Model for the dynamics of a spherical bubble undergoing small shape oscillations between parallel soft elastic layers.
A model is developed for a pulsating and translating gas bubble immersed in liquid in a channel formed by two soft, thin elastic parallel layers having densities equal to that of the surrounding liquid and small, but finite, shear moduli. The bubble is nominally spherical but free to undergo small shape deformations. Shear strain in the elastic layers is estimated in a way which is valid for short, transient excitations of the system. Coupled nonlinear second-order differential equations are obtained for the shape and position of the bubble, and numerical integration of an expression for the liquid velocity at the layer interfaces yields an estimate of the elastic layer displacement. Numerical integration of the dynamical equations reveals behavior consistent with laboratory observations of acoustically excited bubbles in ex vivo vessels reported by Chen et al. [Phys. Rev. Lett. 106, 034301 (2011) and Ultrasound Med. Biol. 37, 2139-2148 (2011)].
Applied Research Laboratories, The University of Texas at Austin, Austin, Texas 78713-8029, USA. m.d.verweij@tudelft.nl
Todd A
TA
Hay
Yurii A
YA
Ilinskii
Evgenia A
EA
Zabolotskaya
Mark F
MF
Hamilton
D003198:Computer Simulation; D003287:Contrast Media / Q000737:chemistry*; D004548:Elasticity; D005740:Gases; D045423:Microbubbles; D009038:Motion; D017711:Nonlinear Dynamics; D009716:Numerical Analysis, Computer-Assisted; D009991:Oscillometry; D011312:Pressure; D013016:Sound; D013314:Stress, Mechanical; D013499:Surface Properties; D013997:Time Factors; D014465:Ultrasonics / Q000379:methods*
D003287:Contrast Media; D005740:Gases