We study experimentally and theoretically the hydrodynamic interaction of pairs of circular inclusions in two-dimensional, fluid smectic membranes suspended in air. By analyzing their Brownian motion, we find that the radial mutual mobilities of identical inclusions are independent of their size but that the angular coupling becomes strongly size dependent when their radius exceeds a characteristic hydrodynamic length. These observations are described well for arbitrary inclusion separations by a model that generalizes the Levine-MacKintosh theory of point-force response functions and uses a boundary-element approach to calculate the mobility matrix for inclusions of finite extent.

A study of the surface energetics of the thinnest substrate-free liquid films, fluid molecular monolayer and multilayer smectic liquid crystal films suspended in air, is reported. In films having monolayer and multilayer domains, the monolayer areas contract, contrary to predictions from the van der Waals disjoining pressure of thin uniform slabs. This discrepancy is accounted for by modeling the environmental asymmetry of the surface layers in multilayer films, leading to the possibility that preferential end-for-end polar ordering of the rod shaped molecules can reduce the surface energy of multilayers relative to that of the monolayer, which is inherently symmetric.

The Stokes paradox, that moving a disk at finite velocity through an infinite two-dimensional (2D) viscous fluid requires no force, leads, via the Einstein relation, to an infinite diffusion coefficient D for the disk. Saffman and Delbrück proposed that if the 2D fluid is a thin film immersed in a 3D viscous medium, then the film should behave as if it were of finite size, and D∼ -ln(aη'), where a is the inclusion radius and η' is the viscosity of the 3D medium. By studying the Brownian motion of islands in freely suspended smectic liquid crystal films a few molecular layers thick, we verify this dependence using no free parameters, and confirm the subsequent prediction by Hughes, Pailthorpe, and White of a crossover to 3D Stokes-like behavior when the diffusing island is sufficiently large.

We study experimentally and theoretically the hydrodynamic interaction of pairs of circular inclusions in two-dimensional, fluid smectic membranes suspended in air. By analyzing their Brownian motion, we find that the radial mutual mobilities of identical inclusions are independent of their size but that the angular coupling becomes strongly size dependent when their radius exceeds a characteristic hydrodynamic length. These observations are described well for arbitrary inclusion separations by a model that generalizes the Levine-MacKintosh theory of point-force response functions and uses a boundary-element approach to calculate the mobility matrix for inclusions of finite extent.

A study of the surface energetics of the thinnest substrate-free liquid films, fluid molecular monolayer and multilayer smectic liquid crystal films suspended in air, is reported. In films having monolayer and multilayer domains, the monolayer areas contract, contrary to predictions from the van der Waals disjoining pressure of thin uniform slabs. This discrepancy is accounted for by modeling the environmental asymmetry of the surface layers in multilayer films, leading to the possibility that preferential end-for-end polar ordering of the rod shaped molecules can reduce the surface energy of multilayers relative to that of the monolayer, which is inherently symmetric.

The Stokes paradox, that moving a disk at finite velocity through an infinite two-dimensional (2D) viscous fluid requires no force, leads, via the Einstein relation, to an infinite diffusion coefficient D for the disk. Saffman and Delbrück proposed that if the 2D fluid is a thin film immersed in a 3D viscous medium, then the film should behave as if it were of finite size, and D∼ -ln(aη'), where a is the inclusion radius and η' is the viscosity of the 3D medium. By studying the Brownian motion of islands in freely suspended smectic liquid crystal films a few molecular layers thick, we verify this dependence using no free parameters, and confirm the subsequent prediction by Hughes, Pailthorpe, and White of a crossover to 3D Stokes-like behavior when the diffusing island is sufficiently large.

Nematic circular drops of the liquid crystals 5CB and MBBA suspended in their isotropic phases exhibit an electric-field-induced deformation into an elliptical shape extended normal to the applied field which is many times larger than that found in nonliquid crystal systems, a result of the low nematic-isotropic interfacial tension. Isotropic drops suspended in a nematic phase also exhibit large deformation, but of opposite sign. In both cases the deformation is proportional to the applied field squared and decreases in amplitude with increasing frequency, a result of the conductivity relaxation of the liquid crystal.