Structure and rheology of fiber-laden membranes via integration of nematodynamics and membranodynamics

This paper presents a study of the structure and dynamics of rigid fiber-laden deformable curved fluid membranes based on an viscoelastic model that integrates the statics of anisotropic membranes, the planar nematodynamics of fibers and the dynamics of isotropic membranes. Fiber-laden membranes arise frequently in biological systems, such as the plant cell wall and in protein–lipid bilayers. Based on the membrane's force and torque balance equations and the fiber's balance of molecular fields, a viscoelastic anisotropic model that provides the governing equations for the membrane's velocity and curvature and the fiber structure (fiber orientation and order) is found. A Helmholtz free energy that incorporates the tension/bending/and torsion membrane elasticity, the Landau–de Gennes fiber ordering, and fiber order-membrane curvature interactions is used to derive elastic moments, torques, and stresses. The corresponding viscous stresses and moments include the Boussinesq–Scriven contributions as well as bending, torsion, and rotational dissipation. A spectral decomposition leads to the main viscoelastic material functions for anisotropic fluid membranes. Applications of the rheological model to cylindrical growth and cylindrical axial stretching show that competing curvo-phobic, curvo-philic interactions under extensional flow predict transitions between axial and azimuthal fiber arrangements, of interest to cellulose fiber orientation in plant morphogenesis.     

Simulating turbulent Dean flow in Cartesian coordinates

A simplified approach to simulate turbulent flows in curved channels is proposed. A set of governing equations of motion in Cartesian coordinates is derived from the full Navier–Stokes equations in cylindrical coordinates. Terms to first order in the dimensionless curvature parameter are retained, whereas higher‐order terms are neglected. The curvature terms are implemented in a conventional Navier–Stokes code using Cartesian coordinates. Direct numerical simulations (DNS) of turbulent flow in weakly curved channels are performed. The pronounced asymmetries in the mean flow and the turbulence statistics observed in earlier DNS studies are faithfully reproduced by the present simplified Navier–Stokes model. It is particularly rewarding that also distinct pairs of counter‐rotating streamwise‐oriented vortices are embedded in the simulated flow field. Copyright © 2008 John Wiley & Sons, Ltd.     

Theory of interfacial dynamics of nematic polymers

 The interfacial momentum and torque balance equations for deforming interfaces between nematic polymers and isotropic viscous fluids are derived and analyzed with respect to shape selection and interfacial nematic ordering. It is found that the interfacial momentum balance equation for nematic interfaces involves bending forces that act normal to the interface, and that interfacial pressure jumps may exist even for planar surfaces. In addition tangential forces on nematic interfaces arise in the presence of surface gradients of the tensor order parameter. The torque balance equation shows that couple stress jumps are balanced by the surface molecular field. The interfacial balance equations are shown to be coupled such that nematic ordering depends on shape and vice versa. The governing dimensionless numbers for deforming nematic polymer interfaces are identified and the limiting regimes are discussed in reference to related experimental data. It is found that the ratio of Frank elasticity to surface anchoring controls whether the surface tensor order parameter deviates from its preferred equilibrium value. Whether the shape is affected, depends on the relative magnitudes of the isotropic surface tension, Frank bulk elasticity, and anchoring energy, and capillary number. Received: 16 April 1999/Accepted: 19 August 1999     

宏纤维压电层合壳结构非线性屈曲分析

以纤维压电MFC （Micro-Fiber Composite）层合圆柱壳为例,研究了其在准静态屈曲下的非线性振动响应。基于Reissner-Mindlin一阶剪切变形假设,采用大转角几何全非线性理论,建立了带有纤维角度的MFC层合壳结构的非线性屈曲与振动分析模型。采用全拉格朗日方程（Total Lagrange Formulation）对非线性模型进行线性化处理,并结合Riks-Wempner弦长控制迭代法进行准静态求解,然后在每个解点进行自由振动分析。通过与文献数据对比验证了所建模型的准确性。并用该计算模型对MFC-d31层合圆柱壳进行屈曲及自由振动分析,研究了几何参数（曲率、厚度、纤维角度和不同外加电压）对频率的影响。结果表明,厚度、曲率和纤维增强角度对结构的临界载荷有显著的影响,且结构的临界载荷随着上述参数的增大而增大;电场强度可对不同纤维角度壳体的自振频率进行调节,能够提高结构的临界载荷;纤维角度越大,电压对结构自振频率调节的效果越明显。     

