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Wang Z, Servio P, Rey AD. Geometry-structure models for liquid crystal interfaces, drops and membranes: wrinkling, shape selection and dissipative shape evolution. SOFT MATTER 2023. [PMID: 38031449 DOI: 10.1039/d3sm01164j] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/01/2023]
Abstract
We review our recent contributions to anisotropic soft matter models for liquid crystal interfaces, drops and membranes, emphasizing validations with experimental and biological data, and with related theory and simulation literature. The presentation aims to illustrate and characterize the rich output and future opportunities of using a methodology based on the liquid crystal-membrane shape equation applied to static and dynamic pattern formation phenomena. The geometry of static and kinetic shapes is usually described with dimensional curvatures that co-mingle shape and curvedness. In this review, we systematically show how the application of a novel decoupled shape-curvedness framework to practical and ubiquitous soft matter phenomena, such as the shape of drops and tactoids and bending of evolving membranes, leads to deeper quantitative insights than when using traditional dimensional mean and Gaussian curvatures. The review focuses only on (1) statics of wrinkling and shape selection in liquid crystal interfaces and membranes; (2) kinetics and dissipative dynamics of shape evolution in membranes; and (3) computational methods for shape selection and shape evolution; due to various limitations other important topics are excluded. Finally, the outlook follows a similar structure. The main results include: (1) single and multiple wavelength corrugations in liquid crystal interfaces appear naturally in the presence of surface splay and bend orientation distortions with scaling laws governed by ratios of anchoring-to-isotropic tension energy; adding membrane elasticity to liquid crystal anchoring generates multiple scales wrinkling as in tulips; drops of liquid crystals encapsulates in membranes can adopt, according to the ratios of anchoring/tension/bending, families of shapes as multilobal, tactoidal, and serrated as observed in biological cells. (2) Mapping the liquid crystal director to a membrane unit normal. The dissipative shape evolution model with irreversible thermodynamics for flows dominated by bending rates, yields new insights. The model explains the kinetic stability of cylinders, while spheres and saddles are attractors. The model also adds to the evolving understanding of outer hair cells in the inner ear. (3) Computational soft matter geometry includes solving shape equations, trajectories on energy and orientation landscapes, and shape-curvedness evolutions on entropy production landscape with efficient numerical methods and adaptive approaches.
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Affiliation(s)
- Ziheng Wang
- Department of Chemical Engineering, McGill University, 3610 University Street, Montréal, Québec, H3A 2B2, Canada.
| | - Phillip Servio
- Department of Chemical Engineering, McGill University, 3610 University Street, Montréal, Québec, H3A 2B2, Canada.
| | - Alejandro D Rey
- Department of Chemical Engineering, McGill University, 3610 University Street, Montréal, Québec, H3A 2B2, Canada.
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Qiu M, Feng JJ, Loudet JC. Phase-field model for elastocapillary flows of liquid crystals. Phys Rev E 2021; 103:022706. [PMID: 33736098 DOI: 10.1103/physreve.103.022706] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/23/2020] [Accepted: 01/19/2021] [Indexed: 11/07/2022]
Abstract
We propose a phase-field model to study interfacial flows of nematic liquid crystals that couple the capillary forces on the interface with the elastic stresses in the nematic phase. The theoretical model has two key ingredients: A tensor order parameter that provides a consistent description of the molecular and distortional elasticity, and a phase-field formalism that accurately represents the interfacial tension and the nematic anchoring stress by approximating a sharp-interface limit. Using this model, we carry out finite-element simulations of drop retraction in a surrounding fluid, with either component being nematic. The results are summarized by eight representative steady-state solutions in planar and axisymmetric geometries, each featuring a distinct configuration for the drop and the defects. The dynamics is dominated by the competition between the interfacial tension and the distortional elasticity in the nematic phase, mediated by the anchoring condition on the drop surface. As consequences of this competition, the steady-state drop deformation and the clearance between the defects and the drop surface both depend linearly on the elastocapillary number.
