Foam column height

The measurement of the decrease in foam column height induced by a-particle irradiation can be considered to belong to the macroscopic techniques. As shown in [325,330,331 ] the rate of foam destruction depends on the activity of the oc-source. 

Applying the relation of parameters n, a, r (Eqs. (4.9) and (4.10)) and the dependence of hydrostatic pressure on foam column height (Eq. (1.39)), it is possible to derive the distribution of local foam expansion ratio along the height H. Assuming a border foam (i.e. neglecting the amount of liquid in films) one obtains from Eq. (4.10) and Eqs. (1.40) and (1.42) which account for the p dependence on r, the following relation... 

Princen and Kiss [13] have divided the profile of the dependence of gas volume fraction in a foam (or volume fraction of the disperse phase in emulsion) on foam column height into three regions, giving the respective analytical expressions for each one of them. 

The analysis in [2] indicates that for a foam at hydrostatic equilibrium that is in contact with the foaming solution, Eqs. (4.15) and (4.16) cannot be employed to calculate the average expansion ratio or the critical foam height, which gives the boundary between the ability of a foam either to drain or to suck in liquid. That is so because the maximum volume of the liquid in a foam is a function of the 5-layer and actually does not depend on the whole foam column height. 

The border profile was studied in order to analyse qualitatively the influence of various foam parameters (surfactant kind and foam film type, foam column height, pressure drop, etc.) on the drainage process as well to check the validity of drainage models [12], The foam was placed in a cylindrical vessel (diameter 2.5 to 4 cm), similar to vessel 6 in Fig. 1.4. It was covered with a lid to prevent evaporation. The pressure above the foam was equal to the atmospheric pressure. The border profile was determined by simultaneous measurement of the capillary pressure at various levels of the foam column, i.e. the r(H) dependence in the direction of liquid flow was evaluated. Thus it was found that the best approximation (among the discussed in Section 5.3.3) appears to be the parabolic model of border profile. 

Fig. S.9. Change in border profile during drainage of a NaDoS foam with CBF at foam column height 2...

In a low expansion ratio foam (n <5-10) the liquid distribution along the foam column height is attained very quickly (within seconds), so that the flowing conditions are fulfilled... 

However, the model applied in this study is hardly realistic, since it is assumed that the foam consists of capillaries (borders) whose length is equal to the foam column height but the liquid capillary rise in them varies with time. 

Changes in V o and wq observed in experiments of foams of the same expansion ratio and dispersity but of different initial liquid distribution along the foam column height reflect the influence of the local foam characteristics on the above mentioned constants. This is not considered in the model on the basis of which Eq. (5.46) is obtained. The equation of the... 

A typical dependence of drainage onset on foam column height at foam expansion ratio n = 70 is given in Fig. 5.14. [6,22], For high foam columns (H > 16 cm) zb is small and does not practically depend on H. It is mainly determined by the hydrodynamic properties of the system (borders size and viscosity), i.e. of the microsyneresis rate. For small foam column heights t0 strongly depends on H and is determined by the rate of internal foam collapse. These dependences indicate that for a quantitative description of drainage detailed... 

The quasi-equilibrium character of expansion ratio distribution along foam column height is also confirmed by the study of the pressure profile (Fig. 5.16). At levels higher than... 

Fig. 5.15. Expansion ratio along foam column height as a function of the time after foam formation line 1...

The foam column height influences strongly the drainage rate. As it was mentioned, the initial moment of liquid outflow from the foam (drainage initiation) is determined by the critical values of expansion ratio, dispersity and height of the foam. It follows from Eq. (5.60) that if two foams have equal expansion ratio and dispersity, then their initial drainage rates should not depend on foam column height. However, with the decrease in foam column... 

Thus, at equal expansion ratio and dispersity, respectively, the drainage rate will strongly decrease with the decrease in foam column height. 

Initial drainage rate of foams from 0.2 % Volgonate solution at various foam column heights... 

Fig. 5.20), followed by a complete cease of drainage during the induction period t0 [24,25], Such a deviation appears also in the study of microsyneresis of local layers in the lower levels of the foam column. The foam expansion ratio for which Eq. (5.46) does not hold, depends significantly on surfactant concentration [25], Surfactant concentrations for which Eq. (5.46) cannot be used are marked with a dash in Table 5.7. The results refer to a 8 cm foam column height, produced by the barbotage method. 

With the increase in surfactant concentration and expansion ratio the capillary pressure during a certain period of time (about 5 min) practically does not change, though its absolute value is far from the equilibrium value (Fig. 5.21,b). When the foam column height is smaller (2 cm), the microsyneresis rate becomes extremely low and only at expansion ratios not exceeding 10 and surfactant concentrations not higher than 0.2% (Fig. 5.21, c curve 2) a slight pressure decrease with time is observed. In all other cases the pressure remains constant for a... 

Fig. 6.8. Kinetic curves of decrease in foam column height (1% NaDoS solution) at various air...

Logarithmic decrease in foam column height is observed also for foams from concentrated solution of NaDoS and pentanol, containing a large quantity of solubilised xylol... 

The total degradation time is often employed as a characteristic of the kinetics of foam column decay. Sometimes the time needed for breaking a certain part of the foam column (for example, 1/2 or 1/5 of its height) is also used. Obviously, either of these characteristics depend strongly on foam column height and foam dispersity. 

The lifetime of a foam being subjected to a pressure drop is affected by the mode of foam formation, the foam column height and foam dispersity. The foam column height... 

A more detailed study on foam behaviour and the features of foam column destruction has been performed in [69-71]. Various kinds of surfactants, different foam column heights, foam dispersity and temperatures, were investigated at Ap pgH, including the range of critical pressure drops pcr. The kinetics of establishing a capillary pressure was also accounted for. Used were ionic (NaDoS) and nonionic (Triton-X-100) surfactants as well as some silicon-organic compounds which differed by the number of siloxane, dimethylsiloxane, oxyethylene and oxypropylene groups (KS-1, BS-3 and KEP-2). 

Fig. 6.13 depicts the xp(Ap) dependence of Triton-X-100 (5 1 O 4 mol dm 3 and 0.4 mol dm"3 NaCl) foams studied at (a) different foam column heights but equal dispersity and (b) different foam dispersity but equal foam column height (1 cm). Fig. 6.14 presents the same tp(Ap) dependence for foams from silicon-organic compounds. 

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