Dynamics of a cylindrical bubble with account for the contact line motion along a heterogeneous surface

The free and forced oscillations of a cylindrical gas bubble clamped between two rigid parallel plates and surrounded by a finite volume of incompressible liquid with a free surface in a homogeneous pulsating pressure field are considered. A model is proposed for describing the substrate surface heterogeneity through the wetting parameter (the Hocking parameter), which is defined as the proportionality coefficient between the contact line velocity and the contact angle deviation. Since only small-amplitude oscillations are considered, the surface heterogeneity is significant only in the vicinity of the contact line. Therefore, it is treated as a function of a single variable. Azimuthal oscillations arise due to the contact line motion along the heterogeneous surface. It is shown that the frequency of the radial oscillations of the bubble is governed by the gas pressure and the radius of the liquid’s outer surface. The specific type of surface inhomogeneity modifies the Hocking parameter by reducing its value, although the qualitative dependence of the frequencies and damping decrements on this parameter remains unchanged. The frequency of the volume oscillations depends on the gas pressure inside the bubble, which may coincide with the frequency of the bubble’s shape oscillations. At the intersection points, damping decrements exhibit local extrema. It is shown that external excitation induces only axisym-metric oscillations; however, surface inhomogeneity also gives rise to azimuthal modes, whose spectrum is determined by the nature of the inhomogeneity.

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