Lehmann rotation of cholesteric droplets: Role of the sample thickness and of the concentration of chiral molecules

We study the role of the sample thickness d and of the concentration C of chiral molecules during the Lehmann rotation of cholesteric droplets of radius R subjected to a temperature gradient PG. Two configurations are studied depending on how the helix is oriented with respect to PG. The first result is that, at fixed C and R, the rotation velocity ω increases with d when the helix is parallel to PG, whereas it is independent of d when the helix is perpendicular to PG. The second result is that, for a given C,ω₀=lim_R→0ω(R) is the same for the two types of droplets independently of d. This suggests that the, as yet unknown, physical mechanism responsible for the droplet rotation is the same in the two types of droplets. The third result is that the Lehmann coefficient ν defined from the Leslie-like relation ω₀=-νG/γ₁ (with γ₁ the rotational viscosity) is proportional to the equilibrium twist q. Last, but not least, the ratio R̄=ν/q depends on the liquid crystal chosen but is independent of the chiral molecule used to dope the liquid crystal.