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Affiliation(s)
- Mingfeng Qiu
- Department of Mathematics, University of British Columbia, Vancouver, British Columbia V6T 1Z2, Canada
| | - James J Feng
- Department of Mathematics and Department of Chemical and Biological Engineering, University of British Columbia, Vancouver, British Columbia V6T 1Z2, Canada
| | - Jean-Christophe Loudet
- Université de Bordeaux, CNRS, Centre de Recherche Paul Pascal (UMR 5031), F-33600 Pessac, France
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Wang Z, Servio P, Rey AD. Mechanogeometry of nanowrinkling in cholesteric liquid crystal surfaces. Phys Rev E 2020; 101:062705. [PMID: 32688582 DOI: 10.1103/physreve.101.062705] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2019] [Accepted: 04/03/2020] [Indexed: 11/07/2022]
Abstract
Biological plywoods are multifunctional fibrous composites materials, ubiquitous in nature. The chiral fibrous organization is found in chitin (insects), cellulosics (plants), and collagen I (cornea and bone of mammals) and is a solid analog of that of cholesteric liquid crystals. The surface and interfaces of plywoods are distinguished by hierarchical topographies and nanowrinkling. In this paper, we present a theory to model the emergence of these surfaces and interfaces using liquid crystal-based shape equations that directly connect material properties with geometric wrinkling. The model applies to liquid crystal precursors of the plywood solid analoges. We focus on wrinkling geometry, wrinkling mechanics, and the mechanogeometry relationships that underlie multifunctionality ubiquitous in biological surfaces. Scaling wrinkling laws that connect mechanical pressures and stresses to folding and bending are formulated and quantified. A synthesis of the connections between mechanics and geometry is achieved using the topology of stress curves and curvature of the wrinkles. Taken together the results show that anchoring is a versatile surface morphing mechanism with a rich surface bending stress field, two ingredients behind many potential multifunctionalities.
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Affiliation(s)
- Ziheng Wang
- Department of Chemical Engineering, McGill University, 3610 University Street, Montréal, Québec H3A 0C5, Canada
| | - Phillip Servio
- Department of Chemical Engineering, McGill University, 3610 University Street, Montréal, Québec H3A 0C5, Canada
| | - Alejandro D Rey
- Department of Chemical Engineering, McGill University, 3610 University Street, Montréal, Québec H3A 0C5, Canada
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Dai Q, Khonsari MM, Shen C, Huang W, Wang X. On the migration of a droplet on an incline. J Colloid Interface Sci 2017; 494:8-14. [PMID: 28131033 DOI: 10.1016/j.jcis.2017.01.055] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/02/2016] [Revised: 01/13/2017] [Accepted: 01/17/2017] [Indexed: 10/20/2022]
Abstract
A liquid droplet placed on a nonuniformly heated solid surface will migrate from a high temperature region to a low temperature region. The present study reports the results of an experimental investigation on the migration behavior of mineral oil droplets subjected to a thermal gradient on an inclined plane. A particular attention is paid to the relationship between the critical inclination angle and thermal gradients. It is shown that there exists a critical inclination angle at which the droplet migration is halted. This critical inclination angle can be readily predicted using analytical expressions derived in this paper. This study puts forward the understanding of the interface phenomenon of thermocapillary migration on an incline. The knowledge of the critical inclination is important in applications where the migration on an incline must be obstructed to retain adequate lubrication in the desired location.
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Affiliation(s)
- Qingwen Dai
- College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics & Astronautics, Nanjing 210016, China; Jiangsu Key Laboratory of Precision and Micro-Manufacturing Technology, Nanjing 210016, China
| | - M M Khonsari
- Department of Mechanical and Industrial Engineering, Louisiana State University, 3283 Patrick Taylor Hall, Baton Rouge, LA 70803, USA.
| | - Cong Shen
- Department of Mechanical and Industrial Engineering, Louisiana State University, 3283 Patrick Taylor Hall, Baton Rouge, LA 70803, USA
| | - Wei Huang
- College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics & Astronautics, Nanjing 210016, China
| | - Xiaolei Wang
- College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics & Astronautics, Nanjing 210016, China; Jiangsu Key Laboratory of Precision and Micro-Manufacturing Technology, Nanjing 210016, China
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5
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Qi XB, Chen Y, Kang XH, Li DZ, Gong TZ. Modeling of coupled motion and growth interaction of equiaxed dendritic crystals in a binary alloy during solidification. Sci Rep 2017; 7:45770. [PMID: 28361933 PMCID: PMC5374713 DOI: 10.1038/srep45770] [Citation(s) in RCA: 35] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/08/2016] [Accepted: 03/02/2017] [Indexed: 11/09/2022] Open
Abstract
Motion of growing dendrites is a common phenomenon during solidification but often neglected in numerical simulations because of the complicate underlying multiphysics. Here a phase-field model incorporating dendrite-melt two-phase flow is proposed for simulating the dynamically interacted process. The proposed model circumvents complexity to resolve dendritic growth, natural convection and solid motion simultaneously. Simulations are performed for single and multiple dendritic growth of an Al-based alloy in a gravity environment. Computing results of an isolated dendrite settling down in the convective supersaturated melt shows that solid motion is able to overwhelm solutal convection and causes a rather different growth morphology from the stationary dendrite that considers natural convection alone. The simulated tip growth dynamics are correlated with a modified boundary layer model in the presence of melt flow, which well accounts for the variation of tip velocity with flow direction. Polycrystalline simulations reveal that the motion of dendrites accelerates the occurrence of growth impingement which causes the behaviors of multiple dendrites are distinct from that of single dendrite, including growth dynamics, morphology evolution and movement path. These polycrystalline simulations provide a primary understanding of the sedimentation of crystals and resulting chemical homogeneity in industrial ingots.
