Theoretical prediction of the shear stress induced by an oscillating
bubble close to a rigid/elastic wall


Targeted drug delivery (the delivery of a drug to a localized site in the human body) is one of the most ambitious goals of modern therapy. The strict localization of the drug activity would result in a significant reduction of drug toxicity, drug dose and in an increased treatment efficacy. Recently, new promising possibilities for targeted drug delivery have been discovered, which are based on using ultrasonically activated microbubbles. Experiments reveal that microbubbles, when oscillating nearby biological barriers (cell membranes), allow drugs and genes to penetrate into individual cells without serious consequences for the cell viability. Experimental observations suggest that the temporary permeabilization of biological barriers is caused by the shear stress that are exerted on cell tissues by acoustic microstreaming.

Work program
Based on previous theoretical works performed by our team, it is possible to calculate the Lagrangian streaming velocity around a free bubble experiencing any arbitrary shape mode oscillation. A first step will be dedicated to the prediction of the shear stress induced by an oscillating bubble in the bulk fluid for a unique, isolated microbubble. A second step will consist in introducing near the bubble a wall, rigid or elastic, to mimic the presence of a biological barrier. The resulting microstreaming and the associated wall shear stress will be investigated for a large set of parameters (bubble size, bubble-wall distance, wall elasticity).

Applicant profile
The candidate should possess a strong mathematical background and perform analytical and numerical modeling, in the field of ultrasound cavitation, nonlinear physics, fluid mechanics. Skills in Mathematica software or Python will be appreciated. The theoretical predictions will be compared to experimental quantification of the wall shear stress on rigid or elastic (biological cells) walls. This work will be performed in the framework of the ANR-DFG project CaviStresse focusing on quantifying the shear stress induced by oscillating bubbles on nearby surfaces.