Near-Field Probe of Thermal Fluctuations of a Hemispherical Bubble Surface

We report measurements of resonant thermal capillary oscillations of a hemispherical liquid gas interface obtained using a half bubble deposited on a solid substrate. The thermal motion of the hemispherical interface is investigated using an atomic force microscope cantilever that probes the amplitude of vibrations of this interface versus frequency. The spectrum of such nanoscale thermal oscillations of the bubble surface presents several resonance peaks and reveals that the contact line of the hemispherical bubble is pinned on the substrate. The analysis of these peaks allows us to measure the surface viscosity of the bubble interface. Minute amounts of impurities are responsible for altering the rheology of the pure water surface.

Figure 1

(a) Experimental setup. The bubble was deposited on a polystyrene (PS) surface, and the cantilever tip was used to probe the vibration of the bubble. (b) Top view and (c) side view images, from which we obtain the bubble radius $R=592\pm 5\mu \mathrm{m}$ and the contact angle of $94\pm 2°$.

Figure 2

Example of the measured PSD curves using a cantilever with stiffness $k_c=0.12\mathrm{N}/\mathrm{m}$. (a) The thermal spectra of the cantilever without the bubble (blue circles) and in contact with the bubble (red circles) deposited on PS surface. (b) The spectrum (circles) and the fitting curve using Eq. (3) (solid line) for the third peak in (a).

Figure 3

(a) The results of the normalized resonance frequencies ${\omega }_n/{\omega }_0$ of the bubble versus the mode numbers. The black solid line connects the resonance frequency for pinned contact lines, and the red solid line for a freely moving contact line, as given in the main text. (b) The results of the effective mass normalized by the cubic power of the radius of the bubble versus the mode number for different bubbles. The dots with different colors and shapes represent the different measurements for different bubbles. The black line represents the theoretical results which was given by Eq. (5).

Figure 4

Damping versus the frequency for different bubbles. The green dashed line corresponds to the viscous damping ${\beta }_n^{\mathrm{vis}}$ as in Eq. (6). The red dotted lines correspond to viscous damping plus boundary damping (${\beta }_n^{\mathrm{vis}}+{\beta }_n^b$), with ${\beta }_n^b$ for $R=644$ and $423\mu \mathrm{m}$. The black solid line is calculated from Eq. (10) and accounts for all terms in Eq. (10), including ${\beta }_n^s$ with the surface viscosity is ${\eta }_s=(1.5\pm 0.2)\times {10}^{-7}\mathrm{Pa}\mathrm{s}\mathrm{m}$.