A model for bubble dynamics in a protein solution

Abstract

This paper presents a model for bubble dynamics in a protein solution, including varying surface tension and dynamic adsorption/desorption of protein onto the bubble surface. We model the protein-coated bubble surface as a linear viscoelastic interface. Two cases are studied to understand the importance of the surface excess stress: (1) bubble dissolution in a protein solution due to gas diffusion; and (2) bubble response to an imposed fluctuating pressure field. In the first case study, the surface excess stress stabilizes the bubble against dissolution. Initially, the surface excess stress is negligible, and the dissolution rate is governed by the Weber number, which compares the gas inertial force and the surface tension force. As the bubble shrinks, the surface excess stress grows and eventually balances the surface tension. After that, the dissolution rate is governed by the protein desorption rate and the elasto-capillary number, which compares the surface tension and the surface dilatational elasticity. Our model predictions for the dissolution process agree with experiments before the bubble buckles. In the second case study, the surface dilatational viscosity and dilatational elasticity add resistance and stiffness to the system, respectively. Including the surface excess stress increases (or reduces) the amplitude of the bubble radius if the frequency of the imposed fluctuating pressure is greater (or less) than a critical value. These results highlight the importance of the surface rheology on the protein-coated bubble dynamics, which has applications in drug delivery and ultrasound contrast agents.