a modified marmottant model to study the effects of a shell rupture on the subharmonic threshold of encapsulated microbubbles

This study considers the radial behavior of a coated microbubble after a shell rupture usingthe marmottant model. the surface tension of the encapsulated microbubble should equalthe free bubble in the rupture state of the marmottant model. despite the assumption thatthe bubble is considered free in the third state, dilatational interfacial viscosity is constantin the equation in this model. this paper assumes that dilatational interfacial viscositydecreases gradually after shell rupture until it becomes zero. the decrease of dilatationalinterfacial viscosity caused by the shell rupture significantly affects radial behavior andthe nonlinear response of the encapsulated microbubble, such as subharmonic response.because the subharmonic response is extensively used in ultrasound imaging, the effectof a decrease in dilatational interfacial viscosity on the subharmonic threshold needs to beinvestigated. in figures showing the radius versus time and the frequency response of thecoated microbubble, it is observed that at high excitation pressure, the proposed model ismore nonlinear than the marmottant model, resulting in a lower subharmonic threshold.