Linear viscoelastic model for bending and torsional modes in fluid membranes

This paper develops and applies a linear viscoelastic model for bending and torsional modes of fluid membranes, based on the nonlinear Cosserat surface fluid model. The linearized fluid membrane model in spherical and cylindrical geometries is shown to decouple bending and torsional viscoelastic modes. It is found that solutions of the membrane viscoelastic model to small-amplitude oscillatory bending and torsion allows for the measurement of the bending and the torsion viscosity. The model and its potential in characterizing the bending and torsion viscoelasticity of membranes complements the on-going efforts to establish the role of curvature in dissipative process of biological membranes.     

Turbulent boundary layer on a mildly curved convex surface

Extensive single point turbulence measurements made in the boundary layer on a mildly curved heated convex wall show that the turbulence heat fluxes and Stanton number are more sensitive to a change in wall curvature than the Reynolds stresses and skinfriction coefficient, and that downstream, as the flow adjusts to new curved conditions, the St/c _f ratio of Reynolds analogy is appreciably lower than in plane wall flow for the same conditions. Details of the turbulence structure in unheated flow have been documented in an earlier paper; temperature field measurements now described comprise mean temperature distributions, the streamwise variation of wall heat flux, profiles of the temperature variance, transverse and streamwise heat fluxes, and triple correlations. Turbulent diffusion of heat flux is drastically reduced even by mild curvature; changes in the heat fluxes are of the same order as changes in the shear stress, that is, an order of magnitude greater than the ratio of boundary layer thickness to wall radius of curvature. The data include plane flow measurements taken in a developed boundary layer upstream of a change in wall curvature.     

气泡碰撞亲疏水曲壁的行为特性研究

气泡碰撞固壁行为和影响因素的研究一直以来都是科学界关注的重点之一, 其在矿物浮选、气膜减阻等工业领域中的应用也极具科研价值. 论文聚焦曲壁对于气泡撞击行为特性的影响研究. 采用高速摄像技术记录气泡碰撞不同曲率半径下亲疏水曲壁的撞击过程, 分析了曲壁润湿性、曲率半径对气泡碰撞固体曲壁的影响规律. 结果表明, 气泡碰撞亲水曲壁时会发生多次弹跳直至离开曲壁; 曲率半径越大, 弹跳次数越少, 且第一次反弹的最远距离越近, 再次发生碰壁时的速度越小. 而碰撞疏水曲壁时会出现碰撞?滑移?附着的现象, 此外针对液膜挤压破裂的现象, 建立理论模型推导出液膜诱导时间的预测公式, 其主要与液膜厚度、液膜临界破裂厚度和液膜被压缩速度有关, 预测误差小于5.0%.      

Dynamics of a fluid sheet on a curved rigid wall with allowance for phase transformation on the free surface

The flow of a three-dimensional sheet on a curved wall is considered. Gravity and surface tension forces act on the sheet while a droplet stream falls on its free surface. The systems of equations of viscous incompressible fluid dynamics on a curved rigid surface and the boundary conditions with allowance for the falling droplet stream are formulated. The problems of steady axisymmetric motion of the sheet on cylindrical and conical surfaces are considered. The effect of the curvature of the rigid wall on the solution is examined. Kharkov. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 42–50, July–August, 1994.     

