A mathematical model of crystallization in an emulsion

A mathematical model incorporating many of the important processes at work in the crystallization of emulsions is presented. The model describes nucleation within the discontinuous domain of an emulsion, precipitation in the continuous domain, transport of monomers between the two domains, and formation and subsequent growth of crystals in both domains. The model is formulated as an autonomous system of nonlinear, coupled ordinary differential equations. The description of nucleation and precipitation is based upon the Becker–Döring equations of classical nucleation theory. A particular feature of the model is that the number of particles of all species present is explicitly conserved; this differs from work that employs Arrhenius descriptions of nucleation rate. Since the model includes many physical effects, it is analyzed in stages so that the role of each process may be understood. When precipitation occurs in the continuous domain, the concentration of monomers falls below the equilibrium concentration at the surface of the drops of the discontinuous domain. This leads to a transport of monomers from the drops into the continuous domain that are then incorporated into crystals and nuclei. Since the formation of crystals is irreversible and their subsequent growth inevitable, crystals forming in the continuous domain effectively act as a sink for monomers “sucking” monomers from the drops. In this case, numerical calculations are presented which are consistent with experimental observations. In the case in which critical crystal formation does not occur, the stationary solution is found and a linear stability analysis is performed. Bifurcation diagrams describing the loci of stationary solutions, which may be multiple, are numerically calculated.

Evaluation by volatile profile of the synergistic antioxidant effect between bovine serum albumin and virgin olive oil phenolic compounds in an oil-in-water emulsion

THE OXIDATIVE STABILITY OF OIL-IN-WATER EMULSIONS, CONTAINING BOVINE SERUM ALBUMIN (BSA) AND VIRGIN OLIVE OIL PHENOLIC COMPOUNDS, WAS STUDIED BY THE DETERMINATION OF THE FORMATION OF VOLATILE OXIDATION PRODUCTS. FOUR OIL-IN-WATER EMULSIONS WITH AND WITHOUT PHENOLS ISOLATED FROM VIRGIN OLIVE OIL AND BSA WERE PREPARED. THESE MODEL SYSTEMS WERE STORED AT 60 degrees C TO ACCELERATE LIPID OXIDATION. VOLATILE OXIDATION PRODUCTS WERE MONITORED EVERY THREE DAYS BY HEADSPACE SOLID-PHASE MICROEXTRACTION COUPLED WITH GAS CHROMATOGRAPHY. ALTHOUGH INDIVIDUALLY OLIVE OIL PHENOLIC COMPOUNDS AND BSA SHOWED A SIGNIFICANT ANTIOXIDANT ACTIVITY, THE COMBINATION OF THESE COMPONENTS SHOWED A VERY GOOD SYNERGY, QUANTIFIED AS 127%. IN FACT, THE EMULSION CONTAINING BOTH PHENOLIC COMPOUNDS AND BSA SHOWED A VERY LOW LEVEL OF OXIDATIVE DETERIORATION AFTER 45 DAYS STORAGE.