Competition of intrinsic and topographically imposed patterns in Bénard–Marangoni convection

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Abstract
The structure of Bénard–Marangoni convection cells can be controlled by periodic topographic patterns on the heated surface that generates the convection. When the periodicity of the topographic pattern matches the intrinsic periodicity of the convection cells, a convective pattern is formed that is 1:1 commensurate with the topographic pattern. Arrays of hexagonal, square, and triangular convection cells were generated over the appropriately designed topographic patterns, and visualized by infrared imaging. For imposed patterns with periodicity in two dimensions, as the ratio of the intrinsic and perturbing length scales changes, the pattern of the convection cells shows sharp transitions between different patterns commensurate with the imposed pattern. For imposed patterns with periodicity in one dimension (i.e., lines) the convection cells use the unconstrained dimension to adapt continuously to the external perturbation. Topographically controlled convection cells can be used to assemble microscopic particles into externally switchable regular lattices.