Anisotropic Boundary Conditions Research Articles

Full discretization of the time dependent Navier–Stokes equations with anisotropic slip boundary condition coupled with the convection–diffusion–reaction equation

Full discretization of the time dependent Navier–Stokes equations with anisotropic slip boundary condition coupled with the convection–diffusion–reaction equation

Birefringence-modulated total internal reflection in liquid crystal shells

The combination of anisotropic boundary conditions and topological constraints acting on a spherical shell of nematic liquid crystal confined between aqueous phases gives rise to peculiar but well-defined configurations of the director field, and thus of the optic axis that defines the impact of the nematic birefringence. While the resulting optics of nematic shells has been extensively investigated in transmission, studies of the reflection behavior are scarce. Here we show that nematic shells exhibit specific light guiding paths mediated by birefringence-modulated total internal reflection (TIR) within the shell. With stabilizers promoting tangential boundary conditions, shells show immobile antipodal spots revealing the locations of maximum effective refractive index, but their intensity is modulated by the polarization of the illuminating light. With normal-aligning stabilizers, shells instead show bright arcs separated by dark spots, and these follow the rotation of the polarization of the illuminating light. Reflection polarizing microscopy thus offers a valuable complement to the more common characterization in transmission, adding data that can be helpful for accurately mapping out director fields in shells of any liquid crystal phase. Moreover, the TIR-mediated light guiding paths may offer interesting handles to localize photopolymerization of reactive liquid crystal shells or to dynamically modulate the response of light-triggered liquid crystal elastomer shell actuators.

Effect of anisotropy and boundary conditions on Darcy and Brinkman porous penetrative convection

We investigate the effects of anisotropic permeability and changing boundary conditions upon the onset of penetrative convection in a porous medium of Darcy type and of Brinkman type. Attention is focussed on the critical eigenfunctions which show how many convection cells will be found in the porous layer. The number of cells is shown to depend critically upon the ratio of vertical to horizontal permeability, upon the Brinkman coefficient, and upon the upper boundary condition for the velocity which may be of Dirichlet type or constant pressure. The critical Rayleigh numbers and wave numbers are determined, and it is shown how an unconditional threshold for nonlinear stability may be derived.HighlightsShows how number of convection cells depends upon the temperature of the upperlayer and the anisotropy of the permeabilityShows how number of convection ceels depends upon the temperature of the upperlayer and the Brinkman coefficientShows how number of convection cells patters depends upon the upper boundarycondition on the velocity or the ambient pressure

Anisotropic slip boundary condition for three-dimensional lattice Boltzmann simulations of liquid microflows

To explore the anisotropic slip on hydrophobic surfaces, a new anisotropic slip boundary condition is proposed for three-dimensional simulations of liquid microflows using the lattice Boltzmann method with adjustable streamwise/spanwise slip length. The proposed boundary condition is derived based on the moment method, which is no longer limited to the assumption of the unidirectional steady flow. Numerical tests validated the effectiveness of the proposed method. Compared with the bounce-back and specular reflection scheme, the proposed method is more accurate and stable for capturing velocity profiles. The proposed method was applied to explore the effects of anisotropic slip on three-dimensional micro-lid-driven cavity flow. The numerical simulation results showed that the anisotropic slip has a greater influence on the flow than the pure streamwise/spanwise slip, and the streamwise slip plays a more important role in influencing the flow than the spanwise slip. The findings may hold significance for efficient development of microfluidic systems and micro-devices.

Three-Dimensional Simulations of Anisotropic Slip Microflows Using the Discrete Unified Gas Kinetic Scheme.

