Hydrodynamic Modeling of Liquid Crystal Flows

Liquid crystals occupy a unique position at the intersection of fluid mechanics and soft condensed matter. Their constituent rod-like or disc-shaped molecules exhibit long-range orientational order while retaining fluidity, leading to rich flow-orientation coupling. Hydrodynamic models typically couple the Navier–Stokes equations, which govern fluid momentum and mass conservation, with additional equations for the molecular orientation or ordering. In the simplest nematic description, a unit vector field—known as the director—captures the average molecular alignment, while more general formulations employ a symmetric traceless tensor (the Q-tensor) to describe both uniaxial and biaxial order. Stress terms arising from elastic distortions (Ericksen stress) and viscous reorientation (Leslie stress) introduce nonlinear feedback between flow gradients and director dynamics. Numerical schemes range from finite-difference and finite-element discretisations to lattice-Boltzmann approaches, enabling the study of defect dynamics, hydrodynamic instabilities and pattern formation. Beyond fundamental interest, hydrodynamic modelling underpins the design of liquid-crystal displays, optofluidic devices, tunable photonic elements and biomimetic locomotion systems, where controlled coupling between flow and molecular order is exploited to achieve responsive materials and micro-scale actuation.

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Hydrodynamic Modeling of Liquid Crystal Flows publication trend

The graph below shows the total number of articles in hydrodynamic modeling of liquid crystal flows across all publications each year (not limited to Nature Index journals).

Technical terms

Nematic phase: A liquid-crystalline state characterised by orientational order of rod-like molecules without positional order.

Director field: A unit vector field representing the local average molecular orientation in nematic liquid crystals.

Ericksen–Leslie equations: A continuum theory coupling Navier–Stokes hydrodynamics with equations for molecular orientation, incorporating elastic and viscous stresses.

Q-tensor: A symmetric, traceless tensor order parameter that generalises the director to describe both uniaxial and biaxial nematic order.

References

1. Analysis and Numerical Approximation of Energy-Variational Solutions to the Ericksen–Leslie Equations. Acta Applicandae Mathematicae (2023).
2. Uniqueness of global weak solutions for the general Ericksen–Leslie system with Ginzburg–Landau penalization in T2. Calculus of Variations and Partial Differential Equations (2023).
3. On the 2D Ericksen–Leslie equations with anisotropic energy and external forces. Journal of Evolution Equations (2021).