Bubble diffusion controlled

Dynamic Adsorption Layer of Buoyant Bubbles. Diffusion-Controlled Transport of Nonionic Surfactants... 

This represents a special case of high-level turbulence at a surface by the formation of steam and the possibility of the concentration of ions as water evaporates into the steam bubbles . For those metals and alloys in a particular environment that allow diffusion-controlled corrosion processes, rates will be very high except in the case where dissolved gases such as oxygen are the main cathodic reactant. Under these circumstances gases will be expelled into the steam and are not available for reaction. However, under conditions of sub-cooled forced circulation, when cool solution is continually approaching the hot metal surface, the dissolved oxygen... 

Diffusion-Controlled Bubble Growth S. G. Bankoff Evaporative Convection... 

Westwater (W4, W5) has written a detailed review of boiling in liquids with emphasis on nucleation at surfaces. Although written in 1956, this is still very useful and it provides a detailed description of the factors affecting nucleation. In a more recent review, Leppert and Pitts (L2) have described the important factors in nucleate boiling and bubble growth, and Bankoff (B2) has reviewed the field of diffusion-controlled bubble growth in nonflowing batch systems. 

Fig. 21. Variation of the extraction efficiency with dimensionless bubble radius for diffusion-controlled and hydrodynamically controlled bubble growth when the bubble population is constant = 0.10, Xo = 0.10, = 5.87.

On the other hand, if bubble growth is diffusion controlled, then the mass transfer coefficient may be meaningful. However, in this case, the surface area for mass transfer is the surface area of the bubbles entrained in the solution and this depends on the volume of liquid in the extraction zone and not on the surface area of the extraction zone. Clearly, attempts to correlate experimental data for the extraction of a volatile component from a polymeric solution containing entrained bubbles using mass transfer coefficients can be misleading or totally erroneous. 

Diffusion-Controlled Bubble Growth S. G. Bankoff Evaporative Convection John C. Berg, Andreas Acrivos, and Michel Boudart... 

The objective is to reduce volatiles to below 50-100-ppm levels. In most devolatilization equipment, the solution is exposed to a vacuum, the level of which sets the thermodynamic upper limit of separation. The vacuum is generally high enough to superheat the solution and foam it. Foaming is essentially a boiling mechanism. In this case, the mechanism involves a series of steps creation of a vapor phase by nucleation, bubble growth, bubble coalescence and breakup, and bubble rupture. At a very low concentration of volatiles, foaming may not take place, and removal of volatiles would proceed via a diffusion-controlled mechanism to a liquid-vapor macroscopic interface enhanced by laminar flow-induced repeated surface renewals, which can also cause entrapment of vapor bubbles. 

As previously stated, this discussion is valid for homogeneous explosives, such as the ones used in the military, since their reactions are predominantly intramolecular. Such explosives are often referred to as ideal explosives, in particular when they can be described using the steady state model of Chapman and Jouguet. In heterogeneous explosives (non-ideal), which are currently used in civil applications, intermolecular (diffusion controlled) mechanisms are predominant for the air bubbles, cavities or cracks (etc.). As a general rule detonation velocities increase proportional to the diameter. 

When the solute is spherical, or close to be so, its radius is easily obtained otherwise, estimations can be made on the basis of the geometry and arrangement of the constituting atoms or ions. For solutes having a complex stucture (e.g., micelles), a distinction should be made between the hydrodynamic radius (which appears in the Stokes-Einstein equation of the diffusion coefficient) and the reaction radius [98]. For Ps, RPs should represent the bubble radius. However, as shown in Table 4.4, the experimental data are systematically very well recovered by using the free Ps radius, RPs = 0.053 nm using the bubble radius results in a calculated value of kD (noted kDb) that is too small by a factor of 2 or 3. Table 4.4 does not include such cases where k kD, as these do not correspond to purely diffusion-controlled reactions. 

Table 4.4 Comparison between experimental Ps reaction rate constants (k ) and diffusion-controlled reaction rate constants calculated from eq. (18) by using either the bubble (kDd, Rb) or the free Ps (kD, RPs = 0.053 nm) radius, (a), unpublished results (b), [82] (c) [61] (d), [84], ox = oxidation sp = spin conversion bs = bound-state formation. The rate constants are in M W. NDMA N-dimethylacetamide 0-NO2 ...

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