Abstract
In this paper, a Freedericksz-like positional transition is found for a spherical micro-droplet suspended in a nematic liquid crystal cell in the presence of an external electric field. Based on the numerical calculation of elastic energy using Green function method, the equilibrium position of micro-droplet is decided through a competition between the buoyant force and the effective force built by the elastic energy gradient existing inside the nematic liquid crystal(NLC) cell. It is shown that the elastic energy dominates the kinetics of micro-droplet until the external field applied reaches a critical value large enough to flatten the elastic energy contour in the central region, which enables the asymmetric buoyant force to drive the liquid droplet abruptly from the cell midplane to a new equilibrium position. It is also found that such a threshold value of external field, which triggers positional transition, depends on thickness $L$ and Frank elastic constant $K$, in a Freedericksz-like manner, but multiplied by a factor of $3\sqrt{\pi}$. An explicit formula proposed for the critical electric field agrees extremely well with the numerical calculation.
Highlights
Behaviors of immiscible liquid, solid, or gas microphase suspensions in a nematic liquid crystal (NLC) cell are of considerable interest due to their promising practical applications in new display devices and materials [1,2,3], triggered and released microcargo [4], and biological detectors [5,6]
The interaction force of spherical particles suspended in NLC is associated with interparticle distance and geological confinement [8], and with the shape of particles, which sometimes plays a crucial role in pair interaction and aggregation behaviors [12]
PHYSICAL REVIEW RESEARCH 1, 033041 (2019) (b) where r is the radius of microdroplet, p = 2.04r2 is the magnitudes of the dipole moment, ρLC − ρaq is the density difference between liquid crystal and microdroplet, g = 9.8 m/s2 is the gravitational acceleration, and z denotes the position of microdroplet
Summary
Solid, or gas microphase suspensions in a nematic liquid crystal (NLC) cell are of considerable interest due to their promising practical applications in new display devices and materials [1,2,3], triggered and released microcargo [4], and biological detectors [5,6]. In most cases the inclusion of particles in a NLC cell tends to create liquid crystal (LC) alignment singularities around the suspended substances, which in general are determined by surface anchoring conditions, particle size, boundary conditions, and external fields [12,23,24,25,26]. It has been widely confirmed and accepted that when a spherical particle is immersed in a NLC, there exist two possible. The interactions of two particles in a NLC are very well understood and the particle-wall interaction has been widely observed experimentally for a single particle immersed in a nematic cell [35,37,38], the properties of a single particle in a uniform NLC cell in the presence of an external electric field theoretically have not been fully addressed
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