Modeling atomic force microscopy and shell mechanical properties estimation of coated microbubbles

We present an extensive comparison with experimental data of our theoretical/numerical model for the static response of coated microbubbles (MBs) subject to compression from an atomic force microscope (afm). The mechanics of the MB's coating is described in the context of elastic thin shell theory. The encapsulated fluid is treated as compressible/incompressible pertaining to a gas/liquid, while the thinning of the liquid film between the MB and the afm cantilever is modeled via introduction of an interaction potential and the resulting disjoining pressure. As the external force increases, the experimental force-deformation (f-d) curves of MBs covered with polymer have an initial linear response (Reissner regime), followed by a non-linear curved downwards response (Pogorelov regime) where buckling takes place. On the other hand, the f-d curve for MBs covered with lipid monolayers initially follows the Reissner regime, but buckling is bypassed to a curved upwards regime where internal gas pressure dominates. The elastic properties, namely Young's modulus and shell thickness, for MB's covered with polymer can be estimated by combining the buckling point and the slope of the Reissner regime or the slopes of Reissner and Pogorelov regimes. Comparison of the present model with afm f-d curves for polymer shows satisfactory agreement. The area dilatation and bending moduli are shown to be the appropriate independent elastic parameters of MBs covered with phospholipid monolayers and are estimated by combination of the transition from Reissner to pressure dominated regime. Simulations and experiments in this case are in excellent agreement.