Foam expansion ratio determination

Another technique for foam expansion ratio determination involves taking samples and can be applied also for foams produced by foam generators. The precision of these direct volume-mass methods depends to a considerable extent on foam uniformity with respect to its expansion ratio and on the sampling conditions [20,21,22], The relative error in the evaluation of n for low expansion ratio foams (n < 100) is about 1-2%. However, for high expansion ratio foams (n > 1000) these methods become inapplicable. 

One of the most widely used methods for foam expansion ratio determination is based on measuring foam electrical conductivity. The expansion ratio of a foam and its conductivity are related according the expression (see Chapter 8)... 

Both Figs. 1.10 and 1.11 indicate that the curvature of the border along its length becomes smaller compared to cross-section curvature even at foam expansion ratios from 40 -80 and rn/a = 0.5-0.35 (r in centimetres, Table 1.1). Hence, at first approximation, the deviation from the border shape typical for a fully polyhedral bubble can be determined by... 

On the other hand a comparison of the ratio between the volumes of real Plateau border and cylindrical border model, obtained by Pertsov et al. [85], with the ratio (rh /rn)2, evaluated from the dodecahedral model [83] indicates that these ratios correlate well only when n > 640 but when n < 300 they differ by almost 30%. However, it should be noted that the method for calculating border volume in [85,86] at low foam expansion ratio differs from the real volume by 10%. Besides, all values of expansion ratio given in the tables of [86] are twice higher. This means that the interpolation equations for calculating the corrections of the volume and hydro- and electrical conductivities in the cylindrical border model must be corrected. The Plateau border cross-section area is determined by Eq. (1.19) when the contact angle between film and border surface is small 6 (or 1 in radians). 

The capillary pressure and foam dispersity were determined simultaneously. After drying the reduced pressure under the porous plate sharply changed to lower values leading to an immediate liquid suck in from the porous plate into the foam. As a result the foam expansion ratio decreased to values at which the condition for polyhedricity was not fulfilled. The capillary pressure and the expansion ratio were measured again for the new state of the foam obtained. 

Determination of Foam Expansion Ratio (Foam Density)... 

The simplest technique for determination of the average by volume expansion ratio (and density) is the direct measurement of the total foam volume and the liquid volume in it (or its mass). Using barbotage methods for foam production the foaming process can be run until the initial solution is completely transformed into foam. Foam expansion ratio and its density are calculated by the formula... 

A method for expansion ratio determination based on measuring heat capacity of a foam is described by Fokina and Kruglyakov [30] (see also Section 8.5). 

An important condition which has to be fulfilled when using this method for foam dispersity determination is the absence of an excess hydrostatic pressure in the foam liquid phase. This pressure is equalized to a considerable extent when an equilibrium distribution the foam expansion ratio and the border pressure along the height of the foam column is established. This can be controlled by measuring the pressure in the Plateau borders at a certain level of the foam column by means of a micromanometer. However, if this condition is overlooked, the hydrostatic pressure can introduce a considerable error in the results of bubble size measurements, especially in low expansion ratio foams. Probably, it is the influence of the unrecorded hydrostatic pressure that can explain the lack of correspondence between the bubble size in the foam and the excess pressure in them, observed by Aleynikov[49]. The... 

A device for foam dispersity determination by measuring the local foam expansion ratio and the pressure in Plateau borders is illustrated in Fig. 4.4. It consists of a glass container equipped with platinum electrodes and a micromanometer. The container bottom is a porous plate (a sintered glass filter). The pressure Ap is measured with a capillary micromanometer and the expansion ratio is determined by the electrical conductivity of the foam. The manometer and the electrodes are positioned so that to ensure a distance of 1.0-1.5 cm between them and the porous plate. When the distance is small the liquid in the porous... 

Fig. 4.4. Schematic of the device for determination of foam dispersity by the local foam expansion ratio ...

