Backflow and Kickback in the Splay Geometry

Backflow in the Planar to Homeotropic Transition Splay Geometry 

It should first be noted that if flow is considered unimportant (for example, this may be the case for some materials when H is very near He) then the switch-on time can be derived analogously to that for the twist geometry given by (5.419), the result being 

This result for Tan is reasonably accurate on physical grounds, as pointed out by Chandrasekhar [38, pp. 163-165]. However, to illustrate the general procedure, we incorporate the effects of flow and follow Pieranski et al [220]. This procedure allows us to investigate possible effects when fields are switched on or off. The method is virtually identical to that needed for the alternative bend homeotropic to planar transition considered in the next Section, where it is known that backflow has a greater influence on the switch-on time. 

Routine calculations reveal that the non-zero components of the rate of strain tensor A in (4.125) and vorticity tensor W in (4.126)2 are 

The non-negativity of the dissipation function then requires that this quadratic form is positive semidefinite. Following the comments after (2.56), it is seen that the inequalities 

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