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Nonlinear radial oscillations of encapsulated microbubbles subject to ultrasound: The effect of membrane constitutive law
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10.1121/1.2909553
/content/asa/journal/jasa/123/6/10.1121/1.2909553
http://aip.metastore.ingenta.com/content/asa/journal/jasa/123/6/10.1121/1.2909553

Figures

Image of FIG. 1.
FIG. 1.

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.

Image of FIG. 2.
FIG. 2.

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); .

Image of FIG. 3.
FIG. 3.

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); .

Image of FIG. 4.
FIG. 4.

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; .

Image of FIG. 5.
FIG. 5.

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; .

Image of FIG. 6.
FIG. 6.

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.

Tables

Generic image for table
TABLE I.

Dimensional resonance frequency of the first harmonic component as a function of area dilatation modulus and acoustic amplitude, recovered from numerical simulations.

Generic image for table
TABLE II.

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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/content/asa/journal/jasa/123/6/10.1121/1.2909553
2008-06-01
2014-04-18
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Nonlinear radial oscillations of encapsulated microbubbles subject to ultrasound: The effect of membrane constitutive law
http://aip.metastore.ingenta.com/content/asa/journal/jasa/123/6/10.1121/1.2909553
10.1121/1.2909553
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