The specific objective of the present work study is to propose an anisotropic slip boundary condition for three-dimensional (3D) simulations with adjustable streamwise and spanwise slip length by the discrete unified gas kinetic scheme (DUGKS). The present boundary condition is proposed based on the assumption of nonlinear velocity profiles near the wall instead of linear velocity profiles in a unidirectional steady flow. Moreover, a 3D corner boundary condition is introduced to the DUGKS to reduce the singularities. Numerical tests validate the effectiveness of the present method, which is more accurate than the bounce-back and specular reflection slip boundary condition in the lattice Boltzmann method. It is of significance to study the lid-driven cavity flow due to its applications and its capability in exhibiting important phenomena. Then, the present work explores, for the first time, the effects of anisotropic slip on the two-sided orthogonal oscillating micro-lid-driven cavity flow by adopting the present method. This work will generate fresh insight into the effects of anisotropic slip on the 3D flow in a two-sided orthogonal oscillating micro-lid-driven cavity. Some findings are obtained: The oscillating velocity of the wall has a weaker influence on the normal velocity component than on the tangential velocity component. In most cases, large slip length has a more significant influence on velocity profiles than small slip length. Compared with pure slip in both top and bottom walls, anisotropic slip on the top wall has a greater influence on flow, increasing the 3D mixing of flow. In short, the influence of slip on the flow field depends not only on slip length but also on the relative direction of the wall motion and the slip velocity. The findings can help in better understanding the anisotropic slip effect on the unsteady microflow and the design of microdevices.

Fluid Injection Under Differential Confinement

Laboratory studies of cavity initiation and propagation in weak or cohesionless materials rely on post-test observations to assess fracture geometry. The experimental setup in this work is a Hele-Shaw cell, which allows for visualization of cavity initiation and propagation within the sand pack, modified to apply differential confinement to a fully 3D specimen. Injection experiments with glycerine at different concentrations and at varying injection rates were conducted with anisotropic boundary conditions on loose sand. The fracture initiation and evolution were observed under various flow rates and viscosities. Infiltration and dislocation of particles were the main mechanisms observed in the tests. Fracture-like channels initially developed in a circular shape due to cavity expansion but then formed rod shapes (shear bands, material fluidization) where an anisotropic stress was applied. This transition from circular to elongated cavity appeared earlier in the tests with higher viscosity fluids, while higher injection rates produced wider openings as the larger volume of fluid was able to displace more particles. Although the cavity showed directionality in all cases, it became less confined to the propagating plane as the flow rate increased. For higher viscosities, the cavities tended to be more circular, whilst for lower viscosities, the cavities showed more directionality. Article Highlights.

Linear stability and energy stability of plane Poiseuille flow with isotropic and anisotropic slip boundary conditions

The linear stability and energy stability of the plane Poiseuille flow with the isotropic and anisotropic slip boundary conditions are theoretically analyzed and numerically calculated in this paper. The asymptotic expansions of the critical parameters for the linear stability and energy stability are derived from the eigenvalue equations characterizing the least stable modes. The critical Reynolds number for the linear stability based on 1.5 times of the bulk mean streamwise velocity is found to be Rl2D≈(1+2741l2)R02D when the non-dimensional isotropic slip length l ≪ 1, where R02D≈5772 is the critical Reynolds number under the no-slip boundary condition. The critical Reynolds numbers for the linear stability are calculated for a wide range of anisotropic slip lengths and are found to be no larger than their counterparts in the isotropic slip cases with the same streamwise slip lengths. In the energy stability analyses of the two-dimensional and three-dimensional plane Poiseuille flows with the isotropic slip boundary condition, the critical Reynolds numbers are found to be RlE2D≈(1+14.95l2)R0E2D and RlE3D≈(1+8.37l2)R0E3D, where R0E2D≈87.6 and R0E3D≈49.6 are their counterparts under the no-slip boundary condition. In the three-dimensional plane Poiseuille flow with the anisotropic slip boundary condition, the critical Reynolds number for the energy stability increases with the increase in streamwise slip length lx and with the decrease in spanwise slip length lz, and its first-order approximation is Rlx,lzE3D≈[1+2.41(lx−lz)]R0E3D.

