Minimization principle for shear alignment of liquid crystals

Abstract

If a static perturbation is applied to a liquid crystal, the director configuration changes to minimize the free energy. If a shear flow is applied to a liquid crystal, one might ask: Does the director configuration change to minimize any effective potential? To address that question, we derive the Leslie-Ericksen equations for dissipative dynamics, and determine whether they can be expressed as relaxation toward a minimum. The answer may be yes or no, depending on the number of degrees of freedom. Using theory and simulations, we consider two specific examples, reverse tilt domains under simple shear flow and dowser configurations under plane Poiseuille flow, and demonstrate that each example shows relaxation toward the minimum of an effective potential. arXiv:1912.11902v1 [cond-mat.soft]

Annihilation trajectory of defects in smectic-C films

“…A second method is to regard topological defects as oriented particles with effective interactions and drag coefficients, and solve the dynamics macroscopically [21]. A third approach is to consider the effects of shear flow as an effective potential acting on the orientational order [29]. In this work, we take the first approach, and use pure relaxational dynamics so that we can see the effects of unequal Frank constants without backflow.…”

Tropisms of the Dowser Texture

“…Our aim here is to review these achievements. In recent works of Giomi et al [ 12 ], Emeršič et al [ 13 ] and Tang and Selinger [ 14 ] the intrinsic importance of the dowser texture also appeared clearly. We will refer to them in Section 6.3 and Section 11.1 .…”

“…More recently, Tang and Selinger developed this theory and presented it in all details in ref. [ 14 ]. Here, we will analyse the flow-asssted homeotropic ⇔ dowser transition in slightly different terms.…”

“…This work corresponds to an effective potential U = −W (see ref. [ 14 ]) which has to be added to the total elastic energy given in Equation ( 6 ): …”

Soft Ferrocholesteric in a Rotating Magnetic Field: Phase Diagrams

“…, где C -константа интегрирования, для определения которой воспользуемся методом эффективного потенциала [20][21][22]. В нашей задаче интегрируемая система уравнений стационарной динамики (11) может быть получена из уравнений Эйлера-Лагранжа при рассмотрении следующей плотности эффективной свободной энергии:…”