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In this paper, based on the numerical calculation of total energy utilizingthe Green's function method, we found that the external electric field appliedto a microparticle-suspended nematic liquid crystal cell, if reaching acritical value, combined with its direction, surface anchoring feature andmolecular dielectric anisotropy, is possible to create an anisotropic "bubble"around the microparticle with a vertical fast "lane", in which themicroparticle can, driven by the asymmetric buoyant force, vertically moveswiftly from the cell's midplane to a new equilibrium position, triggering apositional transition discovered by the author previously. Such a newequilibrium position is decided via a competition between the buoyant force andthe effective force built upon the microparticle by the elastic energy gradientalong the "lane". The threshold value of external field, depends on thickness$L$ and Frank elastic constant $K$ and slightly on the microparticle size anddensity, in a Fr\'{e}edericksz-like manner, but by a factor. For a nematicliquid crystal cell with planar surface alignment, a bistable equilibriumstructure for the transition is found when the direction of the appliedelectric field is (a) perpendicular to the two plates of the cell with positivemolecular dielectric anisotropy, or (b) parallel to the two plates and theanchoring direction of the cell with negative molecular dielectric anisotropy.Except for the formation of a vertical fast "lane", when the electric fieldapplied is parallel to both the two plates and perpendicular to the anchoringdirection, the microparticle suspended in the nematic liquid crystal tends tobe trapped in the midplane, regardless of the sign of the molecular dielectricanisotropy. Such phenomenon also occurs for negative molecular dielectricanisotropy while the external is applied perpendicular to the two plates.

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