Contribution to the modelization of the surfactant concentration influence on droplet size distributions in oil/water emulsions

Abstract

We have worked out a simplified model to forecast the droplet size distribution in emulsions generated by turbulent agitation in a closed vessel. This model is suited only for semidiluted oil/water emulsions stabilized by an ionic surfactant. — In this model, during one step of the calculus, each droplet is submitted to a random transition: it can break into two droplets of half volume, or coalesce with another droplet of same volume, or remain unaltered. — At the instant t, the droplet size distribution is represented by a line vector, the elements of which are the volume percentages of the N possible states for the droplets. During the interval of time dt following the instant t, the random transition is represented by a [N, N] matrix, the elements of which are the transition probabilities in each state. These elements are updated after each step to make allowances for the creation of the oil/water interface and the corresponding surfactant adsorption. The size distribution at the instant t+dt is obtained by multiplying the line vector and the transition matrix. - The transitions result from the competition between the forces driving, breaking and coalescence. The expressions of their probabilities rest essentially on the kinetic theory of gas, the isotropic turbulence theory, and the DLVO theory. — The model has two adjustment parameters: the former linked to the ratio of breaking and coalescence probabilities, the second to the kinetic energy of the droplets in the turbulent medium. A couple of values of these parameters is found to be sufficient to account for the variation of the droplet size distribution in isooctane/water emulsions as a function of the concentration of sodium dodecylbenzene sulfonate.Key wordsTheory of emulsificationlognormal distributiondroplet size distribution surfactantoil/water emulsion