Colloidal diffusion inside a spherical cell

The hydrodynamic hindering of a single-particle dynamics under total confinement is measured by optical microscopy. The three-dimensional trajectories of single-colloidal particles confined in spherical water globules of sizes only a few times the particle’s diameter are tracked as they sample the entire volume of the globule. The hydrodynamic interactions between the particle and the spherical wall produce a dependence of the short-time diffusion on the particle’s distance to the surface and an asymmetry in the radial and tangential components of the local diffusion coefficient, with the diffusion along the tangential direction being faster than along the radial direction. The latter decreasing close to the wall while the former being practically constant.

Figure 1

(a) Transmitted light optical microscope image of a water globule (dark circle) of diameter $2R=6.35\hspace{0.5em}\mu$m immersed in oil containing a single 1 $\mu$m fluorescence polystyrene sphere. (b) Out of focus image of the water droplet in (a) using fluorescence illumination. Here one can see the pattern of rings emerging when the particle is not in focus.

Figure 2

(a) Cartesian components of the 3D trajectory of the particle in Fig. 1. (b) The mean-squared displacement.

Figure 3

(a) Number $N(r)$ of times the particle is found in a shell of radius $r$ and thickness $\Delta r$. (b) The normalized density $P(r)$ of data points at a distance $r$ from the center of the cell.

Figure 4

The radial (circles) and perpendicular (squares) local components of the short-time diffusion coefficient.

Figure 5

Short-time diffusion-coefficient $D_S$ (symbols) vs the effective radius $R_{\text{eff}}$ of the water droplet.