(269f) Achieving Target Emulsion Drop Size Distributions Using Population Balance Equation Models of High Pressure Homogenization
Oil-in-water emulsions are ubiquitous dispersed phase systems with diverse applications that include consumer products, processed foods, polishes, waxes, agricultural sprays and road surfacing materials. In the foods industry, emulsions constitute natural foods as well as numerous processed products such as milk, butter, margarine, ice cream, sauces and desserts. Food emulsions contain edible oils, water and biocompatible surfactants as the major ingredients and vitamins, minerals and/or flavors as minor ingredients. Emulsion system formulation and processing operations both impact the drop size distribution, a key property that influences emulsion rheology, stability, texture and appearance. A typical processed food requires the drop size distribution to be maintained within acceptable limits, which includes achieving a prescribed mean drop size, maintaining small variations about the mean and avoiding very small or large drops that adversely affect product properties such as texture, appearance and food safety. Oil-in-water emulsions are typically formed by first preparing a coarse premix using a low shear stator-rotor type device that mixes the various ingredients into a stable form. This premix is then processed with a high shear device in which relatively large drops are broken into much smaller drops. In high pressure homogenization, the coarse emulsion is passed through a small orifice under very high pressure.
Due to lack of quantitative understanding, new emulsified products are currently developed by combining a broad knowledge of previous product formulations with empirical scientific experimentation. An alternative to brute force experimentation is to utilize a suitable mathematical model to predict the drop size distribution for different emulsion formulations and processing conditions. The population balance equation (PBE) modeling framework is particularly well suited for this problem as functions describing drop breakage and coalescence can be incorporated within a fundamental number balance equation to predict the evolution of the drop size distribution. Several investigators have developed PBE models of high pressure homogenizers. As part of our previous work, we have developed breakage-only PBE models for prediction of the drop volume distribution. Through experimental and computational studies, we showed that our model emulsion system exhibited negligible coalescence due to the low oil-to-surfactant ratio (5% oil, 1% surfactant) used.
In this paper, we incorporate drop coalescence functions to allow the drop volume distribution to be predicted for a much higher oil-to-surfactant ratio (50% oil, 1% surfactant) and utilize the model to achieve target distributions by changing homogenizer operating conditions. Nonlinear optimization is used to estimate six adjustable parameters in the drop breakage and coalescence functions from measured size distributions. The experimentally validated model is used to optimally determine the number of homogenization passes and the pressure of each pass such that specified emulsion drop size properties are achieved in a least-squares sense. Two optimization objectives that differ with respect to the distribution specifications are formulated and experimentally evaluated.