Modelling of CaCO3 nanoparticle formation during overbasing of lubricatingoil additives

A framework of population balance equations has been developed to model for mation of CaCO3 nanoparticles during overbasing of lubricating oil. The pro cess involves carbonation of a reverse micellar solution containing lime, p resent both in the micelles and as a suspension of lime particles in the oi l. The mechanism leading to CaCO3 nanoparticles in this setup consists of a number of elementary events such as CO2 transport from gas to reverse mice lles through the organic phase, reaction in the reverse micellar core, nucl eation of CaCO3, particle growth, and Brownian collisions leading to materi al exchange, both among reverse micellar drops and between drops and lime p articles. A time scale analysis of these steps permits simplification and e nables us to divide the whole process into two stages. The first consists o f reaction of existing lime in micelles and a burst of nucleation of very s hort duration, wherein some reverse micelles beget a single nucleus each. T he number of such nucleated reverse micelles depends on the relative rates of mass transfer, nucleation, and growth by intermicellar Brownian collisio ns. This is followed by a slow growth phase of these initial particles thro ugh Brownian collisions between nucleated reverse micelles and lime particl es. The model predicts the data of Roman et al. (J. Colloid Interface Sci. 1991, 144, 324.), where on average only 10 initial reverse micelles contrib ute to form a CaCO3 nanoparticle. A simplified version of the model, obtain ed in the limit of instantaneous gas transfer, is also able to approximatel y predict the results of Kandori et al. (J. Colloid Interface Sci. 1988, 12 2, 78.) where, in contrast, a huge number of 10(8) reverse micelles contrib ute to form one particle. The model is quite general and can be used for ot her gas-liquid micellar precipitation systems wherein similar relative orde rs of time scales are involved.