Prediction for the bubble dissolution rate in a protein solution

We have developed a model for the bubble dynamics in a protein solution. We model the protein-coated bubble surface as a linear viscoelastic interface, and we use the case of bubble dissolution due to gas diffusion to highlight the importance of the surface excess stress.

Initially, the surface excess stress is negligible due to the low protein concentration on the bubble surface. The Weber number, which compares the gas inertial force and the surface tension force, governs the bubble dissolution rate during this stage. 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. We have also derived a formula for the bubble dissolution rate, enabling extracting the interfacial parameters from the experimentally measured bubble radii. This work provides insight into protein-coated bubbles and helps guide the design of protein-coated bubbles.