On Rayleigh's model of a freely oscillating bubble. I. Basic relations

Theoretical analysis of hydrostatic implodable volumes with solid inner structures

“…(10) is readily solvable using the Runge-Kutta-Nystrom method with a time step on the order of 10 À7 s. Vokurka (1985) showed that the pressure in the liquid surrounding the implodable volume is given by…”

A Simulation for Detecting Nonlinear Echoes from Microbubbles Packets

“…In the equations it is assumed that the receiver is sufficiently far from the microbubble to neglect the Bernoulli pressure (also referred to as the kinetic wave), which decreases with 1/r 4 (Vokurka, 1985;Leighton, 1994). Furthermore, Eq.…”

Monodisperse bubbles and droplets for medical applications

“…4.1 results in the instantaneous bubble radius, R(t). The scattered acoustic pressure wave at the bubble wall in an incompressible medium is given by 36 :…”

“…The bubble is driven into oscillation by the successive wave of high and low pressure. The radial response of the bubble and the subsequent movement of the liquid surrounding the bubble leads to a sound emission which is propagating spherically in all directions 36 . The transducer will pick up the echo emitted within the receiving cone angle of the transducer.…”

“…The nonlinear features of the bubble response, or echo, originate directly from the nonlinearities in the above equation. Once the radial dynamics is known, the pressure emitted by the bubble, p s (t) (in medical ultrasound literature termed the scattered pressure), can be calculated from the conservation of mass and momentum 36 :…”