Miesovicz viscosity

This means that five independent nonzero viscosity coefficients exist. Three of them correspond to flow viscosities. They were first measured by Miesovicz and are called Miesovicz viscosities. The three different possibilities and the corresponding viscosity coefficients % and are illustrated in Figure 4.3. 

The Miesovicz viscosities can be related to the Leslie coefficients by comparing (4.12) to the geometries of Figure 4.3. 

Here ri r]c is the relevant Miesovicz viscosity, and v is the velocity of the sphere. The situation is quite different for semi-infinite and finite barriers, where permeation is necessarily involved in the flow, leading to undulation of layers and arrays of defects. Since it is very difficult to trap and stabilize a sphere vdth a size smaller than the film thickness, as far as we know, the flow of smectics aroimd a sphere has never been studied experimentally. However, experiments when finite particles are moving in the liquid crystal medium, which is at rest far from the particles has been carried out very recently, and it was indeed found that the flow of beads in smectic A and smectic C liquid crystals is purely viscous at sufficiently high speeds. Such technique is analogous to the one-bead micro-rheology ° developed recently to monitor the mechanical properties of viscoelastic soft materials, especially biological systems. i... 

It is instructive to consider the three simple geometries for plane parallel shear flow, the Miesovicz geometries [73], corresponding to the orientations of the director relative to the flow axis and the shear gradient. Choosing v = u(z)x one has the effective shear viscosities ... 

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