Dependence on sample geometry

Figure 9: Labyrinth in the $H = 1~\unit{mm}$ cell (high particle density, wide cell). 1.5  $\unit{\mu m}$ diameter silica spheres. White areas have higher particle density. (a) 4.0 V. (b) 8.0 V. (c) 12.0 V. (d) 20.0 V.

Figure 10: Labyrinth in the $H = 1~\unit{mm}$ cell (low particle density, narrow cell). 1.5  $\unit{\mu m}$ diameter silica spheres. Dark areas have higher particle density. (a) 8.0 V. (b) 16.0 V.

Figures 9 and 10 show that bulk labyrinthine patterns are not strongly affected by the boundaries of the observation channel, but rather extend right up to the walls. Nor are labyrinths oriented in any obvious way by the boundaries. The images in Figs. 9 and 10 were obtained in two cells 1 mm deep, the first with in-plane dimensions $4~\unit{cm} \times 0.9~\unit{cm}$ and the second $4~\unit{cm} \times 0.3~\unit{cm}$ . Despite this difference, both cells produced similar patterns, with any differences being ascribable to differences in particles density. This further illustrates that the transverse boundary condition has little influence on bulk pattern formation in the electroconvective regime. Figures 9 and 10 also highlight the wide range of parameters under which labyrinths form, including cells at least as deep as $H = 1~\unit{mm}$ and at biases as high as 20 V.