Densely-packed particle raft at vertically vibrated air-water interface

Abstract

We investigate the dynamics of a dense raft of millimeter-sized granular particles at a vertically vibrated air-water interface, which displays a rich set of patterns and particle dynamics as we vary the vibration amplitude, frequency, and particle packing fraction. While the classical parametric instability with standing waves still occurs over a certain parameter space, the measured wave dispersion relations indicate an increasing role in the raft's emerging elasticity at higher packing fractions, which induces a decrease in the effective surface tension and an increase in an out-of-plane bending modulus. At higher vibration frequencies and lower amplitudes, we also identified a regime without standing waves in which individual particles exhibit thermal-like motion and transition from diffusive to sub-diffusive transport as the packing fraction increases. Glassy behaviors such as spatial and temporal heterogeneity in particle dynamics occur as well, which is analogous to supercooled liquids. When the vibration amplitude is increased starting in this supercooled regime, a large cavity eventually forms inside the raft with its size and shape related to the vibration frequency and the injected vibration energy. The cavitation results in the coexistence of free surface water waves inside the cavity and thermal-like particle motion in the raft.

Figures (11)

• Figure 1: Schematic of the experiment with a vibrated particle raft and an example snapshot with tracked particle centers labeled as red dots.
• Figure 2: Phase diagram at packing packing fractions (a) $\phi=0.77$ and (b) $\phi=0.90$. The circles represent the data for particles with $d=1.4$ mm, and the triangles for $d$=2.1 mm. (c)-(h) Experimental snapshots for the respective regimes. Specifically, (e)(f)(h) are from $\phi=0.77$ and (c)(d)(g) are from $\phi=0.90$.
• Figure 3: Time series of vibrated raft of $d=1.4$ mm particles in standing-wave regime, $A=0.086$ mm, $f=35$ Hz, demonstrating that wave frequency is half of the vibration frequency.
• Figure 4: (a) A time-averaged experimental image in the regular wave regime for $d=1.4$ mm, $f=20$ Hz, $A=0.124$ mm, and $\phi=0.8113$. (b) The corresponding two-dimensional Fourier transform result, indicating a wavelength of $\lambda=1.72$ cm.
• Figure 5: Regular standing wave patterns for $d=1.4$ mm. (a) Experimental result of angular frequency vs. wave number (circles) for $\phi = 0.77$. The dashed curve represents the fitted Eq. \ref{['eq:dispersion_classic']}, with $R^2 = 0.97$, and the solid curve is fit to Eq. \ref{['eq:dispersion_modified']}, with $R^2 = 0.98$. (b) Experimental result (circle) for $\phi = 0.90$, Eq. \ref{['eq:dispersion_classic']} (dashed curve) with $R^2 = 0.95$, and Eq. \ref{['eq:dispersion_modified']}, with $R^2 = 0.99$. (c) and (d) are the fitted stretch modulus $\gamma_e$ and bending modulus $B$ fitted at various packing fractions $\phi$, receptively. Red circles are results from linear fitting and blue squares are from non-linear fitting to Eq. \ref{['eq:dispersion_modified']}. Error bars represent one standard deviation of the uncertainty estimated from fitting residuals.