Buoyant bubble

In the case of buoyant bubbles (cf. Chapter 9), this dimension will be the bubble radius a(,. Thus, Eq. (7.7) reads... 

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

Dynamic adsorption layers differ from equilibrium layers not only by the existence of an angular dependence but also by the difference in the adsorbed amount averaged over the bubble surface (Sadhal Johnson, 1983). Usually, in foam flotation, the surfactant yield is calculated under the assumption of equilibrium adsorption at the surface of buoyant bubbles. The theory of dynamic adsorption layers lead to substantial changes in the notion of surfactant flotation. Thus, the mechanism of transport at the bubble-solution interface has a substantial effect on the transport process at the surfactant solution-foam boundary. 

The leading part of the mobile surface of a floating bubble is stretched, the lowest part is compressed (Levich, 1962). The newly created sections of the surface are being filled with adsorbed substance, in the compressed part of surface the substance desorbs. The surface concentration on the leading surface of the buoyant bubble is lower than whieh provides a continuous supply of surfactant (or adsorbing inorganic ions) from the bulk to the stretched surface. The surface concentration on the rear part of the buoyant bubble is higher than... 

Use of the Dorn Effect to Check the Incomplete Retardation of a Buoyant Bubble Surface... 

It is well known (Samigin et al., 1964 Usui Sasaki, 1978 Usui et al., 1980) that the potential difference measured in the column of buoyant bubbles arises due to the superposition of the electric fields of individual bubbles, which are caused by their dipole moments induced... 

These results show that at high concentrations (above 7T0- mole/cm ), addition of surfactant increases the degree of retardation of the bubble surface. Thus, under the condition Xb > X th adsorption can considerably deviate from the mean value only in the vicinity of the leading pole of the bubble and the electrokinetic potential can be calculated from the equilibrium adsorption value. When the concentration of the surfactant decreases, retards to a lesser extent the motion of the surface. The condition Xb < Xo is realised when the removal of surfactant to the rear of the bubble is possible, and adsorption is much lower than the equilibrium value over almost the whole bubble surface. This statement needs a confirmation if values of adsorption less than 10 ° mole/cm are taken into account since then a deviation of the electrokinetic potential from Stem potential was observed (Sotskova et al. 1982). Substituting this value and the velocity of the buoyant bubble with a radius of 150 pm condition (8.98) is fulfilled. 

Since the surfactant is not uniformly distributed over the surface of a buoyant bubble, the stagnating effect of the surfactant appears to a greater extent in the neighbourhood of the RSP. Therefore, the surface motion model proposed for the first time by Savic (1953) is very... 

In calculating surfactant transfer to foam, it is usually assumed that the value of surface concentration of surfactant on the surface of a buoyant bubble is equal to r . On the other hand we know that the equilibrium value of surface concentration cannot be established in each case... 

The measurements of buoyant bubble velocity is not suitable for solving these problems and attention must be paid to other experimental techniques, li is clear that investigations of surfactant transfer in foams and of sedimentation potential measurements deserve more attention. 

Dynamic Adsorption Layers of Surfactants at the Surface of Buoyant Bubbles. Kinetic - Controlled Surfactant Transport TO AND from Bubble Surfaces... 

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... 

As it was pointed out in Chapter 8, the experimental verification of the theory of DAL of a bubble has so far been based on investigations of the effect of concentration and surface activity of a surfactant on velocity of buoyant bubbles of different size. As follows from the theory and from experiments, this effect is not very appreciable, it decreases sharply with the decrease of bubble size and of Reynolds number, and at Re < 40 it becomes unnoticeable at all. It was shown in preceding sections that the DAL structure determining the degree of retardation of surface motion has a strong effect on the deposition of small particles on a bubble surface. In this case it is important that papers by Reay Ratcliff (1973, 1975), Collins Jameson (1977), and Anfhms Kitchener (1976,1977) have demonstrated the possibility of... 

It was pointed out in Chapter 8 repeatedly, that it is impossible to discriminate between a complete and a strong retardation by measuring the buoyant bubble velocity. Since the retardation of bubble surface is derived up to now from the value of its buoyancy velocity only, conclusions in the literature about a complete retardation of the bubble surface at Re < 1 cannot be considered as really proven. 

At first glance it would seem possible to avoid transport of such impurities from the surface into the deeper water layers by using higher water columns. Agitation of water by buoyant bubbles unfortunately prevents this. Because of the bubbles some elementary volumes will sink, others rise. A rising bubble sinks a volume of liquid. This is repeated by any rising bubble so there is a liquid flow downwards and simultaneous transport of impurities. 

The presently most powerful technique for obtaining the liquid-vapour or liquid-liquid interfacial tension is based on the shape of a drop or bubble. In essence, the shape of a drop or bubble is determined by balance of surface tension and gravity effects. Surface forces tend to make drops spherical whereas gravity tends to elongate a pendant drop or buoyant bubble. Fig. 26 shows the schematic of an experimental set-up (for details see Chen et al. 1998, Loglio et al. 2001). 

Using the presented computational method we provide a systematic study of diverse shape regimes for a single buoyant bubble, recovering all main regimes in a full agreement with available experimental data (for detailed analysis see (Smolianski et al. )). Next, we present results on the bubble coalescence phenomena. 

---