Internal collapse

Na -loess clay, where batch experiments were analyzed by X-ray diffraction and infrared and far-infrared measurements. The adsorption isotherm (Fig. 8.36) shows that loess clay is selective for cesium cations. The raw material contained a large amount of quartz, and the clay material was a mixture of kaolinite and an interstrati-fied iUite-smectite mineral as a result, equilibrium Cs" adsorption data are not consistent with a single site Langmuir model. Cesium adsorption on this particular soil clay occurs by cation exchange on sites with various cesium affinities. At low concentration, far-infrared spechoscopy shows the presence of very selective adsorption sites that correspond to internal collapsed layers. At high concentration, Cs MAS-NMR shows that cesium essentially is adsorbed to external sites that are not very selective. 

In the process of internal collapse of an isolated foam the total gas content remains constant (in a foam that is in contact with the atmosphere there is a certain decrease in gas quantity resulting from both gas diffusion from the surface bubble layer into the medium and coalescence of surface bubbles). From the equation of the state of a foam [1-3]... 

Separating the total rate of bubble expansion into its constituents, i.e. the rates of the elementary processes, is a complex issue that can only be solved in some special cases. For example, if the foam films are very stable, the average bubble size will increase mainly as a result of diffusion. If the films are very unstable, the internal collapse will be caused by coalescence. 

However, it should be noted that this dependence does not yield a firm criterion of foam stability with respect to its internal collapse [22], Indeed by definition the rate of internal collapse is expressed as... 

There is a certain relation between the processes of internal collapse of the foam and the decrease in its volume but in the general case the character of this relation remains obscure. Many papers have been dedicated to that subject [e.g. 8,21]. The comparison of the time needed to destroy one half of the foam column and the time during which there is no internal foam collapse, has shown [21,59] that these two quantities increase directly proportional to the concentration of fatty alcohols added to the foaming solution (sodium alkylsulphate). 

In the real polydisperse foam along with coalescence there always acts another process of internal collapse. This is the diffusion decrease in the specific surface which is accompanied by structural rearrangement, i.e. shift of knots and borders, and change in their orientation. This leads to the origination of various local disturbances (Act, Apa, AC, etc.). These local disturbances along with the rupture of individual films cause destruction either of other films and borders or of local volumes or of the whole foam (see Sections 6.5 and 6.6). Finally, various external factors can affect the foam (pressure drop, applied to the liquid phase reduced pressure of the liquid vapour above the foam, leading to evaporation the effect of antifoam droplets a-particle irradiation vibration, etc.). 

For foams of low stability the effect of the different factors on foam expansion ratio is difficult to anticipate, since the accelerated internal collapse and the partial destruction of the foam column during foaming lead to an increase in the amount of excess liquid in the foam, to bubble expansion and to increase in surfactant concentration that also affect the rate of drainage. 

The foaming ability of solutions, characterised by the volume of the foam generated, depends on the composition (including the various stabilising additives), temperature, way of foam generation and the stability of the foam with respect to internal collapse and foam... 

In such concentrated disperse systems three types of liquid films form foam films (G/L/G), water-emulsion films (O/W/O) and non-symmetric films (O/W/G). The kinetics of thinning of these films, their permeability as well as the energy barrier impeding the film rupture determine the stability of these systems. They might be subjected to internal collapse, i.e. coalescence of bubbles or droplets and increase in their average size, or to destruction as a whole, i.e. separation into their initial phases - gas, oil and water. 

For stable foams with a not very high expansion ratio (at Ap - 1 kPa) a quantitative relation between the rates of internal foam collapse and foam column decay during its entire lifetime is also established (see Eq. (6.50)). Thus, the foam lifetime can be calculated on the basis of the regularities of its internal collapse mainly from the data about the diffusion bubble... 

In the absence of internal foam collapse when the surfactant concentration in the foam bulk clf is equal to that in the source solution, the first term in Eqs. (10.11) and (10.13) equals unity. When internal collapse occurs, i.e. either through a gas diffusion and coalescence... 

When the foam is stable and the time for the process is short, the accumulation caused by internal collapse is not substantial. For foams of low stability and prolonged process, the accumulation resulting from internal foam collapse and foam column decay is comparable with that occurring in the adsorption layers. In addition, if accumulation is carried out with increase in the expansion ratio in the course of gravitational drainage or by the method of capillary foam drying, then the excess of the substance that accumulates in the bulk sections... 

A positive influence of the internal collapse (internal dephlegmation) on the accumulation ratio (i.e. its increase) was observed only in the cases where a very small cl.o value lies in the range cm < c 0 < cr (cr, corresponds to the saturated adsorption layer). The reason is that desorption from film surfaces during foam collapse increases surfactant concentration in the foam liquid phase, and, as a consequence, the degree of adsorption increases to values that ensure the formation of a small volume of a stable foam. Therefore, it becomes possible to separate the foam from the original solution with Rf>. ... 

A positive effect of the internal collapse on the accumulation ratio due to internal reflux of the solution has been found experimentally in foam separation processes carried out with NaDoBS and lysozyme at cm < < cr, [67,84]. 

The ion pair in eq. (2.10) could revert to reactants, undergo internal transfer of alkyl or halide from the anion to the carbocalion, or react with an external molecule of Grignard reagent. Since the medium is not an hospitable one for ionic species, the lifetime of the ion pair should be short and stereochemistry ntighl be partially preserved, with possible retention of configuration in the internal collapse or inversion in the attack by external reagent. 

In one case total internal collapse resulted in another, shell cxacjdng occurred Successful cures induded reducing fractkmal hole area, stiffening siqiport beams, and avoiding low c raat-... 

The equipment and ducts shall be externally reinforced/strengthened to minimise the chance of internal collapse (implosion) if pressure falls further below atmospheric, e.g. excessive cooling of the condenser. 

Proof of (c). We would like to give an elementary geometric argument. Let a be some critical cell of A of dimension n. Initially, a was attached along its boundary sphere, but after all the internal collapses, the attachment became more intricate. We would like to envision the attaching map as a map of the world drawn on the boundary sphere da. When the attaching map changes, we redraw this map, usually only locally. 

Fig. 11.9. Internal collapses as bonndary snbdivisions the resnlt of collapsing (234,2345) and (345,3456).

As a result, supply chains can no longer be expected to preserve their structure over a long horizon because they risk losing their competitiveness or face internal collapse. The supply chain configuration must be able to respond to changing customer demands and operating environments. Reinforcement and modification... 

A molecular bridge must separate the two hydroxy groups. This ensures that both hydroxy groups act independently and form separate helices. It also buttresses the tube walls against internal collapse. 

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