Isolating curvature effects in computing wall-bounded turbulent flows

An adjoint optimization method is utilized to design an inviscid outer wall shape required for a turbulent flow field solution of the So–Mellor convex curved wall experiment using the Navier–Stokes equations. The associated cost function is the desired pressure distribution on the inner wall. Using this optimized wall shape with a Navier–Stokes method, the abilities of various turbulence models to simulate the effects of curvature without the complicating factor of streamwise pressure gradient are evaluated. The one-equation Spalart–Allmaras (SA) turbulence model overpredicts eddy viscosity, and its boundary layer profiles are too full. A curvature-corrected version of this model improves results, which are sensitive to the choice of a particular constant. An explicit algebraic stress model does a reasonable job predicting this flow field. However, results can be slightly improved by modifying the assumption on anisotropy equilibrium in the model's derivation. The resulting curvature-corrected explicit algebraic stress model (EASM) possesses no heuristic functions or additional constants. It slightly lowers the computed skin friction coefficient and the turbulent stress levels for this case, in better agreement with experiment. The effect on computed velocity profiles is minimal.     

Nonlinear turbulence models for predicting strong curvature effects

Prediction of the characteristics of turbulent flows with strong streamline curvature, such as flows in turbomachines, curved channel flows, flows around airfoils and buildings, is of great importance in engineering applications and poses a very practical challenge for turbulence modeling. In this paper, we analyze qualitatively the curvature effects on the structure of turbulence and conduct numerical simulations of a turbulent Uduct flow with a number of turbulence models in order to assess their overall performance. The models evaluated in this work are some typical linear eddy viscosity turbulence models, nonlinear eddy viscosity turbulence models （NLEVM） （quadratic and cubic）, a quadratic explicit algebraic stress model （EASM） and a Reynolds stress model （RSM） developed based on the second-moment closure. Our numerical results show that a cubic NLEVM that performs considerably well in other benchmark turbulent flows, such as the Craft, Launder and Suga model and the Huang and Ma model, is able to capture the major features of the highly curved turbulent U-duct flow, including the damping of turbulence near the convex wall, the enhancement of turbulence near the concave wall, and the subsequent turbulent flow separation. The predictions of the cubic models are quite close to that of the RSM, in relatively good agreement with the experimental data, which suggests that these models may be employed to simulate the turbulent curved flows in engineering applications.     

Growth and structure of nematic spherulites under shallow thermal quenches

The growth kinetics, shape, interfacial and internal orientation texture of a submicron nematic spherulite arising during the isotropic-to-nematic liquid crystal phase transformation under shallow thermal quenches is analyzed using theory, scaling, and numerical simulations based on the Landau – de Gennes model (The Physics of Liquid Crystals, 2nd edn. Clarendon, Oxford). The numerical computations from this model yield interfacial cusp formation that relaxes through the nucleation of two disclination lines of topological charge +1/2 and subsequently leads to intra-droplet texturing and a net topological charge within the spherulite of +1. The timing of these events suggests that cusp formation at the interface is intimately associated with the interfacial defect shedding mechanism (J. Chem. Phys. 124:244902, 2006) for shallow quenches. These results are different than predictions for deep quenches (J. Chem. Phys. 124:244902, 2006) where interfacial defect shedding leads to four defects and a net topological charge of +2. A liquid crystal dynamic shape equation is derived from the Landau – de Gennes model to account for the interface shape changes in terms of surface viscosity, the driving forces due to the uniaxial nematic-isotropic free energy difference, capillary forces, and friction forces, and used to semi-quantitatively show that during cusp formation and defect shedding, gradient elasticity, capillary forces and friction play significant roles in decelerating and accelerating the surface. An interfacial eigenvalue analysis shows that during the shallow quench, disclination lines nucleate within the interface itself and then texturize the nematic droplet as they migrate from within the interface to the bulk of the growing nematic droplet. After defect shedding, the spherulite is nearly circular and grows with constant velocity, in agreement with experiments. The results shed new light on intra-spherulite texturing mechanisms in phase ordering under weak driving forces.      

