollers and is nipped at the end of the frame to trap the air within the bubble. The nip roUs also draw the film away from the die. The draw rate is controlled to balance the physical properties with the transverse properties achieved by the blow draw ratio. The tube may be wound as such or may be sHt and wound as a single-film layer onto one or more roUs. The tube may also be direcdy processed into bags. The blown film method is used principally to produce polyethylene film. It has occasionally been used for polypropylene, poly(ethylene terephthalate), vinyls, nylon, and other polymers. 

Cavitation has three negative side effects in valves—noise and vibration, material removal, and reduced flow. The bubble-collapse process is a violent asymmetrical implosion that forms a high-speed microjet and induces pressure waves in the fluid. This hydrodynamic noise and the mechanical vibration that it can produce are far stronger than other noise-generation sources in liquid flows. If implosions occur adjacent to a solid component, minute pieces of material can be removed, which, over time, will leave a rough, cinderlike surface. 

Droplets formed from the collapse of the bubble dome (see Fig. 14-89). These are virtually unavoidable. They are generally under 25 Im, which means that their terminal velocities are low and they are invariably entrained. Fortunately, because of their small size, they contribute httle on a weight basis (<0.001 kg hquid/kg vapor), although they dominate on a number basis. 

Cf, C y, and Cq are the concentrations of the substance in question (which may be a colligend or a surfactant) in the feed stream, bottoms stream, and foamate (collapsed foam) respectively. G, F, and Q are the volumetric flow rates of gas, feed, and foamate respectively, is the surface excess in equilibrium with C y. S is the surface-to-volume ratio for a bubble. For a spherical bubble, S = 6/d, where d is the bubble diameter. For variation in bubble sizes, d should be taken as YLnid fLnidj, where n is the number of bubbles with diameter dj in a representative region of foam. 

For effluent streams consisting of only liquid and vapor, hole diameters ranging from Vh to V2. in are recommended. Larger hole diameters (up to 2 in) may be required if the blowdown stream contains solids (polymers and/or catalyst). However, the violently collapsing vapor bubbles create a water hammer effect which increases in severity with hole size. 

Damage will be confined to the bubble-collapse region, usually immediately downstream of the low-pressure zone. Components exposed to high velocity or turbulent flow, such as pump impellers and valves, are subject. The suction side of pumps (Case History 12.3) and the discharge side of regulating valves (Fig. 12.6 and Case History 12.4) are frequently affected. Tube ends, tube sheets, and shell outlets in heat exchanger equipment have been affected, as have cylinder liners in diesel engines (Case History 12.1). 

Across a control valve the fluid is accelerated to some maximum velocity. At this point the pressure reduces to its lowest value. If this pressure is lower than the liquid s vapor pressure, flashing will produce bubbles or cavities of vapor. The pressure will rise or recover downstream of the lowest pressure point. If the pressure rises to above the vapor pressure, the bubbles or cavities collapse. This causes noise, vibration, and physical damage. 

A pump is designed to handle liquid, not vapor. Unfortunately, for many situations, it is easy to get vapor into the pump if the design is not earefully done. Vapor forms if the pressure in the pump falls below the liquid s vapor pressure. The lowest pressure occurs right at the impeller inlet where a sharp pressure dip oeeurs. The impeller rapidly builds up the pressure, which collapses vapor bubbles, eausing cavitation and damage. This must be avoided by maintaining sufficient net positive suetion head (NPSFl) as specified by the manufacturer. 

The most frequently encountered flashing problems are in control valves. Downstream from the control valve a point of lowest pressure is reached, followed by pressure recovery. A liquid will flash if the low pressure point is below its vapor pressure. Subsequent pressure recovery can collapse the vapor bubbles or cavities, causing noise, vibration, and physical damage. 

A vapor poeket on the exchanger s low-pressure side can create a cushion that may greatly diminish the pressure transient s intensity. A transient analysis may not be required if sufficient low-pressure side vapor exists (although tube rupture should still be considered as a viable relief scenario). However, if the low-pressure fluid is liquid from a separator that has a small amount of vapor from flashing across a level control valve, the vapor pocket may collapse after the pressure has exceeded the fluid s bubble point. The bubble point will be at the separator pressure. Transient analysis will prediet a gradually inereasing pressure until the pressure reaches the bubble point. Then, the pressure will increase rapidly. For this ease, a transient analysis should be considered. 

Under cavitating conditions a pump will perform below its head-performance curve at any particular flow rate. Although the pump may operate under cavitation conditions, it will often be noisy because of collapsing vapor bubbles and severe pitting, and erosion of the impeller often results. This damage can become so severe as to completely destroy the impeller and create excessive clearances in the casing. To avoid these problems, the fol-iotving are a few situations to watch ... 

The alternative option for counteracting cavitation damage is the use of a resilient material such as rubber. The mechanical forces attendant on collapse of the bubbles are absorbed by elastic deformation of the resilient material. 

In a gas and liquid system, when gas is introduced into a culture medium, bubbles are formed. The bubbles rise rapidly through the medium and dispersion of the bubbles occurs at surface, forming froth. The froth collapses by coalescence, but in most cases the fermentation broth is viscous so this coalescence may be reduced to form stable froth. Any compounds in the broth, such as proteins, that reduce the surface tension may influence foam formation. The stability of preventing bubbles coalescing depends on the film elasticity, which is increased by the presence of peptides, proteins and soaps. On the other hand, the presence of alcohols and fatty acids will make the foam unstable. 

Foam formation in a boiler is primarily a surface active phenomena, whereby a discontinuous gaseous phase of steam, carbon dioxide, and other gas bubbles is dispersed in a continuous liquid phase of BW. Because the largest component of the foam is usually gas, the bubbles generally are separated only by a thin, liquid film composed of several layers of molecules that can slide over each other to provide considerable elasticity. Foaming occurs when these bubbles arrive at a steam-water interface at a rate faster than that at which they can collapse or decay into steam vapor. 

If bubbles are formed in a liquid which is much below its boiling point, then the bubbles will collapse in the bulk of the liquid. Thus if a liquid flows over a very hot surface then... 

The observed ratio / = Lp/Ln, is quite different from that reported for subcooled flow boiling of water in tubes of 17-22 mm inner diameter. Prodanovic et al. (2002) reported that this ratio was typically around 0.8 for experiments at 1.05-3 bar. The situation considered in experiments carried out by Hetsroni et al. (2003) is however different as the bubbles undergo a significant volume change and the flow is unstable. Ory et al. (2000) studied numerically the growth and collapse of a bubble in a narrow tube filled wifh a viscous fluid. The situation considered in that study is also quite different from experiments by Hetsroni et al. (2003) as, in that case, heat was added to the system impulsively, rather than continuously as we do here. 

A second problem in these studies concerns cavitation dynamics on the nanometer length scale [86]. If sufficiently energetic, the ultrafast laser excitation of a gold nanoparticle causes strong nonequilibrium heating of the particle lattice and of the water shell close to the particle surface. Above a threshold in the laser power, which defines the onset of homogeneous nucleation, nanoscale water bubbles develop around the particles, expand, and collapse again within the first nanosecond after excitation (Fig. 9). The size of the bubbles may be examined in this way. 

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