Scale-up model obtained from the rheological analysis of highly concentrated emulsions prepared at three scales

Abstract

We examine the scale invariants in the preparation of highly concentrated w/o emulsions at different scales and in varying conditions. The emulsions are characterized using rheological parameters, owing to their highly elastic behavior. We first construct and validate empirical models to describe the rheological properties. These models yield a reasonable prediction of experimental data. We then build an empirical scale-up model, to predict the preparation and composition conditions that have to be kept constant at each scale to prepare the same emulsion. For this purpose, three preparation scales with geometric similarity are used. The parameter N¿D^α, as a function of the stirring rate N, the scale (D, impeller diameter) and the exponent α (calculated empirically from the regression of all the experiments in the three scales), is defined as the scale invariant that needs to be optimized, once the dispersed phase of the emulsion, the surfactant concentration, and the dispersed phase addition time are set. As far as we know, no other study has obtained a scale invariant factor N¿Dα for the preparation of highly concentrated emulsions prepared at three different scales, which covers all three scales, different addition times and surfactant concentrations. The power law exponent obtained seems to indicate that the scale-up criterion for this system is the power input per unit volume (P/V).