Two spheres translating in tandem through a colloidal suspension

Using laser tweezers, two colloidal particles are held parallel to a uniformly flowing suspension of similarly sized bath particles at an effective volume fraction ${\varphi }_{\mathrm{eff}}=0.41$. The local deformation in the bath suspension is imaged by confocal microscopy, and, concurrently, the drag forces exerted on both the leading and the trailing probe particles are measured as a function of probe separation and velocity. The bath structure changes in response to the velocity and separation of the probes. A depleted region between probes is observed at sufficiently high velocities. Both probes experience the same drag force and the drag force increases with probe separation. The results indicate that bath-probe and probe-probe hydrodynamic interactions contribute microstructure and drag force and that drag exerted by direct bath-probe collisions is reduced compared to an isolated probe.

Figure 1

Schematic of the experimental configuration. Both probes are held using a time shared optical trap. $U$ indicates the velocity of the flow, and $a_p$ and $a_b$ correspond to the radii of the probe and the bath particle, respectively. The center-to-center distance between the probes is $r$.

Figure 2

Two-dimensional histograms of the bath particle suspension density. Columns indicate the probe separations in terms of the bath particle hydrodynamic radius and the rows represent the Péclet number, as defined in Eq. (1). Dark colors are indicative of regions depleted of bath particles; conversely, bright regions have a greater than average bath particle density. The bright circle at the center of each depleted region indicates the position of the probe particle.

Figure 3

Averaged confocal images of structure taken at ${\mathrm{Pe}}_D=2255$. Probe separations of (a) $6.8a_b$, (b) $7.5a_b$, (c) $9.0a_b$, (d) $9.5a_b$, (e) $28a_b$, and (f) $54a_b$ are shown.

Figure 4

The bath particle density at contact, $g(r,\theta )$, surrounding the probe particles, at probe particle separations of $6.8a_b,9.5a_b$, and $54a_b$. The upper and lower curves correspond to the trailing probe and the leading probe, respectively.

Figure 5

Drag forces on probes in the $z$ direction. Solid and open symbols correspond to the leading and trailing particles, respectively. As indicated in the legend, circles, squares, triangles, diamonds, inverted triangles, and flattened diamonds correspond to center-to-center distances of $6.8a_b,7.4a_b,9.1a_b,9.5a_b,28a_b$, and $54a_b$, respectively. The open black triangles without error bars correspond to the drag force for a single probe in a suspension of volume fraction ${\varphi }_{\mathrm{eff}}=0.37$.

Figure 6

Normalized drag forces for the leading probe. As indicated in the legend, circles, squares, triangles, diamonds, inverted triangles, and flattened diamonds correspond to center-to-center distances of $6.8a_b,7.4a_b,9.1a_b,9.5a_b,28a_b$, and $54a_b$, respectively.