Determination of Director Angle for Flow Aligning Nematic Liquid Crystals under Couette Geometry


Nematic liquid crystals
couette two
ericksen-leslie model

How to Cite

Bagisa Mukherjee. (2016). Determination of Director Angle for Flow Aligning Nematic Liquid Crystals under Couette Geometry. Journal of Advances in Applied & Computational Mathematics, 3(1), 1–3.


We consider steady state flow of nematic liquid crystals in a Couette geometry driven by the relative rotation of the two concentric cylinders. We use the standard Ericksen-Leslie continuum model. The director, a unit vector, represents the average molecular orientation. We assume strong anchoring conditions at the walls of the flow which fixes the director orientation, and find an explicit expression of the director angle as a function of its distance from the common axis of the rotating cylinders.


Calderer MC and Mukherjee B. On Poiseuille flow of liquid crystals, Liquid Crystals 1997; 22: 121-135.

Calderer MC and Mukherjee B. Some mathematical issues in the modeling of flow phenomena of polymeric Liquid crystals. J Rheology 1998; 42: 1519-1536.

Calderer MC and Liu C. Liquid crystal flow: dynamic and static configurations. SIAM J Appl Math 2000; 60-6.

Cladis PE and Torza S. Stability of Nematic Liquid crystals in Couette Flow. Phys Rev Lett 1975; 35: 1283-1286.

de Gennes PG and Prost J. The physics of liquid crystals. Oxford Science Publications, Oxford 1993.

Ericksen J. Conservation laws for liquid crystals. Trans Soc Rheol 1961; 5: 22-34.

Ericksen J. Continuum theory of nematic liquid crystals. Res Mechanica 1987; 21: 381-392.

Ericksen J. Liquid crystals with variable degree of orientation. Arch Ration Mech Anal 1991; 113: 97-120.

Leslie F. Some constitutive equations for liquid crystals. Arch Ration Mech Anal 1968; 28: 265-283.

Leslie F. Theory of flow phenomena in liquid crystals. The Theory of Liquid Crystals, 4, Academic Press 1979: 1-81.

Lin FH and Liu C. Existence of solutions for the Ericksen- Leslie system. Arch Ration Mech Anal 2000; 154(2): 135-156.

Oseen CW. Trans. Faraday Soc 1991; 29: 883.

Pieranski P and Guyon E. Two shear-flow regimes in p-n- Hexyloxybenzilidene-p0-aminobenzonitrile. Phys. Rev. Lett 1974; 32(17): 924-926.

Stewart IW. The static and dynamic continuum theory of liquid crystals Taylor and Francis 2004.

Ch. Hoffmann et al. Nonlinear Defects Separating Spiral Waves in Taylor-Couette Flow. Phys Rev E 80 066308, 2009; 1-8. (DOI: 10.1103/PhysRevE.80.066308).