Coalescence first-order kinetics

For studying emulsion coalescence, it is important to consider the rate constant of flocculation and coalescence. If coalescence is the dominant factor, then the rate K follows a first-order kinetics. 

The rate of coalescence is determined by the rate at which the film thins, and this usually follows a first-order kinetics. 

For that reason, it is preferable in these systems to scavenge the protons by adding a base to the solution and to favor the coalescence by a reduction faster than Ae oxidation which obeys first order kinetics ( 4.2)... 

At first glance the coagulation rate has not manifested itself in die entire destabilization process in the case of slow coalescence [condition (35)]. At any given moment the decrease in flic total droplet concentration is proportional to the momentary total droplet concentration (first-order kinetics), which causes an exponential decrease with time ... 

The second type of coalescence arises from the rupture of films between adjacent bubbles [Vrij and Overbeek, y. Am. Chem. Soc., 90, 3074 (1968)]. Its rate appears to follow first-order reaction kinetics with respect to the number of bubbles [New, Proc. 4th Int. Congr. Suif. Active Substances, Brussels, 1964, 2, 1167 (1967)] and to decrease with film thickness [Steiner, Hunkeler, and Hartland, Trans. In.st. Chem. Fng., 55, 153 (1977)]. Many factors are involved [Biker-man, Foams, Springer-Verlag, New York, 1973 and Akers (ed.). Foams, Academic, New York, 1976]. 

The pseudo first-order rate constants, obs, are obtained by least-squares fits of the measured peak height increase of the relevant coalesced oxygen-17 signal as a function of time to the modified McKay equation (7, 67, 68). The kinetics can be studied by manipulation of... 

It can be seen that the reduction of Pd2 + proceeded slowly and was complete in 20 min. from the start of the introduction of H2 in the first exposure. Unlike in the first H2 exposure, the reduction of Pd in the second, third, and fourth exposures was quickly completed, in less than 3 min. In the latter cases, 10%-20% of the Pd content was oxidized after the introduction of 02 and before the admission of H2. These facts are consistent with the change in the Pd—O and Pd—Pd bonds, as observed in the Fourier transforms of Figure 22.9. The oxidation state of Pd in the first H2 exposure was kinetically analyzed using the data of Figure 22.11 the first-order rate constant k was determined to be 0.28 min-1. In addition, the first-order rate constant of the CN of the Pd—Pd bond was determined independently, based on the data of Figure 22.10. The obtained k value was 0.35 min-1, which is close to that of the kinetic constant k for the reduction of Pd2 +, suggesting the reduction of Pd2 + and the coalescence of Pd clusters progressed simultaneously in H-USY. 

The spirosilane 1 also shows an A3B3 pattern for the -CF3 absorptions in the 19F NMR spectrum in non-coordinating solvents, but the addition of a weak nucleophile, such as methanol, THF or benzaldehyde, results in coalescence of these peaks at, or somewhat above, room temperature. Kinetic studies showed the reaction to be first-order in nucleophile, and at lower temperatures NMR signals corresponding to the formation of a 1 1 adduct of nucleophile and spirosilane, with a structure analogous to that of the siliconate anions, 69, could be observed. Experiments with a series of substituted... 

The previous discussion dealt with Forces and potentials, i.e., equilibrium concepts, so that it indicated the possibility of occurrence of some events, not the velocity at which they could happen. These potential considerations may be brought into a kinetic model similar to a bimotecular reaction rate, in which the probability of coalescence is taken as a function of the repulsive potential. This leads to a second-order kinetic model first proposed by Smoluchovski in 1916. It is useful], to describe an emulsion ripening process in which the reciprocate of tlie number of drops in a given system increases linearly as time elapses. This model has been improved on to calculate the coalescence dynamics of nonde-formable drops (37,38) as well as deformable drops associated with a thin-film hydrodynamic drainage (39.40). 

Batycky et al. (1997) adopted population balances along with a pseudo-first order degradation kinetics to describe the behavior of eroding microparticles. The kinetic mechanism includes both random chain scission and chain-end scission. The change in matrix porosity is accounted for by considering the coalescence of small pores caused by the breakage of polymer chains. 

Flocculation and Coalescence. Flocculation being the primary process, the droplets of the dispersed phase come together to form aggregates. In this process, the droplets have not entirely lost their identity and the process can be reversible. Since the droplets are surrounded by the double layer, they experience the repulsive effect of the double layer. Kinetically, flocculation is a second order reaction since it depends in the first instance on the collision of two droplets and is expressed in the form (31)... 

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