Bubble diffusion interaction

Fig. 10.5. Characteristic curves of the total contribution of molecular attraction forces and electrostatic forces conditioned by the overlap of the diffuse parts of the double layers into the energy W of bubble particle interaction at various distances and the surface charges of the same sign (a) and in the case of recharging the bubble (b) (curve I). in (b) dotted lines characterise the contribution to the energy of interaction of non electrostatic repulsion forces when their effective radius is smaller (curve 2) or greater (curve 3) than the thickness of the double layer.

Gal-Or and Hoelscher (G5) have recently proposed a mathematical model that takes into account interaction between bubbles (or drops) in a swarm as well as the effect of bubble-size distribution. The analysis is presented for unsteady-state mass transfer with and without chemical reaction, and for steady-state diffusion to a family of moving bubbles. 

Interaction by diffusion will seldom occur in two-phase systems, but may be of importance between gas bubbles in a fluidized bed, especially when the fluidized solid is not a catalyst but only a heat carrier. In homogeneous systems, this type of interaction is the normal kind of interaction. 

Foam films are usually used as a model in the study of various physicochemical processes, such as thinning, expansion and contraction of films, formation of black spots, film rupture, molecular interactions in films. Thus, it is possible to model not only the properties of a foam but also the processes undergoing in it. These studies allow to clarify the mechanism of these processes and to derive quantitative dependences for foams, O/W type emulsions and foamed emulsions, which in fact are closely related by properties to foams. Furthermore, a number of theoretical and practical problems of colloid chemistry, molecular physics, biophysics and biochemistry can also be solved. Several physico-technical parameters, such as pressure drop, volumetric flow rate (foam rotameter) and rate of gas diffusion through the film, are based on the measurement of some of the foam film parameters. For instance, Dewar [1] has used foam films in acoustic measurements. The study of the shape and tension of foam bubble films, in particular of bubbles floating at a liquid surface, provides information that is used in designing pneumatic constructions [2], Given bellow are the most important foam properties that determine their practical application. The processes of foam flotation of suspensions, ion flotation, foam accumulation and foam separation of soluble surfactants as well as the treatment of waste waters polluted by various substances (soluble and insoluble), are based on the difference in the compositions of the initial foaming solution and the liquid phase in the foam. Due ro this difference it is possible to accelerate some reactions (foam catalysis) and to shift the chemical equilibrium of some reactions in the foam. The low heat... 

The second term in Equations (1) and (2) accounts for diffu-sional transfer across the bubble boundary. (A factor e /(1+e p is sometimes (e.g. 49) included in the bracket of Eq. 2 o account for the dense phase diffusional resistance.) There is some question (30) of the extent to which there is interference between the bulk flow and diffusion terms. Nevertheless, most experimental evidence suggests that the two terms are additive and that the diffusional term is described by the penetration theory. With these changes, and including a small enhancement factor for bubble interaction. Sit and Grace (35) have recommended the following equations as being in best accord with existing experimental data ... 

MTBE is eliminated with pseudo-first order reaction kinetics [108-111]. The reaction rate is dependent on the frequency and power density of the ultrasound. At higher frequency, the elimination of MTBE is much faster. For each frequency the power density shows an optimum, since the interaction of and influence on cavitation bubble size, collapse time, transient temperature and internal pressure is very complex. Initial MTBE concentration was also observed to be of influence the reaction rate decreased with increasing MTBE concentration. This indicates that the reaction is limited by OH radical diffusion. 

The overlap of the secondary double layer of approaching drops or bubbles causes electrostatic interaction before their diffuse layers overlap. 

If a solid particle crosses the diffusion layer of a bubble or drop it also includes the long range interaction caused by a local disturbance of the adsorption layer. This leads to Marangoni effects and influences the film drainage between particle and bubble or drop. Local desorption of surfactant from one surface and its adsorption on the other also causes interaction. 

The situation is still more complex in the presence of surfactants. Recently, a self-consistent electrostatic theory has been presented to predict disjoining pressure isotherms of aqueous thin-liquid films, surface tension, and potentials of air bubbles immersed in electrolyte solutions with nonionic surfactants [53], The proposed model combines specific adsorption of hydroxide ions at the interface with image charge and dispersion forces on ions in the diffuse double layer. These two additional ion interaction free energies are incorporated into the Boltzmann equation, and a simple model for the specific adsorption of the hydroxide ions is used for achieving the description of the ion distribution. Then, by combining this distribution with the Poisson equation for the electrostatic potential, an MPB nonlinear differential equation appears. 

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