Dynamics of a single bubble

Iskander Akhatov, Nail Gumerov, Elvira Nasibullayeva, Ekaterina Butyugina

Objective:

To study the dynamics of a single spherical bubble in an isotropic acoustic field

Dynamics of the bubble and gas concentration near the bubble wall

Without external sound field, bubbles of any size are unstable because the pressure inside the bubble is larger than in the liquid, and therefore the bubble will dissolve slowly due to a continuous mass flux from the interior of the bubble into the liquid. In the presence of a periodic acoustic field the bubble starts to oscillate. During the expansion period gas diffuses from the liquid into the bubble, and during the contraction cycle the diffusion process takes place in the opposite direction. This phenomenon is called rectified diffusion and leads to a growth of the bubble.

By solving the problem of the bubble dynamics numerically one can observe the change of the gas concentration in its wall (video on the right). Red line indicates the gas concentration near the bubble wall during several periods of the external sound field. It begins to decrease with the growth of the bubble due to mass flux from the liquid. While decreasing, the bubble gives back the gas to the liquid and the gas concentration at the bubble wall increases.

Finally, the results of numerical simulations show that the approximate theories of rectified diffusion describe well cases of small driving pressure amplitudes and relatively large bubbles. In the case of small initial radii and/or bubble oscillations driven by high amplitude driving pressures numerical solutions can deviate substantially from the asymptotic solutions and a full diffusion problem should be solved. For this purpose we have developed a method for computing the dynamics of a spherical bubble in an isotropic acoustic field.

Results:

We showed that the change in mass of the bubble due to diffusion can significantly affect the gas pressure in the bubble. Also, we detected the modes of bubble oscillations with small amplitude at which the mass flux taking into account leads to oscillations of the bubble with a "Giant Response" rapidly. When it happen, the rate of rectified diffusion increases dramatically.