A modified Rayleigh-Plesset equation for a liquid-crystalline shelled microbubble

Premanufactured shelled microbubbles are currently used in the medical profession as ultrasound imaging agents. Recent research is focussing on using these shelled microbubbles for localised drug delivery. Presently, there exists no mathematical model for a liquid-crystalline shelled microbubble. For the very rst time, using Leslie-Erikson theory, a theoretical model is developed for a gas loaded shelled microbubble that is composed of a nematic liquid-crystalline material. Current mathematical models assume that the shells are viscoelastic in nature and are typically modelled as a Maxwell uid. However, this approach is totally inappropriate for a liquid-crystalline material which is non-Newtonian in nature. We show that liquid-crystalline shelled microbubbles possess dierent physical properties from commercial shelled microbubbles. We have found that nematic liquid-crystalline shelled microbubbles have a relaxation time that is 10 times longer than certain commercial shelled microbubbles. The authors propose that these signicantly dierent physical properties may enhance localised drug delivery via sonoporation. This is due to their longer relaxation time which enhances acoustic microstreaming and significantly increases the magnitude of the wall shear stress.