Critical retardation effects

Accounting for the influence of surface-active contaminants is complicated by the fact that both the amount and the nature of the impurity are important in determining its effect (G7, L5, Rl). Contaminants with the greatest retarding effect are those which are insoluble in either phase (L5) and those with high surface pressures (G7). A further complication is that bubbles and drops may be relatively free of surface-active contaminants when they are first injected into a system, but internal circulation and the velocity of rise or fall decrease with time as contaminant molecules accumulate at the interface (G3, L5, R3). Further effects of surface impurities are discussed in Chapters 7 and 10. For a useful synopsis of theoretical work on the effect of contaminants on bubbles and drops, see the critical review by Harper (H3). Attention here is confined to the practically important case of a surface-active material which is insoluble in the dispersed phase. The effects of ions in solution or in double layers adjacent to the interface are not considered. 

If a system of chemical kinetic equations is non-linear and the reaction mechanism includes an interaction step between various substances, bifurcations are possible. They account for the effects of critical retardation. Let us illustrate this by the simplest (non-chemical) example. Consider the differential equation... 

Figures 5.37 and 5.38 show the critical thicknesses of rupture, Rp for foam and emulsion films, respectively, plotted vs. the film radius." In both cases the film phase is the aqueous phase, which contains 4.3 x 10 M SDS + added NaCl. The emulsion film is formed between two toluene drops. Curve 1 is the prediction of a simpler theory, which identifies the critical thickness with the transitional one." Curve 2 is the theoretical prediction of Equations 5.270 to 5.272 (no adjustable parameters) in Equation 5.171 for the Hamaker constant the electromagnetic retardation effect has also been taken into account. In addition, Eigure 5.39 shows the experimental dependence of the critical thickness vs. the concentration of surfactant (dodecanol) for aniline films. Figures 5.37 to 5.39 demonstrate that when the film area increases and/or fhe electrolyte concentration decreases the critical film thickness becomes larger.

Surface active agents (surfactant) are either present as impurities that are difficult to remove from a system or they are deliberately added to fluid mixtures to manipulate interfacial flows. It has been well known that the presence of surfactant in a fluid mixture can critically alter the motion and deformation of bubbles moving through a continuous liquid phase. Probably, the best-known example is the retardation effect of surfactant on the buoyancy-driven motion of small bubbles. Numerous experimental studies have shown that the terminal velocity of a contaminated spherical bubble is significantly smaller than the classical Hadamard-Rybczynski prediction... 

On the other hand, the system may be overcooled (oversaturated) due to the long induction period of formation of the new phatse particles and/or the absence of heterogeneous nuclei (if the solution was carefully cleared prior to cooling). Indeed, according to the majority of patterns of formation of the new phase particles, the induction period on the binodal seems to be infinitely long. In this case, the system will remain transparent (the melastable state) till a certain overcooling level is reached. Moreover, the effect of critical retardation may complicate the situation. 

In this region of the state diagram, there appears the effect of critical retardation of relaxational i)rocesses due to the small values of the diffusion coefficient D. 

In addition, the effects of gas phase retardants can change both A and E. If E is increased, our critical temperature criterion for extinction must accordingly be increased to maintain effectively a critical constancy for E/T. These chemical effects are complex and specific, and we will not be able to adequately quantify them. It is sufficient to remember that both velocity (flame stretch) and chemistry (retardant kinetics) can affect extinction. We will only examine the temperature extinction criterion. 

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