Prediction of droplet sizes for oil-in-water emulsion systems assisted by ultrasound cavitation: Transient scaling law based on dynamic breakup potential

The dynamics of droplet breakup during emulsification is a complicated process due to the interplay between multiple physico-chemical and hydrodynamic factors, especially in an energy-intensive ultrasound-assisted emulsification process. In this work, by mapping the physical processing parameters of ultrasound emulsification into a reduced domain that is governed by the power density and the initial average droplet diameter, a dimensionless parameter that resembles the dynamic breakup potential (η) was established via dimensional analysis. In addition to shedding important insights into the emulsification process, η further facilitates the establishment of a transient scaling relationship that is a function of the characteristic value (a) of the emulsion system. Experimental case study on a cellulose nanocrystals (CNC)-based olein-in-water emulsion system prepared via ultrasound cavitation confirmed the validity of the scaling relationship and sub-universal self-similarity was observed. Using the proposed model, good predictions of the transient of droplet size evolution were attained where the value of η, i.e. the proportionality constant, can be conveniently computed using data from a single time point. Application on other emulsion systems further suggested that the value of a possibly indicates the relative minimum size limit of a particular fluids-emulsifier system. Our approach is general, which encourages widespread adoption for emulsification related studies.