Entry coefficient

The concentration of monomers in the aqueous phase is usually very low. This means that there is a greater chance that the initiator-derived radicals (I ) will undergo side reactions. Processes such as radical-radical reaction involving the initiator-derived and oligomeric species, primary radical termination, and transfer to initiator can be much more significant than in bulk, solution, or suspension polymerization and initiator efficiencies in emulsion polymerization are often very low. Initiation kinetics in emulsion polymerization are defined in terms of the entry coefficient (p) - a pseudo-first order rate coefficient for particle entry. 

Another condition necessary for the realisation of the defoaming properties is the positive value of the so-called entry coefficient. The authors [47] argue that drops of the antifoam penetrate into the films separating the foam bubbles. The positive entry coefficient is... 

A theoretical analysis shows (see, e.g., Reference 674) that if the so-called entry coefficient ... 

Entry Coefficients, Spreading Coefficients, and Thin Film Forces... 

If an oil is to emerge into the air-water surface and subsequently spread, then there are certain requirements that must be satisfied concerning the so-called entry and spreading coefficients. If drops of oil dispersed in an aqueous phase are to emerge spontaneously into the air-liquid surface, the entry coefficient E defined by... 

Selection of the appropriate values of the three surface tensions should, however, take account of the extent to which the antifoam and aqueous solution have been pre-equilibrated. Thus, we could follow Ross [4] and define three entry coefficients. First, the initial entry coefficient... 

GENERALIZED ENTRY COEFFICIENTS, PSEUDOEMULSION FILMS, AND THIN FILM FORCES... 

It may be readily shown [28,31] that the generalized entry coefficient is related to the interaction free energy/unit area, W(h), of the pseudoemulsion film where... 

If we set = 0 in Equations 3.19 through 3.21 and therefore 11awo( ) = 0. then we are considering entry to form an oil-air surface having the properties of the pure oil (i.e., uncontaminated with any film or adsorbed monolayer) whence E and WQi) become equivalent. Physically this situation mnst correspond closely to that represented by the classic initial entry coefficient (or even in some circumstances the classic equilibrium entry coefficient) where the film tension is replaced by the air-oil surface tension, Oao. of the pure oil. 

Equation 3.19. In this example we have A < 0, C < 0,. 6 > 0, A > 5, C > 5, and A + C > so that the integral of Equation 3.19 is negative and the generalized entry coefficient positive for films at both thickness h = h and h = fi. These two situations correspond to stable equilibrium and metastable eqnilibrinm films, respectively, where the former is characterized by the highest entry coefficient and the lowest film tension. The classic equilibrium entry coefficient E is concerned with the stable equilibrium so we should have E = E Qi = h. ... 

FIGURE 3.5 Schematic disjoining pressnre isotherm with negative generalized entry coefficient at imposed capillary pressnre where the latter is lower than the height of secondary... 

The condition E <0 clearly means that the arrangement shown in Figure 3.5 cannot be realized at equilibrium (or at all). As pointed out by Hirasaki [28], it should not therefore be regarded as in conflict with the requirement, given by Equation 3.11, that the classic equilibrium entry coefficient should have a minimum value of zero. Thus the latter derives from Antonow s rule [20], which deals with equilibrium behavior and is only valid for systems in which the equilibrium disjoining pressure is zero. 

There would appear then to be two situations where the existence of a secondary maximum in the disjoining pressure isotherm could result in inhibition of entry of an oil drop into the equilibrium configuration at the surface of a foaming solution where the classic equilibrium entry coefficient is positive (and where an oil-air surface is... 

The initial entry and spreading coefficients of some hydrocarbons on water are shown in Table 3.1. These coefficients are calculated from the relevant surface tensions of the pure oils and of course do not therefore concern mutually equilibrated fluids. However, the low mutual solubilities of water and hydrocarbons mean that there is essentially no difference between initial and semi-initial spreading coefficients. The initial entry coefficients are seen to be positive for all homologues. It is also seen that homologues higher than n-octane exhibit initial spreading coefficients... 

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