Entering coefficient

Foam stability in the presence of oil can be described from thermodynamics in terms of the spreading and entering coefficients S and E respectively. These coefficients are defined as follows ... 

These agents may operate via a number of mechanisms, but the most common ones appear to he those of entry and/or spreading. The defoamer must first of all he insoluble in the foaming liquid for these mechanisms to function. Second, the surface tension of the defoamer must be as low as possible. The interfacial tension between defoamer and foamer should be low. but not so low that emulsification of the defoamer may occur. Third, the defoamer should be dispersible in the foaming liquid. It was first shown in I fM8 that thermodynamically the entry of the defuamcr droplet into a bubble surface occurs when the entering coefficient has a positive value. The physics of bubbles is described in entry on Foam. 

The thin liquid films bounded by gas on one side and by oil on the other, denoted air/water/oil are referred to as pseudoemulsion films [301], They are important because the pseudoemulsion film can be metastable in a dynamic system even when the thermodynamic entering coefficient is greater than zero. Several groups [301,331,342] have interpreted foam destabilization by oils in terms of pseudoemulsion film stabilities [114]. This is done based on disjoining pressures in the films, which may be measured experimentally [330] or calculated from electrostatic and dispersion forces [331], The pseudoemulsion model has been applied to both bulk foams and to foams flowing in porous media. 

In the study of the mechanism of heterogeneous defoaming along with the spreading coefficients the so-called enter coefficient (destruction coefficient) is used to estimate the instability of aqueous foam films... 

Since information about the instability of asymmetric films provided from the spreading and enter coefficients is incomplete, it has been proposed [541,542] to use generalised spreading coefficients 5s on the basis of Eqs. (3.157-3.160). By definition the generalised spreading coefficient is [541]... 

If the value of the equilibrium generalised enter coefficient Ee is determined from experimental data about interfacial and surface tension, its values are usually close to zero (of the order of decimal parts of mN m 1), the error being 0.3 mN m 1 [541]. As mentioned in [51], since Ee and se are not very accurate, they cannot be employed to predict the penetration of oil drops from the aqueous films onto the interface. 

Comparison of the spreading and entering coefficients with the stability of non-symmetric films has been considered by Lobo and Wasan [52]. The results are presented in Table 9.4. 

The antifoaming action can be rationalised [28] in terms of the balance between the entering coefficient E and the Harkins [29] spreading coefficient S, which are... 

If an insoluble agent is dispersed in the liquid interior of foam lamellae, then, from thermodynamics, it can penetrate or enter the gas—liquid interface if the entering coefficient, E, is positive (originally defined (55) as a rupture coefficient, R). E is defined, for unit surface areas, as... 

Robinson and Woods (73) used a similar, thermodynamic approach, but they found better correlation between the defoaming action and the entering coefficient (E) that is, the change from configuration a to c (Figure 22) defined as... 

Boussinesq number concentration diffusivity surface diffusivity entering coefficient Gibbs elasticity... 

Spreading and Entering Coefficients. From thermodynamics, a defoamer would be predicted to spread as a lens over a foam if its spreading coefficient is positive, (17, 45). The spreading coefficient, S, for an oil—foam system is given by... 

The spreading and entering coefficients have correlated with foam sensitivity to oil in a number, but not in all, of the cases. As already noted, the degrees of foam sensitivity to oil (Figure 2) observed in microvisual experiments have been compared to the thermodynamic predictions based on S and E in Figure 8 (37, 40, 47). In these comparisons, the predictions were not always borne out Depending on the oil studied, on the order of one-half of the surfactant solutions predicted to produce foams of type C actually produced foams of type B. The predictions of which surfactants would produce foams of type A were much better for the heavier oils than for the lighter oils. Even quantitative measurements of lamella rupture frequency in the microvisual experiments showed that satisfactory correlations with 5 or were not obtained (37, 40, 47). 

The mechanisms for foam sensitivity to oils can also be compared to the results from core-flood experiments in which foams were made to flow through porous rock in the presence of residual oil. Holt and Kristiansen (26, 27, 56) studied foams flowing in cores under North Sea reservoir conditions and found that the presence of residual oil could reduce the effectiveness of flowing foams. They compared their results with the spreading and entering coefficients and found foam sensitivity to be correlated with the (oil) spreading coefficient. 

If an antifoam is to be effective it must be able to enter the film that makes up the foam bubbles and spread across the film surface. Equations 1 and 2 define the entering coefficient, E, and the spreading coefficient, 5, of an antifoam with respect to a particular foaming medium. 

If a bitumen droplet and a gas bubble collide, their mutual attachment is thermodynamically favourable if the attachment coefficient is positive (often referred to as an entering coefficient originally defined by Robinson and Woods [114] for defoamers). The attachment coefficient, A, is given as ... 

Entering Coefficient. A measure of the tendency for an insoluble agent to penetrate, or enter , an interface (usually gas—liquid or liquid— hquid). Entering is thermodynamically favored if the entering coefficient is greater than zero. When equilibria at the interfaces are not achieved instantaneously, reference is made to the initial and final (equihbiium) entering coefficient. See also Spreading Coefficient. 

As briefly discussed earlier, a widely accepted mechanism for antifoaming action is that first the oil drop enters the air/water interface, and in a secondary step, begins to spread over the foam film, so causing rupture. An entering coefficient ( ) and a spreading coefficient (S) have been defined in terms of the change in free energy when the oil droplet enters the interface or spreads at the surface. These are defined as follows ... 

To enter coefficients into COMSOL , expand General Form PDE (g) and click General Form PDEl. In the General Form PDE page, expand Conservative Flux and enter each component in F = [f F ] from Equation [7.11] into the box as... 

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