The Anisotropic Fluid Case

The Ericksen-Leslie theory from Section 4.2.5 will be used with all director gradients and the elastic energy being set to zero, so that we are dealing with an anisotropic fluid. Incorporating the gravitational potential the relevant dynamic equations 

The velocity is independent of time t and therefore v = (v V)v. Using the general formula stated at equation (C.4) in Appendix C (with n set to v), the physical components of v are therefore given by 

Similarly, since n is independent of t, the same formula can be applied again to show that the physical components of h = (v V)n are 

The non-zero physical components of the rate of strain tensor A and vorticity tensor W are obtained by applying the formulae (C.ll) to (C.17) in Appendix C, giving 

We are now in a position to solve equations (5.239) before proceeding to solve (5.238). 

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