Numerical Study on the Surface Stability of an Encapsulated Microbubble in the Ultrasound Field

The surface stability problem of an encapsulated microbubble in an ultrasound field is numerically addressed. To predict the nonlinear process, the continuity equation and Navier-Stokes equation are directly solved by means of a boundary-fitted finitevolume method on an orthogonal curvilinear coordinate system. The bubble is insonified by an ultrasound pulse consisting of a burst of 10 cycles, of which the first and last two periods are modified by a Gaussian envelope. The simulation code reproduces a shape oscillation of a gas bubble with an initial radius of 30μm at a pressure frequency of 130kHz as shown in experimental and theoretical studies [1]. The effects of the membrane on the shape oscillation are investigated through simulations of a micrometersized bubble encapsulated with a neo-Hookean membrane at an ultrasonic frequency of 1MHz. The encapsulated bubble presents a second-order shape instability, while the gas bubble of the same size keeps spherical because the surface tension significantly suppresses the shape oscillation. The strain-softening features with increasing the oscillation amplitude are characterized by a larger expansion and the higher harmonics when the bubble ∗Address all correspondence to this author. contracts. NOMENCLATURE a amplitude of shape mode e rate of strain Eb bending modulus f frequency of driving acoustic pressure F membrane force g acceleration of gravity Gs surface shear elastic modulus h metric coefficients K bending strain m bending moment p pressure q transverse shear tension r radius of bubble s azimuthal direction t time Tf period of driving acoustic pressure u velocity