Numerical and experimental evaluation of the anisotropic behavior and boundary condition of a structural concrete

In this study, an evaluation of the effect of casting and loading direction as well as the boundary condition at the interface of loading platen and specimen of a structural concrete, is presented. This work allows to measure experimentally, the influence of the boundary conditions created by the loading platen and the concrete specimen. The experimental tests shows that the ratio between the unconfined and confined compressive strength, measured in cube samples, is on average 0.35. Therefore, it is possible to observe that the increase of axial compressive strength due to confinement is high. By utilizing the Lattice Discrete Element Method (LDEM) implemented on Abaqus/Explicit software, a detailed study and analysis is carried out on the influence of the boundary condition on the concrete strength, the influence of the loading direction relative to the casting direction as well as the interaction of these two parameters. To conduct this study, an implementation of LDEM is proposed. With the LDEM simulations it is possible to find the same behavior observed experimentally, both in changing boundary conditions and in the direction of casting and loading. The fracture mechanism found with LDEM predicts that for a Fixed boundary condition, the loading direction is not so significant. However, the effect of the loading direction is maximized when the boundary condition is frictionless. Through the use of LDEM, it is possible to capture the magnitude and the failure mechanism that occurs in this case. The degree of confidence of the results was validated through analysis of variance (ANOVA multiple factors) and a correlation was found.

Modeling of Magnetically Biased Graphene Coupler at Terahertz Frequency Through an Improved Anisotropic WCIP Method

This article presents an improved anisotropic wave concept iterative process (WCIP) algorithm for the analysis of a novel type of tunable graphene-based coupler at the terahertz band for different physical graphene parameters. Through the novel technique of implementation of the anisotropic boundary conditions in the WCIP method, we can integrate the anisotropic surface conductivity matrix into this algorithm without implying a volumetric discretization. Numerical examples are presented to verify the efficiency of the proposed algorithm. The numerical simulation results demonstrate that the performance of the coupler can be controlled by varying the chemical potential and the magnetic field, and a little change was obtained with the variation of the relaxation time and the temperature of graphene.

Large graphene-induced shift of surface-plasmon resonances of gold films: Effective-medium theory for atomically thin materials

Despite successful modeling of graphene as a 0.34-nm thick optical film synthesized by exfoliation or chemical vapor deposition (CVD), graphene induced shift of surface plasmon resonance (SPR) of gold films has remained controversial. Here we report the resolution of this controversy by developing a clean CVD graphene transfer method and extending Maxwell-Garnet effective medium theory (EMT) to 2D materials. A SPR shift of 0.24 is obtained and it agrees well with 2D EMT in which wrinkled graphene is treated as a 3-nm graphene/air layered composite, in agreement with the average roughness measured by atomic force microscope. Because the anisotropic built-in boundary condition of 2D EMT is compatible with graphene's optical anisotropy, graphene can be modelled as a film thicker than 0.34-nm without changing its optical property; however, its actual roughness, i.e., effective thickness will significantly alter its response to strong out-of-plane fields, leading to a larger SPR shift.

Some comments on electromagnetic oscillations in anisotropic cavities-wave equations and boundary conditions

Some comments on electromagnetic oscillations in anisotropic cavities-wave equations and boundary conditions

Coulomb-like elastic interaction induced by symmetry breaking in nematic liquid crystal colloids

It is generally thought that colloidal particles in a nematic liquid crystal do not generate the first multipole term called deformation elastic charge as it violates the mechanical equilibrium. Here, we demonstrate theoretically and experimentally that this is not the case, and deformation elastic charges, as well as dipoles and quadrupoles, can be induced through anisotropic boundary conditions. We report the first direct observation of Coulomb-like elastic interactions between colloidal particles in a nematic liquid crystal. The behaviour of two spherical colloidal particles with asymmetric anchoring conditions induced by asymmetric alignment is investigated experimentally; the interaction of two particles located at the boundary of twist and parallel aligned regions is observed. We demonstrate that such particles produce deformation elastic charges and interact by Coulomb-like interactions.

