Correct Use of the Lifshitz-Slyosov-Wagner Expression for the Calculation of the Average Radius of an Oil-In-Water (o/w) Emulsion Subject to Coalescence

TL;DR

This paper critically examines the Lifshitz-Slyozov-Wagner theory's application to oil-in-water emulsions, demonstrating that coalescence invalidates the standard expression and proposing necessary corrections for accurate average radius calculation.

Contribution

The study shows that the traditional LSW expression is incorrect when coalescence occurs and provides corrected formulations validated through experiments and theory.

Findings

LSW theory does not hold in the presence of coalescence

Corrected expressions improve radius estimation in coalescing emulsions

Experimental data supports the need for modified LSW approach

Abstract

The analytic expression proposed by Lifshitz-Slyozov and Wagner (LSW theory) for the linear variation of the cube average radius (R3) of an emulsion as function of time (t) is commonly used to appraise the effect of Ostwald ripening. However, we proved here both experimentally and theoretically that such approach is incorrect in those cases in which the coalescence of the drops cannot be prevented. In this event, the expression of LSW should be corrected in order to account for the actual average radius of the emulsion at each time, and instead of the radius predicted by the equations of LSW without consideration of the coalescence process.