Nematic tactoid population

Tactoids are pointed, spindlelike droplets of nematic liquid crystal in an isotropic fluid. They have long been observed inorganic and organic nematics, thermotropic phases as well lyotropic colloidal aggregates. The variational problem determining the optimal shape a droplet is formidable has only attacked selected classes shapes director fields. Here, by considering special class admissible solutions for bipolar droplet, we study prevalence population all equilibrium each three that may be (tactoids primarily among them). We show how affected dimensionless measure $\ensuremath{\alpha}$ drop's volume ratios ${k}_{24}$ ${k}_{3}$ saddle-splay constant ${K}_{24}$ bending ${K}_{33}$ material to splay ${K}_{11}$. Tactoids, particular, prevail $\ensuremath{\alpha}?16.2+0.3{k}_{3}\ensuremath{-}(14.9\ensuremath{-}0.1{k}_{3}){k}_{24}$. Our (and fields) sufficiently different from those employed so far unveil rather role ${K}_{24}$.