For evaluating the geometric coefficient B it is necessary to determine foam expansion ratio and electrical expansion ratio , which is equal to k[/kF (where kL and kF are the specific electrical conductivities of the solution and the foam, respectively). 

In the middle of cells and in faces that are perpendicular to the flowing direction, the borders are branched, which means that the effective number of borders, equivalent to that in a real system, is different from five. The number of independent borders with constant by height radius and length L can be determined by the electro-hydrodynamic analogy between current intensity and liquid flow rate through borders, both being directly proportional to the cross-sectional areas [6,35]. This analogy indicates that the proportionality coefficients (structural coefficients B = 3) in the dependences border hydroconductivity vs. foam expansion ratio and foam electrical conductivity vs. foam expansion ratio, are identical [10]. From the electrical conductivity data about foam expansion ratio it follows... 

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... 

Hence, the rate of decrease in specific surface area can be determined if the values of adsorption, foam expansion ratio and rate of increase in bulk surfactant concentration in the foam liquid are known. 

Fig. 6.1 depicts the experimental time dependence of foam expansion ratio, surfactant concentration in the flowing out solution as well as the rate of internal foam collapse. Within the whole time interval the rate of diminishing of specific foam surface area for a sulphonol foam is less than that for a NP20 foam, though the difference is not significant. Probably this is related to the fact that in the initial stage of internal foam collapse the rate deF/dx is determined by the gas mass-transfer that does not depend considerably on the surfactant kind. 

Pertsov et al. [19] and Kann [20] have proposed a logarithmic time dependence of the foam expansion ratio in order to determine the rate of bubble expansion. This approach is reasoned by the fact that at hydrostatic equilibrium further increase in foam expansion ratio occurs only when excess liquid is released with decreasing foam dispersity. It was experimentally established that at the final stage of internal foam collapse this increase in foam expansion ratio can be expressed by an exponential function [19,21]... 

Chemin [21] and Chistyakov et al. [44] have determined the change in bubble number in a unit contact area ns with time and have shown that the rate of the decrease in cell number dnjdr depends linearly on ns for all foam expansion ratios studied. Similarly to the lg R(r), this dependence consists of two parts. This is an expected result, since at constant foam volume the average bubble size Ry and their number Nb are related by the expressions... 

At constant gas supply the change in the foam expansion ratio would be determined only by the effect of various factors on the rate of drainage. 

In t vs. dv/dl co-ordinates this equation yields a straight line, beginning at the coordinates origin. For a foam this reological dependence is given by a curve, the slope of which as well as its ordinate axis-intercept, are determined by the foam expansion ratio. However, several other types of empirical relation have been proposed instead of Eq. (8.10) [19-22], The simplest and most widely used is the equation of Shvedov-Bingham... 

A conclusion has been drawn in [67] that the extinction of the luminous flux (7//o, where, 7o is the intensity of the incident light and 7 is the intensity the light passed through the foam) is a linear function of the specific foam surface area. A similar dependence has been used also for the determination of the specific surface area of emulsions [68]. Later, however, it has been shown [69,70] that the quantity 7//o depends not only on the specific surface area (or dispersity) but also on the liquid content in the foams, i.e. on the foam expansion ratio, that during drainage can increase without changing the dispersity. Since foam expansion ratio and dispersity are determined by the radii of border curvatures and film thicknesses, all the structural elements of the foam will contribute to the optical density of foams. This means that... 

The results from the additional experiments with pressure dump [72] have shown that the main reason for change in the slope angles in the dependence considered is the inaccuracy of foam expansion ratio (dispersity) determination. 

The high sensitivity of optical density to changes in foam expansion ratio and dispersity can be used as a background for developing optical techniques for the determination of these foam parameters. The theory of extinction of the luminous flux by the foam in which multiple light scattering is accounted for has been developed in [76]. 

On the basis of these dependences a technique has been proposed for the determination of the average bubble size R and foam expansion ratio [78]... 

