Figure 1

Experimental setup. (a),(b) A silica bead embedded in a smectic film drifts down the film under the influence of gravity $g$. The film is inclined from the horizontal by an angle $\delta$ and the bead is observed using a reflected light microscope. Smectic islands were studied in similar fashion. When the Saffman length ${\ell }_S$ is comparable to or exceeds the film width, the hydrodynamics are dominated by confinement effects. (c) Snapshots of a bead ($a\sim 15\mu \mathrm{m}$) shortly before contacting the LC film (top) and once immersed in the film (bottom), obtained using a telescope slightly inclined to the film plane.Reuse & Permissions

Figure 2

(a) Composite stroboscopic image of a bead of radius $44\mu \mathrm{m}$ moving with terminal velocity $2300\mu \mathrm{m}/\mathrm{s}$ down a rectangular 8CB film 2.5 mm wide, 400 nm thick, and tilted by 13°. The streamlines, which are visualized using tracer particles, are indicated as red loops, with the flow field on either side of the bead sketched with green arrows. The blurred shadow at top is from the glass fiber used to deposit the bead. (b) Film flow velocity profile $v_z(x)$ measured from the center of the bead to the edge of the film, normalized by the bead velocity. The theoretical curve is obtained from a finite-element solution of the Navier-Stokes equations.Reuse & Permissions

Figure 3

Scaled mobility of beads as a function of reduced radius in films with thicknesses ranging from 100 nm to $22\mu \mathrm{m}$ and of width $W=4.0\mathrm{mm}$, inclined by $\delta =14°$. When the Saffman length ${\ell }_S<W$ (right), the mobility is determined by air-film coupling and is reproduced by Eq. (1) (red curve). When ${\ell }_S>W$ (left), the response of the fluid is dominated by confinement effects. The inset shows the difference between the measured bead mobilities and SD/HPW theory as a function of $W/2{\ell }_S$. The blue and red lines show theoretical predictions in the confinement and SD regimes, respectively. The bead mobilities merge smoothly with the beginning of the island data (open symbols).Reuse & Permissions

Figure 4

Scaled mobility of embedded beads vs the ratio of film width to bead radius for rectangular films of thickness $875\pm 10\mathrm{nm}$ tilted by 14°. The film width $W$ was varied from 4 mm to about 1.9 mm. The red curve is a fit using Eq. (3).Reuse & Permissions

Figure 5

Mobility of smectic islands in freely-suspended 8CB films. (a) Top view of an island in a thin film. The Saffman region is greatly exaggerated in this illustration, ${\ell }_S$ being much smaller than the film radius in these experiments. (b) Side view of a five-layer island of radius $a$ in an $N=2$ film. The viscosities of the film and the surrounding fluid (air) are $\eta$ and ${\eta }^{\prime }$, respectively. (c) Scaled mobility $b^{\prime }$ as a function of reduced radius $\epsilon$ of a 22-layer island in an $N=4$ film (●) and of a 13-layer island in an $N=5$ film (◇). The mobilities of these islands are around the crossover between the hydrodynamic regime dominated by dissipation in the film due to SD air-film coupling and that dominated by Stokes-like dissipation in the air at even larger $\epsilon \gg 1$. The mobilities are in qualitative agreement with SD/HPW theory as approximated by Petrov and Schwille [15] (red curve). The number of smectic layers was determined using optical reflectivity and we assumed a smectic layer spacing of $d=3.17\mathrm{nm}$ [16]. The inset shows the scaled mobility of the 22-layer island as a function of island radius $a$, together with the SD/HPW theory (solid curve) and the Stokes-like prediction for $\epsilon \gg 1$ (dashed curve). Scatter in the experimental data is due to backlash of the film stage goniometer.Reuse & Permissions