Formation of a fast lane for positional transition in a microparticle-suspended nematic liquid crystal cell

In this paper, based on the numerical calculation of total energy utilizing the Greens function method, we found that the external electric field applied to a microparticle-suspended nematic liquid crystal cell, if reaching a critical value, combined with its direction, surface anchoring feature and molecular dielectric anisotropy, is possible to create an anisotropic bubble around the microparticle with a vertical fast lane, in which the microparticle can, driven by the asymmetric buoyant force, vertically move swiftly from the cells midplane to a new equilibrium position, triggering a positional transition discovered by the author previously. Such a new equilibrium position is decided via a competition between the buoyant force and the effective force built upon the microparticle by the elastic energy gradient along the lane. The threshold value of external field, depends on thickness $L$ and Frank elastic constant $K$ and slightly on the microparticle size and density, in a Fr{e}edericksz-like manner, but by a factor. For a nematic liquid crystal cell with planar surface alignment, a bistable equilibrium structure for the transition is found when the direction of the applied electric field is (a) perpendicular to the two plates of the cell with positive molecular dielectric anisotropy, or (b) parallel to the two plates and the anchoring direction of the cell with negative molecular dielectric anisotropy. Except for the formation of a vertical fast lane, when the electric field applied is parallel to both the two plates and perpendicular to the anchoring direction, the microparticle suspended in the nematic liquid crystal tends to be trapped in the midplane, regardless of the sign of the molecular dielectric anisotropy. Such phenomenon also occurs for negative molecular dielectric anisotropy while the external is applied perpendicular to the two plates.