Abstract
AbstractIn order to model the flow of nematic crystals, the theoretical framework according to Ericksen and Leslie is applied. The essentials of the theory are compiled and then specialized to Couette flow. The profiles for linear velocity and orientation angle will be computed and, in particular, we shall also study the rise in temperature due to viscous dissipation, which is frequently ignored by mechanicians. Analytical and numerical solutions for the fields are derived for different boundary conditions and will subsequently be discussed.
Highlights
This short note is geared toward a description of the flow of fluids with internal rotational degrees of freedom, liquid crystals
In order to model the flow of nematic crystals, the theoretical framework according to Ericksen and Leslie is applied
The numerical solutions are obtained with Mathematica.[34]
Summary
This short note is geared toward a description of the flow of fluids with internal rotational degrees of freedom, liquid crystals. The flow behavior of such materials can be described by the theory of Ericksen and Leslie ([1] or [2]). In a nutshell, they restrict themselves to the description of rigid rod-like molecules, the motion of which is captured by introducing a single vector quantity, the so-called director, d. The most popular application of the director theory is in context with electromagnetic fields, e.g., in order to analyze optical effects. The aim of this paper, is to analyze a classical problem of fluid mechanics with the Ericksen–Leslie theory and to provide solutions, which have not been presented in the literature yet
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