Toroidal Droplets Research Articles

Generation and Stability of Toroidal Droplets in a Viscous Liquid

We use a simple method to generate toroidal droplets and study how they transform into spherical droplets. The method relies on the viscous forces exerted by a rotating continuous phase over a liquid which is extruded from an injection needle; the resultant jet is forced to close into a torus due to the imposed rotation. Once formed, the torus transforms into single or multiple spheres. Interestingly, we find there are two routes for this process depending on the aspect ratio of the torus. For thin tori, classical hydrodynamic instabilities induce its breakup into a precise number of droplets. By contrast, for sufficiently fat tori, unstable modes are unable to grow, and the torus evolves through a different route; it shrinks towards its center to coalesce onto itself, to finally form a single spherical droplet.

Watching molecules reorient in liquid crystal droplets with multiphoton-excited fluorescence microscopy

A new form of time-resolved multiphoton-excited fluorescence imaging is described and used to study electric-field-induced reorientation dynamics in polymer-dispersed liquid crystal (LC) films. This method provides information on the static and dynamic LC orientation via polarization-dependent three-photon excitation of the nematic ultraviolet chromophores in these materials. Static fluorescence images are obtained with ≈235 nm resolution in all three dimensions. In dynamics studies, the three-photon-excited fluorescence is recorded as a function of time and position over individual LC droplets, as an applied electric field is switched on and off. Time-resolved images with ≈235 nm spatial resolution and 200 μs time resolution are obtained. Movies depicting the local reorientation dynamics are prepared from these data and are presented for common ellipsoidal LC droplets and for novel toroidal droplets. The field-induced reorientation dynamics within the ellipsoidal droplets are shown to be more complex (i.e., spatially variable) than in the toroidal droplets. Dynamical complexity is concluded to arise from LC organizational complexity in the droplets. The bipolar configuration found in ellipsoidal droplets incorporates bend and splay deformations of the nematic phase and two disclination points. In contrast, toroidal droplets incorporate a simpler toroidal configuration in which only bend deformations occur.

Polymer-Dispersed Liquid Crystal Films Studied by Near-Field Scanning Optical Microscopy

Topographic and near-field scanning optical microscopy images of nematic liquid crystalline (LC) droplets dispersed in polymer films are presented. It is conclusively shown that the topographic images provide information invaluable to a complete understanding of the droplet formation process, shape, and internal LC organization. The topographic data indicate that the droplets are encapsulated in a thin, relatively solid polymer shell. Many droplets in these films are observed to take on spheroidal and discoidal shapes. A new class of toroidal droplets, possibly formed by droplet rupture during film formation, is also observed and characterized. Polarization-dependent optical images are employed to determine the LC organization in these droplets.

A spectral boundary element approach to three-dimensional Stokes flow

A novel method is introduced for solving the three-dimensional Stokes equations via a spectral element approach to the boundary integral method. The accuracy and convergence of the method are illustrated through applications involving rigid particles, deformable droplets and interacting particles. New physical results are obtained for two applications in low Reynolds number flow: the permeability of periodic models of a porous membrane and the instability of a toroidal droplet subject to non-axisymmetric perturbations. Further applications are described in the companion paper (Higdon & Muldowney 1995).

Plate-to-nematoid transition of self-organized layers in liquid crystal systems

We observed self-organized plates growing in some mesogenic mixtures as the first stage of nucleation of the mesomorphic phase and transformation of the plates into multiphase bifilar filaments (called nematoids). The liquid crystal plates and subsequent nematoids are freely suspended inside the isotropic melt. The creation of the plates and their transition to nematoids were observed in mixtures of nematic, smectic B and non-mesogenic chiral dopant. The maximum size of the plates depends on the concentration of the mixtures and varies from 0.1 to more than 1nm. Study of the fringe deflection profiles in Pluta birefracting microinterferometry revealed that the nematoids have bifilar internal organization. Two modes of creation of the nematoids can be distinguished: (a) formation of initial toroidal droplets and then nematoids and (b) intermediate formation of nematoids by rolling of the plates. Four main types of temporal and thermal evolution of the nematoids can be specified: (a) immediate fast shrinkage to droplet, (b) segmentation, (c) splitting along the longitudinal axis, and (d) double-spiralling. In all cases, the final stage of evolution is a liquid crystalline droplet which can be a source of secondary nematoids growing at diminished temperature.