Zero-thickness interface models are developed to describe the encapsulation of microbubble contrast agents. Two different rheological models of the interface, Newtonian (viscous) and viscoelastic, with rheological parameters such as surface tension, surface dilatational viscosity, and surface dilatational elasticity are presented to characterize the encapsulation. The models are applied to characterize a widely used microbubble based ultrasound contrast agent. Attenuation of ultrasound passing through a solution of contrast agent is measured. The model parameters for the contrast agent are determined by matching the linearized model dynamics with measured attenuation data. The models are investigated for its ability to match with other experiments. Specifically, model predictions are compared with scattered fundamental and subharmonic responses. Experiments and model prediction results are discussed along with those obtained using an existing model [Church, J. Acoust. Soc. Am. 97, 1510 (1995) and Hoff et al., J. Acoust. Soc. Am. 107, 2272 (2000)] of contrast agents.

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Two nonlinear interfacial elasticity models-interfacial elasticity decreasing linearly and exponentially with area fraction-are developed for the encapsulation of contrast microbubbles. The strain softening ͑decreasing elasticity͒ results from the decreasing association between the constitutive molecules of the encapsulation. The models are used to find the characteristic properties ͑surface tension, interfacial elasticity, interfacial viscosity and nonlinear elasticity parameters͒ for a commercial contrast agent. Properties are found using the ultrasound attenuation measured through a suspension of contrast agent. Dynamics of the resulting models are simulated, compared with other existing models and discussed. Imposing non-negativity on the effective surface tension ͑the encapsulation experiences no net compressive stress͒ shows "compression-only" behavior. The exponential and the quadratic ͑linearly varying elasticity͒ models result in similar behaviors. The validity of the models is investigated by comparing their predictions of the scattered nonlinear response for the contrast agent at higher excitations against experimental measurement. All models predict well the scattered fundamental response. The nonlinear strain softening included in the proposed elastic models of the encapsulation improves their ability to predict subharmonic response. They predict the threshold excitation for the initiation of subharmonic response and its subsequent saturation.

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