General Stress Tensor for Nematic Liquid Crystals

General Stress Tensor for Nematic Liquid Crystals 

The general theoretical ftamewoik for describing the hydrodynamics of liquid crystals has been developed principally by Leslie and Ericksen. Their approaches account for the fact that the stress tensor depends not only on the velocity gradients, but also on the orientation and rotation of the director. Accordingly, the stress tensor is given by 

Note that all the other terms on the right-hand side of Equation (3.59) involve the director orientation, except the fourth term, ot ojp.This is the same term as that for an isotropic fluid [cf Eq. (3.57)], that is, a4=2ri. 

Therefore, in this formahsm, there are six so-called Leslie coefficients, aj,ot2. Ms, which have the dimension of viscosity coefficients. It was shown by Parodi that 

In the next few sections we will study particular cases of director axis orientation and deformation and we will show how these Leslie coefficients are related to other commonly used viscosity coefficients. 

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