Eqs. (8.66) - (8.68) show that thermal conductivity decreases with the increase in foam expansion ratio. Since the thermal conductivity of water (At = 0.63 V m 1 K1) is about 25 times higher than that of air (Ac = 0.024 V m 1 K 1), at n = 20-25 the thermal conductivity of a foam is mainly determined by that of the gas phase. 

However, the VL F value for a spherical foam is substantial and amounts to 48% of the total foam volume for a simple cubic packing and to 26% for a hexagonal close packing. For the latter the foam expansion ratio varies from 2.01 to 3.85 which may introduce large errors into the calculation of the //IIlln value. In a polyhedral foam the liquid volume can be neglected with respect to the foam volume but for the determination of //min( ) more detailed information on the structure of the foam is needed. 

Eqs. (10.11) and (10.12) indicate that when T = const and n = const, the accumulation ratio is determined by foam dispersity, while for r = const and a - const, it is determined by the foam expansion ratio and the capillary pressure. 

The main factor determining the critical pressure of a foam moving in a porous medium is the increase in the foam expansion ratio. Here again the critical pressure depends... 

Determination of foam expansion ratio (foam density) 357... 

The foam expansion ratio can be characterised by the liquid volume fraction in the foam, which is the sum of the volume fractions of the films, plateau borders and vertexes. Alternatively, the foam density can be used as a measure of the foam expansion ratio. The reduced pressure in the foam plateau border can be measured using a capillary manometer [4], while the bubble size and shape distribution in a foam can be determined by microphotography of the foam. Information about the liquid distribution between films and plateau borders is obtained from the data on the border radius of curvature, the film thickness, and the film-to-plateau border number ratio obtained in an elementary foam cell. 

Another characteristic of foam is the concentration in which it is used. A 3% foam concentrate is mixed at a ratio of 97 parts water to 3 parts foam concentrate. Similarly, a 6% foam concentrate is mixed at a ratio of 94 parts water to 6 parts foam concentrate. Another key consideration is the 25% drainage time—the time required for 25% of the foam s liquid to drain from the foam. This characteristic can be used to measure foam stability, and in combination with the expansion ratio, it can be used to determine how the thickness of the foam blanket will vary with time (NFPA 471, 1989). This dictates the rate at which foam will have to be added to the initial blanket to ensure continued mitigation effects. Second, the drainage time can be used to determine the water, both total quantity and rate, that will have to be dealt with to prevent the incident from becoming an environmental incident as well. 

The edges of this dodecahedron sized a - 8.5 cm. When the volume of the rubber balloon at inflation became bigger than the volume of the sphere inscribed in the dodecahedron, the balloon was deformed by the dedecahedron faces and took a shape close to the respective shape of a bubble in a monodisperse dodecahedral foam with a definite expansion ratio. The expansion ratio of the foam was determined by the volume of liquid (surfactant solution or black ink in the presence of sodium dodecylsulphate) poured into the dodecahedron. An electric bulb fixed in the centre of the balloon was used to take pictures of the model of the foam cell obtained. The film shape and the projection of the borders and vertexes on the dodecahedron face are clearly seen in Fig. 1.10. 

In order to compare the structural parameters of the foam model studied by Kruglyakov et al. [18] with the respective parameters of a real polydisperse foam (individual bubbles of different degree of polyherdisity) Kachalova et. al. [19] performed measurements of the average border radius of curvature of foams with variable expansion ratio. The foam studied, generated by the set-up shown in Fig. 1.4, was obtained from a nonionic surfactant solution of Triton-X-100 (a commercial product) to which NaCl (0.4 mol dm 3) was added. The expansion ratio was determined conductometrically with correction of the change in electrolyte concentration due to the internal foam destruction. The electrolyte concentration... 

Values of experimenlal atxp and calculated acai cell sizes of a foam from NP-20. Foam dispersity is determined by the method for measuring local expansion ratio and capillary pressure. 

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