Modeling and simulation of single droplet drying in an acoustic levitator

Abstract

We present a mathematical model for the full drying process of a single protein formulation droplet taking into account the convective impact arising from its levitation by a standing ultrasound wave. Using the finite element method allows us to compute the evaporation rate directly from the fully resolved heat and mass transfer within and around the levitated droplet. We apply our model to simulate the drying kinetics of pure water and aqueous phosphoglycerate kinase (PGK) droplets under various levitation and drying conditions. Empirical data from the literature are used to validate and discuss our numerical results. The acoustic streaming turns out to accelerate not only the first but also the second drying stage. Moreover, the dehydration of the protein molecules is found to be primarily responsible for their enzymatic inactivation throughout the drying process.

Keywords:

• Single droplet drying
• acoustic levitation
• acoustic streaming
• protein denaturation
• finite element simulation

Acknowledgments

We are very grateful for the scientific discussions with our project partners Prof. Dr. Dagmar Fischer, Prof. Dr. Stefan Will, Dr. Stefan Seyferth, Dr. Felix Prihoda, and Julian Perlitz from the Institutes of Pharmaceutical Technology and Engineering Thermodynamics at the Friedrich–Alexander Universität (FAU) Erlangen–Nürnberg. In memory of our esteemed colleague Prof. Dr. Geoffrey Lee, we dedicate our manuscript to him and his outstanding pharmaceutical research.

Disclosure of interest statement

The authors report there are no competing interests to declare.

Notes

1 COMSOL Multiphysics^® version 6.0.0.405. www.comsol.com. Registered trademark of COMSOL AB, Stockholm, Sweden.

Additional information

Funding

This work was supported by the German Research Foundation (DFG) under Grant BA 1727/12-1 and via Research Training Group 2339 Interfaces, Complex Structures, and Singular Limits.