Bubble surface, residual mobility

Large A-values correspond to the predomination of sedimentation at small A-values the influence of a residual mobility on collision can predominate, even at the strongly retarded surface of a bubble. If the normal component of liquid velocity is proportional to cos 0 the angular dependence diminishes in the derivation of Eq. (10.30) because the normal component of the sedimentation velocity is proportional to cos 0 too. 

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. 

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. 

Let us emphasise that this ratio does not depend on bubble radius which simplifies the description of the common recovery of disperse particles and molecular impurities. As seen fi om Eq. (10.49) the fluxes can be comparable. Thus, we can conclude that the role of the residual mobility can increase if the recovery of molecular surface active impurities is taken into account. 

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). 

As shown in Section 10.12, effective microflotation is possible as a two-stage process. At the first stage the problem of residual mobility does not arise because bubbles of decimicron dimension are used. At the second stage the use of bubbles of millimetre size is technologically effective if their surface is not completely retarded. Methods to obtain intermediate-size... 

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. 

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),... 

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. 

For apparent slip, a thin gas-liquid layer with a modified viscosity and/or mobility is created near the solid surface. At room temperature and pressure, there is always some residual gas dissolved in a liquid. Critical level of shear might induce cavitations in a liquid, and the generated gas bubbles might adhere to the solid surface forming a thin layer at the interface onto which the liquid can slip. The other factor can be the critical shear rate at which a microscopic surface roughness or cormgation can favor the... 

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