(611d) Oscillation of Particles On An Interface Due to Surface Tension Gradients
In the 19th century, Lord Rayleigh studied the erratic motion of camphor scrapings on water in air [P. R. Soc. London 47 (1889) 364-367]. More recently, Nakata and Hayashima [J. Chem. Soc. Faraday Trans. 94 (1998) 3655-3658] identified two modes in the motion of isolated camphor scrapings. The motion of camphor scrapings occurs due to surface tension gradients around the particles. These gradients are maintained by the sublimation of camphor from the water surface into the air above. We describe a qualitatively similar system in which the particles exhibit a sustained oscillation in contrast to the erratic motion of camphor scrapings. In our system, the particles are calcium propionate powder, which is less dense than water and floats on the air-water interface while dissolving. We hypothesize that the synchronized motion is due to surface tension gradients along the interface and the interaction between nearby particles.
The oscillating system was characterized by measurements of the particle motion and the physical properties of calcium propionate solutions. High speed imaging (211 fps) was used to record the oscillation of the powder on the surface of solutions with varying initial calcium propionate concentrations. The three frames shown below illustrate the motion of the particles. The image sequences were analyzed using particle image velocimetry (PIV) to quantify the temporal and spatial structure of the oscillation; two sample velocity fields are provided below. A typical frequency of the oscillation in the velocity at a fixed point on the surface is 2 Hz. The surface tensions of calcium propionate solutions with varying concentations were determined with the pendant drop method. The surface tension decreases with increasing calcium propionate concentration.
We also compare the experimental results with a one-dimensional model to gain insight into the observed behaviour. The predicted dependence of the oscillation frequency on the initial solute concentration is compared with the experiments. The model predicts fast dissolution at low initial concentrations, oscillation at moderate concentrations, and no motion at high concentrations, three modes of behaviour that are also seen in the experiments.
Sample velocity fields after PIV analysis in a 1.7 cm wide by 2.4 cm high region of the powder-covered surface. Colours and arrow lengths represent velocity magnitude. Motion is towards the centre in the first field and away from the centre in the second (140 ms later).