Effects of adsorbed films on gas bubble radial oscillations

Abstract

Adsorption films’ mechanical properties are discussed. With regard to a problem of bubble oscillations in a surfactant solution, dynamical boundary conditions at the bubble wall are modified by including a new term to account for a normal force component caused by dilational elasticity of an adsorbed film. Consequently, the Rayleigh–Plesset equation acquires a term which affects the restoring force of bubble oscillations. A linearized theory (for small-magnitude oscillations) is developed which shows that the film dilational elasticity induces a change in the mean radius and a shift in the natural frequency of bubble oscillations. These effects become extremely important when a capillary component 2σ/R0 accounts for at least 20% of the total pressure inside the bubble.

The influence of surface adsorption on microbubble dynamics

“…Equation (3.8) can be compared with those derived by Glazman (1983) and Marmottant et al (2005) which, although derived by different means, can be shown to represent special cases of equation (3.8) for particular values of x and Z. It should be noted that damping due to thermal conduction and acoustic radiation has been neglected in this derivation as the discussion is focused on the effect of the coating; and it has been shown by Stride (2005) that both these types of damping are negligible compared with viscous effects for bubbles smaller than 50 mm radii and excitation pressures for which the coating would be expected to remain intact.…”

Fundamentals of Cavitation

“…The term (2χ/R)(R 0 /R) 2 accounts for the dilational elasticity of the shell (Glazman 1983), and 12l sh e _ R R RÀe ð Þ is due to the shell's viscous damping, where ε and μ sh are the thickness and the viscosity coefficient of the shell, respectively. Because this model can only be applied to small-amplitude oscillations, it is always assumed that the velocity in the shell is not very high.…”

Theoretical characterisation of the radial and translational motion of coated microbubbles under acoustic excitation

“…Glazman [9] and Morgan et al [10] built on previous studies of oceanic bubbles, to develop models that consider the vibrations of surfactant coated microbubbles, which treated the shell as an absorbed surface layer instead of a discrete shell. Although these treatments are essentially the same as [6], they use different functional relationships to describe the effective elasticity and viscosity of the shell.…”

“…Although these treatments are essentially the same as [6], they use different functional relationships to describe the effective elasticity and viscosity of the shell. However there was an error in Glazman's derivation in [9]which was propagated by Morgan but later corrected by Marmottant et al [11] who produced a model that described the effect of the shell through an area dependent interfacial tension with a constant surface viscosity.…”