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Affiliation(s)
- Xin Bo Qi
- Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang, Liaoning, 110016, P. R. China
| | - Yun Chen
- Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang, Liaoning, 110016, P. R. China
| | - Xiu Hong Kang
- Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang, Liaoning, 110016, P. R. China
| | - Dian Zhong Li
- Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang, Liaoning, 110016, P. R. China
| | - Tong Zhao Gong
- Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang, Liaoning, 110016, P. R. China
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Ullrich B, Auernhammer GK, Sam EM, Vollmer D. Tracer colloids close to an isotropic–nematic domain interface with phase transition-induced solute transport. Colloids Surf A Physicochem Eng Asp 2010. [DOI: 10.1016/j.colsurfa.2009.11.023] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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Chakraborty S. Order parameter description of electrochemical-hydrodynamic interactions in nanochannels. PHYSICAL REVIEW LETTERS 2008; 101:184501. [PMID: 18999834 DOI: 10.1103/physrevlett.101.184501] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/01/2008] [Indexed: 05/27/2023]
Abstract
A novel phase-field model is developed for the quantitative modeling of the complex electrochemical-hydrodynamic interactions in narrow fluidic confinements. Through an order parameter variation, this model captures the underlying excluded volume effects, solvation interactions, and preferential polarizabilities in a self-consistent fashion, without resorting to computationally prohibitive molecular dynamics simulations. Agreement with molecular dynamics predictions is found to be quantitative.
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Affiliation(s)
- Suman Chakraborty
- Department of Mechanical Engineering, Indian Institute of Technology, Kharagpur-721302, India.
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An Energetic Variational Formulation with Phase Field Methods for Interfacial Dynamics of Complex Fluids: Advantages and Challenges. MODELING OF SOFT MATTER 2008. [DOI: 10.1007/0-387-32153-5_1] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
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9
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Zhou C, Yue P, Feng JJ. Simulation of Neutrophil Deformation and Transport in Capillaries using Newtonian and Viscoelastic Drop Models. Ann Biomed Eng 2007; 35:766-80. [PMID: 17380390 DOI: 10.1007/s10439-007-9286-x] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/12/2006] [Accepted: 02/23/2007] [Indexed: 11/26/2022]
Abstract
It is well known that neutrophils take much longer to traverse the pulmonary capillary bed than erythrocytes, and this is likely due to differences in the structure and rheology of the cells. In this study, we simulate the transit of a neutrophil in a capillary using a Newtonian drop model and a viscoelastic drop model. The cell membrane is represented by an interface with isotropic and constant tension, and the cell motion and deformation are described by a phase-field method. The governing equations are solved using finite elements in an axisymmetric geometry, and the thin interfaces are resolved by mesh adaptivity. With a fixed pressure drop, the entry of a cell into a capillary consists of several stages in which the flow rate varies in distinct manners. The entrance time is consistent with experimental measurements. It decreases with the pressure drop, increases with the cell viscosity and generally decreases with the relaxation time of a viscoelastic cytoplasm. The capillary geometry has a strong effect on the entry and transit of a neutrophil. The entrance time increases sharply when the capillary diameter decreases or when the capillary is constricted by a pinch.
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Affiliation(s)
- Chunfeng Zhou
- Department of Chemical and Biological Engineering, University of British Columbia, Vancouver, BC, Canada, V6T 1Z3
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Yu W, Zhou C. Coalescence of droplets in viscoelastic matrix with diffuse interface under simple shear flow. ACTA ACUST UNITED AC 2007. [DOI: 10.1002/polb.21185] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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Wu Y, Yu W, Zhou C. The influence of electric field-induced orientation on the retraction of a liquid crystal droplet immersed in a flexible polymer matrix. J Colloid Interface Sci 2006; 303:546-51. [PMID: 16942777 DOI: 10.1016/j.jcis.2006.07.082] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/24/2006] [Revised: 07/27/2006] [Accepted: 07/30/2006] [Indexed: 10/24/2022]
Abstract
We measured the apparent interfacial tension between a liquid crystal and a flexible polymer by deformed droplet retraction method. An external electric field is applied to change the director orientation in liquid crystal droplet. The deformation and recovery of a single liquid crystal droplet dispersed in a polydimethylsiloxane (PDMS) matrix were realized by a transient shear flow and observed by polarized optical microscope. In order to control the director orientation in LC droplet, the electric field is applied perpendicular and parallel to the flow field, respectively. The different orientation induced by electric field in liquid crystal droplet has different behavior during droplet retraction and affect the apparent interfacial tension between liquid crystal and flexible polymer.
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Affiliation(s)
- Youjun Wu
- Department of Polymer Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, People's Republic of China
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