Capsules are closed membranes made of polymers. They are increasingly used in cosmetics and 
pharmaceutics to encapsulate active agents in order to accomplish controlled delivery. For example, in 
medicine, they are used to transport and release cure or contrast agents to targeted sites within the human 
body. The delivery takes place either by mass transfer through the capsule membrane or by complete break-
up of the entire capsule. Mass transfer from unbroken capsules have been extensively studied numerically at 
BMBI, see Refs [1-7]. The present project aims to model numerically the rupture of a capsule membrane when 
subjected to strong applied flows.  Such event allows sudden and importance release of the capsule cargo, as 
reported experimentally in Ref. [8].  

The student will participate in developing a new numerical method to model the rupture of the capsule 
membrane using physics-based approaches. The capsule will be modeled as a closed spring network, as 
done in Ref. [1], and the mechanism of brittle materials break-up will be implemented. The developed 
numerical method will be used to model the event of the capsules rupture as a function of the membrane 
elastic properties and the strength of the applied flow.   

References:   

[1] C. Bielinski, L. Xia, G. Helbecque, B. Kaoui, Mass transfer from a sheared spherical rigid capsule, Physics 
of Fluids 34, 031902 (2022)   

[2] C. Bielinski, B. Kaoui, Numerical method to characterise capsule membrane permeability for controlled 
drug delivery, International Journal for Numerical Methods in Biomedical Engineering, e3551 (2021)   

[3] C. Bielinski, N. Le, B. Kaoui, Unsteady mass transfer from a core-shell cylinder in crossflow, Physical 
Review Fluids 6 (2), 023501 (2021)   

[4] B. Kaoui, Algorithm to implement unsteady jump boundary conditions within the lattice Boltzmann 
method, The European Physical Journal E 43, 23 (2020)   [5] B. Kaoui, Computer simulations of drug release 
from a liposome into the bloodstream, European Physical Journal E 41 (2), 20 (2018)  
 
[6] B. Kaoui, M. Lauricella, G. Pontrelli, Mechanistic modelling of drug release from multi-layer capsules, 
Computers in Biology and Medicine 93, 149 (2018)   

[7] B. Kaoui, Flow and mass transfer around a core-shell reservoir, Physical Review E 95, 063310 (2017)  
 
[8] A. Le Goff, B. Kaoui, G. Kurzawa, B. Haszon, A.-V. Salsac, Squeezing bio-capsules into a constriction: 
deformation till break-up, Soft Matter 13, 7644 (2017)