Hydrodynamic Theories for Flows of Active Liquid Crystals and the Generalized Onsager Principle

Yang, Xiaogang; Li, Jun; Forest, M. Gregory; Wang, Qi

doi:10.3390/e18060202

Cited by 46 publications

(36 citation statements)

References 54 publications

(70 reference statements)

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“…It should be noted that here we neglect the Marangoni flow that is likely to be formed due to the orientational-driven surface tension gradients [35][36][37]. Other effects and processes such as 3D orientation structures, strong nonlinearities, hydrodynamic [38,39], and viscoelastic effects [40][41][42] discussed elsewhere are beyond the scope of this paper. The generalized Cahn-Hoffman capillary vector Ξ [43,44], is the fundamental quantity that reflects the anisotropic contribution of CLC in the capillary shape equation.…”

Section: Governing Equationsmentioning

confidence: 99%

Surface Anchoring Effects on the Formation of Two-Wavelength Surface Patterns in Chiral Liquid Crystals

2019

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We present a theoretical analysis and linear scaling of two-wavelength surface nanostructures formed at the free surface of cholesteric liquid crystals (CLC). An anchoring model based on the capillary shape equation with the high order interaction of anisotropic interfacial tension is derived to elucidate the formation of the surface wrinkling. We showed that the main pattern-formation mechanism is originated due to the interaction between lower and higher order anchoring modes. A general phase diagram of the surface morphologies is presented in a parametric space of anchoring coefficients, and a set of anchoring modes and critical lines are defined to categorize the different types of surface patterns. To analyze the origin of surface reliefs, the correlation between surface energy and surface nano-wrinkles is investigated, and the symmetry and similarity between the energy and surface profile are identified. It is found that the surface wrinkling is driven by the director pressure and is annihilated by two induced capillary pressures. Linear approximation for the cases with sufficient small values of anchoring coefficients is used to realize the intrinsic properties and relations between the surface curvature and the capillary pressures. The contributions of capillary pressures on surface nano-wrinkling and the relations between the capillary vectors are also systematically investigated. These new findings establish a new approach for characterizing two-length scale surface wrinkling in CLCs, and can inspire the design of novel functional surface structures with the potential optical, friction, and thermal applications.

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Section: Governing Equationsmentioning

confidence: 99%

Surface Anchoring Effects on the Formation of Two-Wavelength Surface Patterns in Chiral Liquid Crystals

2019

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“…Although OVP has been widely applied with great successes in the study of inert soft matter dynamics, it is rarely used in the study of active soft matter dynamics. 65,[82][83][84] In the present work, we will show that OVP can be readily extended to include biochemical activity and conveniently applied to study the emergent structures and behaviors of active soft matter. OVP can not only be applied to formulate thermodynamically consistent models, but also be used to generate approximate solutions for the complex dynamics of active soft matter.…”

Section: Introductionmentioning

confidence: 90%

Onsager's variational principle in active soft matter

Wang

Qian

2021

Soft Matter

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“…[3,4]. Given the system's free energy, the gradient flow model is derived using the generalized Onsager principle or equivalently the second law of thermodynamics [5][6][7][8]. Gradient flow models can be either energy dissipative or energy conservative globally.…”

Section: Introductionmentioning

confidence: 99%

Local Energy Dissipation Rate Preserving Approximations to Driven Gradient Flows with Applications to Graphene Growth

et al. 2021

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We develop a paradigm for developing local energy dissipation rate preserving (LEDRP) approximations to general gradient flow models driven by source terms. In driven gradient flow models, the deduced energy density transport equation possesses an indefinite source.Local energy-dissipation-rate preserving algorithms are devised to respect the mathematical structure of both the driven gradient flow model and its deduced energy density transport equation. The LEDRP algorithms are also global energy-dissipation-rate preserving under proper boundary conditions such as periodic boundary conditions. However, the contrary may not be true. We then apply the paradigm to a phase field model for growth of a graphene sheet to produce a set of LEDRP algorithms. Numerical refinement tests are conducted to confirm the convergence property of the new algorithms and simulations of graphene growth are demonstrated to benchmark against existing results in the literature.

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Hydrodynamic Theories for Flows of Active Liquid Crystals and the Generalized Onsager Principle

Cited by 46 publications

References 54 publications

Surface Anchoring Effects on the Formation of Two-Wavelength Surface Patterns in Chiral Liquid Crystals

Surface Anchoring Effects on the Formation of Two-Wavelength Surface Patterns in Chiral Liquid Crystals

Onsager's variational principle in active soft matter

Local Energy Dissipation Rate Preserving Approximations to Driven Gradient Flows with Applications to Graphene Growth

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