Bubble surface, mobile

Processes Leading to the Increase of Bubble Surface Mobility and to Intensification of Microflotation. 

Two factors which can sharply increase bubble surface mobility and intensify the second stage of microflotation are usually not taken into accoimt and even not discussed. 

The bubble surface mobility has no effect on surface concentration if Eq. (8.71) holds. However, its strong decrease in the vicinity of the front pole of the bubble is possible under condition (8.72). For each surfactant, a possibly significant surface concentration decrease in the vicinity of the front pole can be estimated from the data given in Fig. 8.2. Thus, a principle possibility exists to formulate a relationship between the equilibrium contact angle and the size of floating bubbles, the surfactant concentration and its surface activity. At the present stage of the DAL theory such a relationship can be obtained only for weak retardation of the most part of the surface of a large bubble under a potential distribution of the liquid velocity. 

N. D. Denkov, S. Tcholakova, K. Golemanov, K. P. Ananthpadmanabhan, and A. Lips. The role of surfactant type and bubble surface mobility in foam rheology. Soft Matter, 5 3389-3408, 2009. 

The presence of surfactant adsorption monolayers decreases the mobility of the droplet (bubble) surfaces. This is due to the Marangoni effect (see Equation 5.282). From a general viewpoint, we may expect that the interfacial mobility will decrease with the increase of surfactant concentration until eventually the interfaces become immobile at high surfactant concentrations (see Section 5.5.2, above) therefore, a pronounced effect of surfactant concentration on the velocity of film drainage should be expected. This effect really exists (see Equation 5.286, below), but in the case of emulsions it is present only when the surfactant is predominantly soluble in the continuous phase. 

The substitution of the above equation into the generalized Laplace equation (with the dependence of capillary pressure on the z coordinate accounted for) yields the Laplace equation in the differential form, the numerical integration of which leads to the exact mathematical description of the drop or bubble surface shape in the gravitational field [6,14]. The exact description of the equilibrium surface shape is of importance in the evaluation of surface tension from the experimental data at interfaces with high mobility, such as liquid-gas and liquid-liquid ones (See Chapter 1,4). 

The state of the surface of a floating bubble depends on its size. Surfaces of reasonably large bubbles are mobile. As a result, adsorbed surfactants are pulled down to the rear of the bubble, i.e. even under steady-state conditions the value of adsorption on a mobile bubble surface is different from that on an immobile one, T (at the same surfactant concentration in the bulk). 

Total Amount of Surfactant at Mobile Bubble Surfaces... 

The problem of total amount of surfactant on a mobile bubble surface is important for bubble fractionation. In bubble fractionation (Clarke Wilson 1983) surface active material is transferred to the upper section of a liquid column through adsorption on rising bubbles followed by the release at the top of the column as the bubbles burst or accumulate in foam. 

The stagnant cap theory permits a quantitative evaluation of the variation of the total amount of surfactant adsorbed at the bubble as a function of its buoyant velocity. The discussion of these results are avoided since they are restricted to Re 1 and experimental data about the mobility of the bubble surface at small Reynolds numbers do not exist. 

In sea and tap water (both containing impurities) the bubble velocity decreases along its path too. However, the contamination level is not sufficient to suppress the mobility of the bubble surface completely. The non-monotonous concentration and height dependence of the rising velocity cannot be interpreted by the presence of these impurities. 

We emphasise this statement because in many papers the identity of buoyant bubbles and solid spheres is considered as the ground for neglecting the specificity of the particle capture by a bubble. To discriminate the "solid body" regime and regime of the residual surface mobility let us introduce the condition... 

Due to rapid decrease of the retardation coefficient with increasing bubble dimension, a residual surface mobility remains for big bubbles. The transport stage for sufficiently small bubbles and solid spheres is identical. The characteristic bubble value which describes the boundary between the two ranges of bubble dimensions can be determined from Eq. (10.35) after substitution of Xb as a function of bubble radius, according to Eq. (8.106),... 

