Layer Reduction in Driven 2D-Colloidal Systems through Microchannels

The transport behavior of a system of gravitationally driven superparamagnetic colloidal particles is investigated. The motion of the particles through a narrow channel is governed by magnetic dipole interactions, and a layered structure forms parallel to the walls. The arrangement of the particles is perturbed by diffusion and the motion induced by gravity leading to a density gradient along the channel. Our main result is the reduction of the number of layers. Experiments and Brownian dynamics simulations show that this occurs due to the density gradient along the channel.

Figure 1

(a) SEM pictures of the channel: Shown are an overview of the channel and a zoom to the region of the channel entrance. Some dried particles inside and outside of the channel can be seen as well. (b) Simulation results of the linear fits to the local density (neglecting the first and last 10% of the channel) in dependence of the inclination $\alpha$.

Figure 2

(a) Video microscopy snapshot of colloidal particles moving along the lithographically defined channel ($692\times 60\mu \mathrm{m}$, $\Gamma \approx 72$). (b) Simulation snapshots for a channel with ideal hard walls ($573.3\times 45\mu \mathrm{m}$, $\Gamma =640.5$); (c) the same as in (b) with the particles at the walls kept fixed ($573.3\times 45\mu \mathrm{m}$, $\Gamma =5026$). The rectangles mark the region of the layer reduction.

Figure 3

Local lattice constants $d_x$ and $d_y$ and local particle density (a) in the experiment and (b) in the BD simulation. The results are obtained for the systems in Figs. 2a, 2b, respectively. (c) Potential energies per particle of different layer configurations as a function of the particle density. The dots mark the perfect triangular lattices for 5, 6, and 7 layers. Also shown are parts of the configurations with 7 and 6 layers at the intersection point. (d) Plots of the layer order parameter for the configuration snapshot in Fig. 2b. Multiple points of layer reductions can be identified. For smaller overall densities, we found reductions down to just two layers in simulations.

Figure 4

Snapshots of defect configurations obtained from a Delaunay triangulation of the particles moving in the channel. The particles are coded according to the number of nearest neighbors they have. Open circles mark the bulk particles with 6 nearest neighbors and the edge particles; × corresponds to fivefold symmetry and ▿ to sevenfold symmetry. (a) Experiment: In order to minimize the effects of fluctuations on a short time scale, 50 images have been averaged. (b) BD simulation for a channel with parallel walls. (c) Equilibrium BD simulation for a channel with nonparallel walls ($\Delta L_y=1\sigma$ between both channel ends, $\Gamma =153.9$, and the channel has 10 times the length of the excerpt shown). In addition to the defect at the layer reduction, defects can be seen close to the walls, because the particle density of the layers at the wall is higher than for “bulk” particles [16, 17].