A recursive methodology for the solution of semi-analytical rectangular anisotropic thin plates in linear bending

• Novel application of Adomian Decomposition Method for elasticity problems. • New semi-analytical solutions of anisotropic thin plate in bending. • A new recursive methodology driven by a constitutive decomposition. • A starting isotropic solution progressively enhanced by anisotropic influence. • Plate results for several aspect and anisotropic ratios and boundary conditions. A new recursive methodology is introduced to solve anisotropic thin plates bending problems, which is based on three concepts: (a) the plate differential operator additively decomposed obeying a material constitutive hierarchy; (b) the plate displacement field expanded into an infinite series and (c) an homotopy-like scheme applied to determine each term of the series. The pb-2 Rayleigh–Ritz Method is adopted to construct the solution space. Convergence conditions are presented and related to the differential operator decomposition and material’s anisotropy degree. Different cases of geometry, loading and boundary conditions were studied using the methodology and excellent agreement with available solutions was found.

Flat Optics for Surface Waves

The name flat optics (FO) has been introduced in a recent paper by Capasso’s group for denoting light-wave manipulations through a general type of penetrable or impenetrable metasurfaces (MTSs). There, the attention was focused on plane waves, whereas here we treat surface waves (SWs) excited on impenetrable impedance surfaces. Space variability of the boundary conditions imposes a deformation of the SW wavefront, which addresses the local wavector along not-rectilinear paths. The ray paths are subjected to an eikonal equation analogous to the one for geometrical optics (GO) rays in graded index materials. The basic relations among ray paths, ray velocity, and transport of energy for both isotropic and anisotropic boundary conditions are presented for the first time. This leads to an elegant formulation which allows for closed form analysis of flat operational devices (lenses or beam formers), giving a new guise to old concepts. It is shown that when an appropriate transformation is found, the ray paths can be conveniently controlled without the use of ray tracing, thus simplifying the problem and leading to a flat version of transformation optics, which is framed here in the general FO theory.

Modeling of Magnetized Graphene From Microwave to THz Range by DGTD With a Scalar RBC and an ADE

This paper presents a discontinuous Galerkin time-domain (DGTD) method for the transient analysis of magnetized graphene from the microwave to terahertz (THz) frequencies. By considering the atom thick graphene layer as an infinitely thin conductive sheet with finite surface conductivity, a frequency-dependent anisotropic resistive boundary condition (RBC) is obtained. Based on this RBC, the direct volumetric discretization of graphene layer is avoided. Instead of directly deriving the numerical flux for DGTD considering the presence of this anisotropic and dispersive RBC, an auxiliary surface polarization current governed by a first-order time-dependent partial differential equation (PDE) is introduced over the graphene with the purpose to obtain an isotropic and simultaneously nondispersive RBC. In this way, the new formulated numerical flux expression derived from the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Rankine–Hugoniot jump relations</i> is isotropic, and no time-domain convolution is involved in the finalized matrix equations. To verify the applicability and accuracy of the proposed algorithm, the Faraday rotation and the surface plasmon resonance of a plane wave through magnetically biased graphene are investigated. For open-region scattering problems, a hybrid DGTD and time-domain boundary integral (TDBI) method is applied to rigorously truncate the computational domain.

Metasurface transformation for surface wave control.

Metasurfaces (MTSs) constitute a class of thin metamaterials used for controlling plane waves and surface waves (SWs). At microwave frequencies, they are constituted by a metallic texture with elements of sub-wavelength size printed on thin grounded dielectric substrates. These structures support the propagation of SWs. By averaging the tangential fields, the MTSs can be characterized through homogenized isotropic or anisotropic boundary conditions, which can be described through a homogeneous equivalent impedance. This impedance can be spatially modulated by locally changing the size/orientation of the texture elements. This allows for a deformation of the SW wavefront which addresses the local wavevector along not-rectilinear paths. The effect of the MTS modulation can be analysed in the framework of transformation optics. This article reviews theory and implementation of this MTS transformation and shows some examples at microwave frequencies.

