On the macroscopic modeling of the rheology and Ostwald ripening of dilute stabilized emulsions

Abstract

Stabilized-emulsions often undergo Ostwald ripening owing to the higher solubility of the smaller droplets. Their rheological properties are a direct result of the interplay between their microstructure and flow, which in turn affect their processing as well as their applications. In a recent study [Mwasame et al., “On the macroscopic modelling of dilute emulsions under flow,” J. Fluid Mech. 831, 433–473 (2017)], the use of a unit determinant conformation tensor to represent morphological changes has been advanced within the context of a thermodynamically consistent theory for a dilute monodisperse emulsion. The resulting model was validated against previously developed asymptotic theory that was also used to obtain all model parameters. In the present work, the first key innovation is to show how this theory can be extended to allow for multiple conformation tensors, subject to a single joint constraint originating from the mass conservation of the dispersed phase, in order to allow for the representation of dilute polydisperse emulsions undergoing Ostwald ripening. The second enabling innovation of this work is to show how to introduce correct dissipative terms into the dissipation bracket to account for mass transfer processes. The approach is illustrated for the particular case of a bidisperse emulsion. The model illustrates how multiple transport phenomena and thermodynamic effects can be seamlessly combined within a thermodynamically consistent approach. This work allows for not only the coexistence of a bimodal population of droplets but also the evaluation of their deformability and effective rheology in the presence of Ostwald ripening as the largest size droplets increase in mass at the expense of the smaller ones.