Both CMC and surface activity increase with higher homologs. As it was shown in Section 10.2.4. the residual mobility of a bubble influences the microflotation at high Reynolds number and at K < lO- cm. At K > lO cm a residual mobility in a contaminated water can be provided by micellisation. Indeed this high surface activity is possible for sufficiently high homologs, corresponding to rather low values of the CMC, for example 10- - lO M. Thus the mobility of a bubble surface can preserve at K >10 - 10 cm and c < 10 - lO M. However, this conclusion relates to sufficiently big bubbles and the formation of an f s.fz. only. 

The conclusion cannot be generalised with respect to other surface active species. For example, proteins can remarkably decrease the surface tension at very small concentrations (Izmailova et al., 1988). However, these data relate to equilibrium conditions. Thus, it is not excluded that under dynamic conditions, i.e. during the adsorption on a mobile bubble surface, the increase of surface concentration is retarded by slow adsorption kinetics. 

There are two small parameters in Eq. (10.42), (n - T ) and Up /a. The first or the second term can predominate in Eq. (10.42). The bubble buoyancy cannot be sensitive to the existence of f s.fz., not even at very small angle rt - T. In Section 8.7.3 this was proven for small Re. The coincidence of the measured bubble velocity with that calculated for a solid sphere is not the ground to calculate the collision efficiency neglecting the mobility of the bubble surface. Its influence can predominate according Eq. (10.2.23). 

We can conclude that the residual surface mobility cannot be neglected even in the case of very contaminated water from the river Kalmius. However, it is valid for bubbles of larger dimension, approximately 1 mm. Concerning sea water or tap water, residual surface mobility can appear even in the intermediate range of Reynolds numbers. 

At microflotation the process of deposition of disperse particles and molecular contaminants on a bubble surface proceed in parallel. If the rates of these processes are commensurable in the process of microflotation the level of impurities in the bulk decreases. It means that their adsorption on bubbles surfaces decreases too, leading to the increase of the residual mobility. 

Maximum water purification can create the conditions for new results with respect to the mobility of a bubble surface because in experiments performed earlier the water was not... 

Extension of these principles to the flotation of small-sized particles require, first, the inclusion of the hydrodynamic factor because particles deposit on a bubble from the stream of liquid flowing around it, and second, the consideration of mobility of the bubble surface if the level of the impurities which retard the surface movement is not very high. The second factor is manifest in flotation, and the specific feature of this process is connected with it. 

The effect of gravity on the collision efficiency is small if the bubble surface is mobile and substantial at stagnant bubble surface. 

Dynamic Adsorption Layer and Microflotation in Contaminated Water. Residual Mobility of Bubble Surface and Collision Efficiency... 

Soluble substances exist which can immobilise the surface even of large bubbles present in water at extremely low concentrations. The problem of the effect of residual mobility of a bubble surface loses its meaning if these impurities are contained in water. However, their influence on surface mobility can be hampered at retarded adsorption kinetics. At a given surface tension decrease due to impurities a critical bubble dimension exists. For bubbles exceeding the critical size a residual surface mobility is present. Eq. (10.40) interrelates the critical bubble size with the surface tension drop. On the basis of Eq. (10.45) it was shown that residual mobility is important even for highly contaminated river water at high Reynolds numbers (cf. Section 10.2.7). 

Let us point out two more aspects of this problem, which contribute to the preservation of a noticeable mobility of the bubble surface. It is expected that in the development of microflotation technology, increasingly deeper purification from dispersed particles and therefore from molecular contaminations can be attained under the condition of a remarkable residual mobility. 

Another aspect is connected with a joint consideration of two processes affecting a residual mobility. At the beginning a high initial collision efficiency is retained since the process of adsorption of molecular impurities on the bubble surface is not too fast. Then the decrease of residual mobility slows down due to drop of concentration of molecular impurities. Thus, a joint action of two factors considered above separately can provide a prolonged preservation of surface mobility. 

Retardation of the surface of the film between particle and bubble under the effect of DAL exerts an opposite effect on h. Such paired effects of the DAL is possible only if a surfactant fulfils the condition (8.71). Such surfactants can also effect on h twice. If the surfactant concentration is low also the surface concentration on the leading bubble surface is low. For the same reason the DAL does not determine the retardation of the surface film but affects h only through the bubble buoyancy velocity. The effect of each surfactant on the mobility of the leading bubble surface as a function of concentration and surface activity can be evaluated from the data given in Fig. 8.2. 

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