Mechanical Boundary Conditions Bias Fibroblast Invasion in a Collagen-Fibrin Wound Model

Because fibroblasts deposit the collagen matrix that determines the mechanical integrity of scar tissue, altering fibroblast invasion could alter wound healing outcomes. Anisotropic mechanical boundary conditions (restraint, stretch, or tension) could affect the rate of fibroblast invasion, but their importance relative to the prototypical drivers of fibroblast infiltration during wound healing—cell and chemokine concentration gradients—is unknown. We tested whether anisotropic mechanical boundary conditions affected the directionality and speed of fibroblasts migrating into a three-dimensional model wound, which could simultaneously expose fibroblasts to mechanical, structural, steric, and chemical guidance cues. We created fibrin-filled slits in fibroblast-populated collagen gels and applied uniaxial mechanical restraint along the short or long axis of the fibrin wounds. Anisotropic mechanical conditions increased the efficiency of fibroblast invasion by guiding fibroblasts without increasing their migration speed. The migration behavior could be modeled as a biased random walk, where the bias due to multiple guidance cues was accounted for in the shape of a displacement orientation probability distribution. Taken together, modeling and experiments suggested an effect of strain anisotropy, rather than strain-induced fiber alignment, on fibroblast invasion.

Mechanically Guided Cell Migration: Less of a Stretch than Ever

Mechanically Guided Cell Migration: Less of a Stretch than Ever

Characteristics of journal bearings with anisotropic slip

The effects of anisotropic slip on the lubrication performances of journal bearings are analyzed. The anisotropic slip boundary conditions on bearing surfaces or/and on journal surfaces are modeled from Navier slip boundary condition with orthogonal principal slip lengths. The modified Reynolds equation considering anisotropic slip is then derived and solved numerically by the finite element method. The effects of principal slip lengths on the load capacities and friction force of journal bearings are discussed. The related Couette and Poiseuille flow correctors in the modified Reynolds equation and in the shear stress are presented to assist our discussion.

Influence of an anisotropic slip-length boundary condition on turbulent channel flow

The effects of an anisotropic Navier slip-length boundary condition on turbulent channel flow are investigated parametrically by direct numerical simulations. The slip-length boundary condition is made direction dependent by specifying the value of the slip length independently for the streamwise and spanwise direction. The change in drag is mapped versus a wide range of streamwise and spanwise slip-length combinations at two different friction Reynolds numbers, \documentclass[12pt]{minimal}\begin{document}$Re_{\tau _0}=180$\end{document}Reτ0=180 and \documentclass[12pt]{minimal}\begin{document}$Re_{\tau _0}=360$\end{document}Reτ0=360. For moderate slip lengths both drag-reducing and drag-increasing slip-length combinations are found. The percentage drag increase saturates at approximately 60% for high spanwise slip. Once a threshold value for the streamwise slip length is exceeded, drag is reduced in all cases irrespective of the value of the spanwise slip length. The Reynolds number appears to have only little influence on the change in drag for the moderate Reynolds numbers studied here. A detailed comparison with the implicit theoretical formula of Fukagata et al. [Phys. Fluids 18, 051703 (2006)], which relates the change in drag with the streamwise and spanwise slip length, has been made. In general, this formula gives a fair representation of the change in drag; a modified version of this relation is presented, which improves the prediction for the change in drag for small slip length values and reduces the number of free parameters contained in the model. The effects of the slip-length boundary condition on the flow are further investigated using mean flow and turbulence statistics. For drag-neutral slip-length combinations the level of turbulent fluctuations is approximately unchanged. The presence of a slip-length boundary condition affects both the level of wall-shear stress fluctuations and the degree of intermittency of the wall-shear stress probability density function. The correlation statistics of the velocity field show that a high spanwise slip length causes a disruption of the near-wall streaks, while high streamwise slip favours an increasing streak regularity.