曲面薄膜结构褶皱失稳力学

薄膜结构褶皱失稳在微观和宏观尺度会出现相似的形貌,在过去二十年里引发了学者们极大的研究兴趣.而几何曲率对薄膜结构的失稳临界、形貌选择和后屈曲演化起着至关重要的作用.本文回顾近二十年来平面和曲面薄膜结构褶皱失稳力学研究进展,聚焦曲率影响下的薄膜拉伸和膜基结构在各种激励下的稳定性问题.有限应变板壳理论模型和数值计算方法的发...     

A rheological theory for liquid crystal thin films

A macroscopic rheological theory for compressible isothermal nematic liquid crystal films is developed and used to characterize the interfacial elastic, viscous, and viscoelastic material properties. The derived expression for the film stress tensor includes elastic and viscous components. The asymmetric film viscous stress tensor takes into account the nematic ordering and is given in terms of the film rate of deformation and the surface Jaumann derivative. The material function that describes the anisotropic viscoelasticity is the dynamic film tension, which includes the film tension and dilational viscosities. Viscous dissipation due to film compressibility is described by the anisotropic dilational viscosity. Three characteristic film shear viscosities are defined according to whether the nematic orientation is along the velocity direction, the velocity gradient, or the unit normal. In addition the dependence of the rheological functions on curvature and film thickness has been identified. The rheological theory provides a theoretical framework to future studies of thin liquid crystal film stability and hydrodynamics, and liquid crystal foam rheology. Received: 9 October 2000 Accepted: 6 April 2001     

Free vibration of composite laminated plate with complicated cutout

Abstract

This paper presents the free vibration analysis of a composite laminated square plate with complicated cutout. The problem formulation is based on the higher order shear deformation plate theory HDST C⁰ coupled with a curved quadrilateral p-element. The elements of the stiffness and mass matrices are calculated analytically. The curved edges are accurately represented using the blending function method. A calculation program is developed to determine the fundamental frequencies for different physical and mechanical parameters such as the cutout shape, plate thickness, fiber orientation angle, and boundary conditions. The results obtained show a good agreement with the available solutions in the literature. New results for the fundamentals frequencies of a composite laminated plate with complicated cutout are presented.     

Computational analysis of liquid crystalline elastomer membranes: Changing Gaussian curvature without stretch energy

Liquid crystalline elastomers (LCEs) can undergo extremely large reversible shape changes when exposed to external stimuli, such as mechanical deformations, heating or illumination. The deformation of LCEs result from a combination of directional reorientation of the nematic director and entropic elasticity. In this paper, we study the energetics of initially flat, thin LCE membranes by stress driven reorientation of the nematic director. The energy functional used in the variational formulation includes contributions depending on the deformation gradient and the second gradient of the deformation. The deformation gradient models the in-plane stretching of the membrane. The second gradient regularises the non-convex membrane energy functional so that infinitely fine in-plane microstructures and infinitely fine out-of-plane membrane wrinkling are penalised. For a specific example, our computational results show that a non-developable surface can be generated from an initially flat sheet at cost of only energy terms resulting from the second gradients. That is, Gaussian curvature can be generated in LCE membranes without the cost of stretch energy in contrast to conventional materials.     

Theoretical and experimental investigations of the flow of a viscous fluid near the line of intersection of a cylindrical surface and a flat surface

Flow along a corner was investigated at large Reynolds numbers in, for example, [1–3]. The present author [4] considered flow in the neighborhood of a corner formed by the intersection of a plane and a concave cylindrical surface, the main attention being devoted to the formation of the three-dimensional boundary layer on the plane near the corner. It was shown that the curvature of one of the intersecting surfaces changes the flow pattern qualitatively. In the present paper, we report an investigation of the formation of the flow on a concave cylindrical surface near such a corner and consider how the flow is rearranged in the neighborhood of a corner in, for example, a channel of rectangular cross section that has an initial straight section and then a bend with a discontinuity of the curvature of the line of intersection of the concave and flat sides of the channel. The results are given of some experimental investigations of flow near the line of intersection of a flat wall and a curved (concave and convex) wall at a bend in a rectangular channel.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 64–68, January–February, 1983.I thank G. M. Bam-Zelikovich for constant interest in the work and A. I. Ruban for a number of extremely helpful comments.     

