Bubble expansion

These studies consider the dynamics of a single bubble that grows in infinity space, which is filled by superheated liquid. Under these conditions the bubble expansion depends on inertia forces or on intensity of heat transfer. In the case when inertia forces are dominant the bubble radius grows linearly in time (Carey 1992) ... 

The bubble dynamics in a confined space, in particular in micro-channels, is quite different from that in infinity still fluid. In micro-channels the bubble evolution depends on a number of different factors such as existence of solid walls restricting bubble expansion in the transversal direction, a large gradient of the velocity and temperature field, etc. Some of these problems were discussed by Kandlikar (2002), Dhir (1998), and Peng et al. (1997). A detailed experimental study of bubble dynamics in a single and two parallel micro-channels was performed by Lee et al. (2004) and Li et al. (2004). 

Now the bubble collapse is discussed using the Rayleigh-Plesset equation. After the bubble expansion, a bubble collapses. During the bubble collapse, important terms in the Rayleigh-Plesset equation are the two terms in the left hand side of (1.13). Then, the bubble wall acceleration is expressed as follows. 

In Fig. 1.4a, an example of the radius-time curve for a stably pulsating bubble calculated by the modified Keller equation is shown for one acoustic cycle [43]. After the bubble expansion during the rarefaction phase of ultrasound, a bubble strongly collapses, which is the inertial or Rayleigh collapse. After the collapse, there is a bouncing radial motion of a bubble. In Fig. 1.4b, the calculated flux of OH... 

In a multibubble field, every pulsating bubble radiates secondary acoustic wave called acoustic cavitation noise. The pulsation of a bubble is driven by both the primary ultrasound and the acoustic cavitation noise. The influence of the latter on the bubble pulsation is called bubble-bubble interaction [89, 90]. Generally speaking, the bubble-bubble interaction suppresses the bubble expansion as shown in Fig. 1.16 [38, 89-91]. Further studies are required on this topic. 

Whilst sodium bicarbonate is the primary blowing agent, it is common compounding practice to use it in conjunction with a proportion of a weak acid, such as stearic or oleic acid, whose function is to trigger the reaction and assist in the uniform decomposition of the bicarbonate. The higher than normal fatty acid level will also act as a process aid, facilitating the bubble expansion process. 

As soon as the bubble expansion causes P(r) to exceed Po, one can express the dynamics of the event as... 

If bubble expansion is neglected between the entrance and the section under consideration, and if Ql is the true liquid flow in the film... 

Once issued from the fiber tip, the bubble rises because of buoyancy and grows because CO2 gas diffuses into the bubble. Expansion as a bubble rises to lower pressure also contributes to the bubble size increase, but the effect is negligible in the case of champagne and beer bubbles. To understand the ascent dynamics, it is necessary to know the viscosity of beer and champagne. Beer viscosity depends on its sugar content. A typical viscosity of beer is about 1.44 times that of pure water (Zhang and Xu, 2008). If the temperature is 9°C, the viscosity is 0.0019 Pa s. The ascent velocity of a bubble depends on its size (the specific size limit is based on the physical property of beer) as follows ... 

Foam instability is expressed mainly by the processes of excess (referring to equilibrium quantity) liquid outflow, diffusion gas transfer from smaller to larger bubbles and coalescence. If the vapour pressure of the solvent in the surrounding medium of foam is lower than its saturated vapour pressure, then the process of evaporation influences significantly foam collapse. Finally, if a foam is produced from a gas phase, the main component of which is the solvent vapour, condensation of these vapours appears to be the determining process of bubble expansion. 

The decrease in foam dispersity results from both bubble coalescence and diffusion bubble expansion. So, depending on the surfactant kind and the time elapsed after foam formation, one of these processes can have a prevailing effect on the rate of foam collapse. 

Separating the total rate of bubble expansion into its constituents, i.e. the rates of the elementary processes, is a complex issue that can only be solved in some special cases. For example, if the foam films are very stable, the average bubble size will increase mainly as a result of diffusion. If the films are very unstable, the internal collapse will be caused by coalescence. 

