Total scattering cross section vs scaled forcing frequency, when , 1, 1.5, and 2, for (a) a free bubble, (b) a KV, (c) a MR , and (d) a SK membrane; and for a free bubble and an encapsulated microbubble, respectively.
Time evolution of the (a) external microbubble radius, (b) interfacial velocity, and (c) pressure load , for a MR membrane on resonance when and 2 ( and , respectively); .
Time evolution of the (a) external microbubble radius, (b) interfacial velocity, and (c) pressure load , for a SK membrane on resonance when and 2 ( for both cases); .
Area dilatation vs sound amplitude for (a) a MR membrane with different values, , 0.5, and 1 (the behavior of a KV membrane is also shown for reference) and (b) a SK membrane with different values, , 2, and 3; .
Fundamental and second harmonic components of the scattering cross section vs forcing frequency for a SK membrane with and nonzero residual stresses at , , 0 and 0.01; .
Comparison between experimental measurements (Sarkar et al., 2005) and predictions based on the Church–Hoff, the constant elasticity, the Newtonian, and the strain softening model, of the fundamental and subharmonic signals when (a), (b) and (c), (d) , for Sonazoid microbubbles.
Dimensional resonance frequency of the first harmonic component as a function of area dilatation modulus and acoustic amplitude, recovered from numerical simulations.
Harmonic content of the scattering cross section for (a) a KV, (b) a MR , and (c) a SK membrane, when and 2. To obtain the actual dimensions one has to multiply the harmonic content by , where in these simulations.
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