Simulation of liquid sloshing in curved‐wall containers with arbitrary Lagrangian–Eulerian method

There are many challenges in the numerical simulation of liquid sloshing in horizontal cylinders and spherical containers using the finite element method of arbitrary Lagrangian–Eulerian (ALE) formulation: tracking the motion of the free surface with the contact points, defining the mesh velocity on the curved wall boundary and updating the computational mesh. In order to keep the contact points slipping along the curved side wall, the shape vector in each time advancement is defined to modify the kinematical boundary conditions on the free surface. A special function is introduced to automatically smooth the nodal velocities on the curved wall boundary based on the liquid nodal velocities. The elliptic partial differential equation with Dirichlet boundary conditions can directly rezone the inner nodal velocities in more than a single freedom. The incremental fractional step method is introduced to solve the finite element liquid equations. The numerical results that stemmed from the algorithm show good agreement with experimental phenomena, which demonstrates that the ALE method provides an efficient computing scheme in moving curved wall boundaries. This method can be extended to 3D cases by improving the technique to compute the shape vector. Copyright © 2007 John Wiley & Sons, Ltd.     

Capillary instabilities in a thin nematic liquid crystalline fiber embedded in a viscous matrix

$m$ to take into account non-axisymmetric modes. Capillary instabilities in nematic fibers reflect the anisotropic nature of liquid crystals, such as the orientation contribution to the surface elasticity and surface bending stresses. Surface gradients of bending stresses provide additional anisotropic contributions to the capillary pressure that may renormalize the classical displacement and curvature forces that exist in any fluid fiber. The exact nature (stabilizing and destabilizing) and magnitude of the renormalization of the displacement and curvature forces depend on the nematic orientation and the anisotropic contribution to the surface energy, and accordingly capillary instabilities may be axisymmetric or non-axisymmetric, with finite or unbounded wavelengths. Thus, the classical fiber-to-droplet transformation is one of several possible instability pathways while others include surface fibrillation. The contribution of the viscosity ratio to the capillary instabilities of a thin nematic fiber in a viscous matrix is analyzed by two parameters, the fiber and matrix Ohnesorge numbers, which represent the ratio between viscous and surface forces in each phase. The capillary instabilities of a thin nematic fiber in a viscous matrix are suppressed by increasing either fiber or matrix Ohnesorge number, but estimated droplet sizes after fiber breakup in axisymmetric instabilities decrease with increasing matrix Ohnesorge number. Received November 26, 2001 / Published online May 21, 2002 Communicated by Epifanio Virga, Pavia     

An experimental study of flow-induced fiber orientation and concentration distributions in a concentrated suspension flow through a slit channel containing a cylinder

Flow-induced fiber orientation and concentration distributions were measured in a concentrated fiber suspension (CFS) and a dilute one (DFS). The channel has a thin slit geometry containing a circular cylinder. In the previous work, many researchers have qualitatively studied fiber orientation and concentration distributions in injection-molded products of fiber-reinforced plastics. In the present work, however, they are quantitatively estimated by direct observation of fibers in the concentrated suspension flow. For the CFS, some fibers rotate in an expansion part between the channel wall and the circular cylinder, and the fiber orientation becomes almost random state. On the other hand, fibers are perfectly aligned along the flow direction owing to the elongational flow near the centerline downstream of the cylinder. The fiber concentration has a flat distribution except near the channel wall and the centerline. For the DFS a minimum in the fiber concentration distribution was clearly observed on the centerline, and two peaks beside the centerline and near the channel wall. This characteristic distribution is caused by the fiber-wall and fiber-cylinder interactions. It is found that the obstacle such as the circular cylinder in the channel significantly affects the fiber orientation downstream of the obstacle for the CFD, while it affects the fiber concentration distribution for the DFS.