Pertsov et al. [19] and Kann [20] have proposed a logarithmic time dependence of the foam expansion ratio in order to determine the rate of bubble expansion. This approach is reasoned by the fact that at hydrostatic equilibrium further increase in foam expansion ratio occurs only when excess liquid is released with decreasing foam dispersity. It was experimentally established that at the final stage of internal foam collapse this increase in foam expansion ratio can be expressed by an exponential function [19,21]... 

The comparison of the experimentally determined rate of decrease in the number of foam cells in a foam from an aqueous NaDoS solution, with that calculated from the equation for the diffusion bubble expansion, supports the conclusion that coalescence contributes significantly to the internal foam collapse. This has been evidenced by New [28], Film rupture in the foam was registered directly by a camera. 

If the kinetics of bubble expansion in a foam is determined by coalescence and is described by N = N0cxp(-r/rn), then the probability for film rupture does not depend on bubble area. This contradicts the theories of film rupture [e.g. 57,58] and probably means that there are other processes (along with coalescence) influencing bubble expansion (diffusion or... 

The a(r) curves for foams from NP20 and NaDoBS are given in [41] and data about the rate of change in their specific surface area are reported in [17], In all experiments the rate in bubble expansion is significantly higher for foams from nonionic surfactants. 

A more important fact is the change in the mechanism of foam column destruction with the increase in the applied pressure drop. For example, at small pressure drops a slow diffusion bubble expansion along with the corresponding slow rate of structural rearrangement (either zero or very slow rates of coalescence) occurs in a NaDoS foam with CBF or NBF. This is expressed in the layer-by-layer reduction of foam column height ending with the disappearance of the last bubble layer. In such a foam the critical pressure of the foam column destruction is not reached at any dispersity, and only the foam column height and the rate of internal foam collapse determine the foam lifetime. 

For foams of low stability the effect of the different factors on foam expansion ratio is difficult to anticipate, since the accelerated internal collapse and the partial destruction of the foam column during foaming lead to an increase in the amount of excess liquid in the foam, to bubble expansion and to increase in surfactant concentration that also affect the rate of drainage. 

The study of plastic (Bingham) viscosity (rj ) has shown [34] that it varies in the range from 0.1 to 10 Pa s r strongly falls with the viscosity of the dispersion medium and bubble expansion but weakly increases the expansion ratio. 

Concurrently, special measures are necessary to reduce the rate of gas diffusion transfer and the related to it bubble expansion and increase in polydispersity. To produce a foam with bubbles of maximum uniform size additives are also introduced that decrease the rate of solving, desorption and molecular gas diffusion (often such substance increase also the surface viscosity). Besides, if it is possible, a gas with low solubility and diffusion rate can be used as a disperse phase. 

The study of the foam lifetime versus concentration for the widely used foaming agents Volgonate (at Ap = 10 kPa) indicates that foam stability decreases visibly at concentrations less than 0.1%. The rate of diffusion bubble expansion gradually decreases, starting from concentrations -1%. Additional rise in foam stability is obtained with addition of various additives (electrolytes, water soluble polymers, fatty alcohols, etc.). 

In most processes, some expansion by puffing of the flow stream by water vapour pressure is required to achieve low-density expanded products. Bubble expansion has been comprehensively reviewed recently by Kokini and Moraru (2003). The extent and nature of expansion of the structures so formed are critical to their subsequent use and in-mouth texture. Highly expanded stmetures (0.1 g/ml), when eaten dry, give crisp textures, which melt in the mouth as plasticisation by saliva causes their cell walls to collapse. Hardness increases as bulk density increases, but many of the denser products are designed to be eaten in a rehydrated state as meat-like analogue products. Not surprisingly, the rate of stmeture collapse on hydration also increases as bulk density decreases, since these materials are both hydrophilic and porous. 

Nonetheless, the correlations they obtained with product structure are very informative. The melt penetration was defined as the temperature above the 7) /moisture curve at the point of extrusion. (Note that from the arguments presented above, this parameter will correlate positively with both the steam-driving pressure for expansion and inversely with melt elasticity and viscosity, that is, conditions for rapid bubble expansion.) The second parameter measured was the moisture and temperature of the expanded product immediately after the die, and its value was compared to the midpoint of the measured Tg of the ingredient mix at the same water content. 

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