TY - JOUR
T1 - On poiseuille flow of liquid crystals
AU - Carme Calderer, M.
AU - Mukherjee, Agisa
PY - 1997
Y1 - 1997
N2 - We consider Poiseuille flow of polymeric liquid crystals corresponding to large values of the velocity gradient. The model employed [Ericksen, 1991] proposes governing equations for the velocity field, v, the pressure p, the director n, and the order parameter s. The constitutive functions for the Leslie coefficients αi derived from the molecular theory of Doi [1981] play a crucial role in the modelling. In addition to the Ericksen number, E, the present model exhibits a new non-dimensional parameter ℐ, that represents the contribution of the elastic free energy of non-gradient type with respect to Frank-Oseen’s elasticity. One of the goals of the analysis was to examine the role of s in describing singularities as well as in obtaining regimes which are not predicted by the previous Leslie-Ericksen model. In particular, solutions are obtained that correspond to domain structures parallel to the flow. Such domains are separated by singular lines across which the director experiences jumps of, approximately, ±45 degrees with respect to the flow direction. A condition on the size of ℐ is required in order to support such layered structures. The contribution of the energy associated with I turns out to play the role of an elastic surface energy which is, otherwise, neglected in the present model.
AB - We consider Poiseuille flow of polymeric liquid crystals corresponding to large values of the velocity gradient. The model employed [Ericksen, 1991] proposes governing equations for the velocity field, v, the pressure p, the director n, and the order parameter s. The constitutive functions for the Leslie coefficients αi derived from the molecular theory of Doi [1981] play a crucial role in the modelling. In addition to the Ericksen number, E, the present model exhibits a new non-dimensional parameter ℐ, that represents the contribution of the elastic free energy of non-gradient type with respect to Frank-Oseen’s elasticity. One of the goals of the analysis was to examine the role of s in describing singularities as well as in obtaining regimes which are not predicted by the previous Leslie-Ericksen model. In particular, solutions are obtained that correspond to domain structures parallel to the flow. Such domains are separated by singular lines across which the director experiences jumps of, approximately, ±45 degrees with respect to the flow direction. A condition on the size of ℐ is required in order to support such layered structures. The contribution of the energy associated with I turns out to play the role of an elastic surface energy which is, otherwise, neglected in the present model.
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U2 - 10.1080/026782997209487
DO - 10.1080/026782997209487
M3 - Article
AN - SCOPUS:0004727331
SN - 0267-8292
VL - 22
SP - 121
EP - 135
JO - Liquid Crystals
JF - Liquid Crystals
IS - 2
ER -