Measurement of the Translational and Rotational Brownian Motion of Individual Particles in a Rarefied Gas

We measured the free Brownian motion of individual spherical and the Brownian rotation of individual nonspherical micrometer-sized particles in rarefied gas. Measurements were done with high spatial and temporal resolution under microgravity conditions in the Bremen drop tower so that the transition from diffusive to ballistic motion could be resolved. We find that the translational and rotational diffusion can be described by the relation given by Uhlenbeck and Ornstein [Phys. Rev. 36, 823 (1930)]. Measurements of rotational Brownian motion can be used for the determination of the moments of inertia of small particles.

Figure 1

Scanning electron microscopy image of the SiC particles used for the measurements of Brownian rotation.

Figure 2

Trajectory of a single ${\mathrm{SiO}}_2$ sphere with $s\approx 0.8\mu \mathrm{m}$ radius [13]. The trajectory consists of 1024 measurements (black points) and spans a total of 2.2 s. The scale bar indicates $10\mu \mathrm{m}$.

Figure 3

(a) Histogram of the one-dimensional motion of the ${\mathrm{SiO}}_2$ particle in Fig. 2 for the time steps (from top to bottom) $\Delta t=1\times \Delta t_0$, $2\times \Delta t_0$, $4\times \Delta t_0$ with $\Delta t_0=2.16\mathrm{ms}$. (b) Histogram of the one-dimensional rotation of the SiC particle in Fig. 5 for the time steps (from top to bottom) $\Delta t=1\times \Delta t_0$, $2\times \Delta t_0$, $4\times \Delta t_0$ with $\Delta t_0=1.08\mathrm{ms}$. The solid curves in (a) and (b) are best-fitting Gaussians.

Figure 4

Mean square one-dimensional displacement of the particle in Fig. 2 as a function of the time interval between measurements (data points with error bars). The solid line is the best-fitting relation following Eq. (8) for the translational Brownian motion.

Figure 5

Snapshots of the orientation of a SiC whisker during a microgravity experiment [13]. The displayed frames show each 18th image and were recorded at time steps of 19.5 ms. The size of each image is $47\times 47\mu {\mathrm{m}}^2$.

Figure 6

Mean square angular displacement as a function of the time interval between measurements (data points with error bars). The solid line is the best-fitting relation after Eq. (9) for the rotational Brownian motion.