Miesowicz viscous coefficient

The above three viscous coefficients are defined as the Miesowicz viscous coefficients. 

In reality, it is difficult to measure the six Leslie coefficients. However, it may be easier to measure the Miesowicz viscous coefficients which are related to the order parameter and rj... 

The relations are shown in Figure 6.12 where the Miesowicz viscous coefficients are plotted as a function of the order parameter of long rods in solution. The Doi and Edwards theory gives the order parameter vs. the concentration shown in Figure 6.13, in which the order parameter starts at... 

It would be very instructive to relate the experimental (Miesowicz) and theoretical (Leslie) coefficients of viscosity. Our task now is to use the viscous tensor (9.20) and find the relationships between the coefficients for each of the three basic orientations of the director, namely = 1, iiy = 1, or = 1. At first, we shall prepare some combinations of parameters useful in all the geometries mentioned ... 

A technique pioneoed by Miesowicz is based on the observation of damping of very small oscillations of a thin glass plate cmnpletely immersed in the investigated liquid [5-7]. The oscillation anq>litude. A, decreases with time due to viscous drag on the plate, and the rate of decrease can be related to the viscosity of the liquid. The damping coefficient has the form... 

So far we have introduced four Miesowicz viscosities. Two other viscosities can be proposed by considering the following. The director n in Fig. 4.1(a), if free to move, will rotate due to a viscous torque the viscosity coefficient 71 is introduced to describe this situation and characterises the torque associated with a rotation of n. For this reason 71 is often called the rotational viscosity or twist viscosity. The coefficient 71 generally determines the rate of relaxation of the director. Also, a rotation of n due to body forces will induce a flow. The viscosity coefficient 72 characterises the contribution to the torque due to a shear velocity gradient in the nematic and is sometimes referred to as the torsion coefficient in the velocity gradient it leads to a coupling between the orientation of the director and shear flow. The two viscosities 71 and 72 have no counterpart in isotropic fluids. We therefore have a total of six viscosities four Miesowicz viscosities plus 71 and 72. It turns out, as will be seen in the problems to be discussed in later Sections, that 7i and 72 are precisely the viscosities introduced in the constitutive theory at equations (4.78) and (4.79), namely. 

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