Microrheology in Restricted Geometry
Flow phenomena in restricted geometries have been intensively studied in the last years with implications to different physical, chemical and biological systems. One of the traditional areas of these studies is the motion of proteins in lipid membranes that date back to the middle of seventies. Most rheological investigations of membranes have been made by observing Brownian motion in flat lipid membranes and spherical vesicles as well as in liquid crystal films, with the mobility of the inclusions calculated from the diffusion coefficient by means of the Einstein relation. Such approach requires a model describing the relation between the mobility and the parameters of the system such as the inclusion size, the viscosity of the material, and others
Flow in two dimensions represents an exceptional case in hydrodynamics, including the well-known singularity of the diffusion coefficient (the Stokes paradox). It has been shown theoretically that various hydrodynamic regimes may occur in 2D.
However, direct experimental studies of those regimes are still lacking for the difficulty of experimental realization of a 2D fluid whose parameters could be varied in a wide range. In our experiments we demonstrate a variety of 2D hydrodynamical regimes and test the existing models using a direct ”falling ball” rheology technique in fluid smectic films which are particularly well suited for measuring mobilities in 2D because they form homogeneous freely suspended films that are quantized in thickness (consisting of an integer number of smectic layers, which can be selected), and are stable for many hours.
However, direct experimental studies of those regimes are still lacking for the difficulty of experimental realization of a 2D fluid whose parameters could be varied in a wide range. In our experiments we demonstrate a variety of 2D hydrodynamical regimes and test the existing models using a direct ”falling ball” rheology technique in fluid smectic films which are particularly well suited for measuring mobilities in 2D because they form homogeneous freely suspended films that are quantized in thickness (consisting of an integer number of smectic layers, which can be selected), and are stable for many hours.
Video of a water/glycerin droplet traveling across the freely suspended films. Typical size of the droplet is between 10 - 50 microns and the velocity is in order of hundreds of microns per second.
Video of a silica bead traveling across a smectic-A bubble.
We also study coupling between the advective flow and the director field (given by the average tilt direction of the molecules) in freely suspended films of the smectic-C phase. We have shown that the relaxation of the director deformation is accompanied by the advective flow. This effect is particularly well seen in relaxation of so-called target patterns created by a rotating electric field.