Vesicle dynamics in time-dependent elongation flow: wrinkling instability

We present experimental results on the relaxation dynamics of vesicles subjected to a time-dependent elongation flow. We observed and characterized a new instability, which results in the formation of higher-order modes of the vesicle shape (wrinkles), after a switch in the direction of the velocity gradient. This surprising generation of membrane wrinkles can be explained by the appearance of a negative surface tension during the vesicle deflation, which tunes itself to alternating stress. Moreover, the formation of buds in the vesicle membrane was observed in the vicinity of the dynamical transition point.     

Elastic response and wrinkling onset of curved elastic membranes subjected to indentation test

Starting from a polymeric-fluid droplet, by vulcanization of the fluid free surface, curved elastic membranes, several nanometers thick and a few millimeters in diameter, which enclose a constant fluid volume, are produced. In an indentation-type test, carried out by pushing the membrane along its normal by means of a micro-needle, under some conditions, wrinkles are likely to appear around the contact region. Interestingly, we observe that the instability does not significantly alter the force-displacement relation: the relation between the force and the displacement remains linear and the associated stiffness is simply proportional to the tension of the membrane. In addition, we determine that the wrinkles develop when the stretching modulus of the membrane compares with its tension, which provides a useful method to estimate the elastic constant.     

Wrinkle formations in axi-symmetrically stretched membranes

We study experimentally the main features of wrinkles that form in an initially stretched and flat elastic membrane when subjected to an axi-symmetric traction force at the center. The wavelength and amplitude of the wrinkle pattern are accurately characterized as the membrane tension and the traction forced are varied. We show that wrinkles are the result of a supercritical instability and appear for a well-defined critical traction force that is a function of the membrane tension. Wrinkle length and amplitude increase as the traction force is increased further. By contrast, both quantities decrease as the membrane tension is increased. Calculations based on symmetry arguments and elastic-energy minimization are in good agreement with experiments and provide a simple way to investigate configurations that are difficult to access experimentally. Such problems include wrinkles in elastic nano-films on finite-thickness viscous substrates used in semiconductor technology or in cellular forces detection.Received: 10 August 2004, Published online: 19 October 2004PACS: 46.32. + x Static buckling and instability - 87.19.St Movement and locomotion - 85.40.Ls Metallization, contacts, interconnects; device isolationJ.-C. Géminard: Permanent address: Laboratoire de Physique, Ecole Normale Supérieure de Lyon, 64, Allée dItalie, 69364 Lyon cedex 07, France     

耦合界面张力的三维流体界面不稳定性的格子Boltzmann模拟

采用介观格子Boltzmann方法模拟界面张力作用下三维流体界面的Rayleigh-Taylor (RT)不稳定性的增长过程,主要分析表面张力对流体界面动力学行为及尖钉和气泡后期增长的影响机制.首先发现三维RT不稳定性的发生存在临界表面张力(σ_c),其值随着流体Atwood数的增大而增大,且数值预测值与理论分析结果σ_c=(ρ_h-ρ₁)g/k~2一致.另外,随着表面张力的增大,不稳定性演化过程中界面卷吸程度和结构复杂性逐渐减弱,系统中界面破裂形成离散液滴的数目也显著减少.相界面的后期动力学行为也从非对称发展转向始终保持关于中轴线对称.尖钉与气泡振幅在表面张力较小时对其变化不显著,当表面张力增大到一定值后,可以有效地抑制尖钉与气泡振幅的增长.进一步发现,高雷诺数三维RT不稳定性在不同表面张力下均经历4个不同的发展阶段:线性阶段、饱和速度阶段、重加速和混沌混合阶段.尖钉与气泡在饱和速度阶段以近似恒定的速度增长,其渐进速度的值与修正的势流理论模型结果一致.受非线性Kelvin-Helmholtz旋涡的剪切作...     

Darrieus–Landau instability of premixed flames enhanced by fuel droplets

Recent experiments on spray flames propagating in a Wilson cloud chamber have established that spray flames are much more sensitive to wrinkles or corrugations than single-phase flames. To propose certain elements of explanation, we numerically study the Darrieus–Landau (or hydrodynamic) instability (DL-instability) developing in premixtures that contain an array of fuel droplets. Two approaches are compared: numerical simulation starting from the general conservation laws in reactive media, and the numerical computation of Sivashinsky-type model equations for DL-instability. Both approaches provide us with results in deep agreement. It is first shown that the presence of droplets in fuel–air premixtures induces initial perturbations which are large enough to trigger the DL-instability. Second, the droplets are responsible for additional wrinkles when the DL-instability is developed. The latter wrinkles are of length scales shorter than those of the DL-instability, in such a way that the DL-unstable spray flames have a larger front surface and therefore propagate faster than the single-phase ones when subjected to the same instability.     

Limits of filopodium stability

Filopodia are long, fingerlike membrane tubes supported by cytoskeletal filaments. Their shape is determined by the stiffness of the actin filament bundles found inside them and by the interplay between the surface tension and bending rigidity of the membrane. Although one might expect the Euler buckling instability to limit the length of filopodia, we show through simple energetic considerations that this is in general not the case. By further analyzing the statics of filaments inside membrane tubes, and through computer simulations that capture membrane and filament fluctuations, we show under which conditions filopodia of arbitrary lengths are stable. We discuss several in vitro experiments where this kind of stability has already been observed. Furthermore, we predict that the filaments in long, stable filopodia adopt a helical shape.     

Wrinkling of pressurized elastic shells

We study the formation of localized structures formed by the point loading of an internally pressurized elastic shell. While unpressurized shells (such as a ping-pong ball) buckle into polygonal structures, we show that pressurized shells are subject to a wrinkling instability. We study wrinkling in depth, presenting scaling laws for the critical indentation at which wrinkling occurs and the number of wrinkles formed in terms of the internal pressurization and material properties of the shell. These results are validated by numerical simulations. We show that the evolution of the wrinkle length with increasing indentation can be understood for highly pressurized shells from membrane theory. These results suggest that the position and number of wrinkles may be used in combination to give simple methods for the estimation of the mechanical properties of highly pressurized shells.     

The Compressible Viscous Surface-Internal Wave Problem: Stability and Vanishing Surface Tension Limit

This paper concerns the dynamics of two layers of compressible, barotropic, viscous fluid lying atop one another. The lower fluid is bounded below by a rigid bottom, and the upper fluid is bounded above by a trivial fluid of constant pressure. This is a free boundary problem: the interfaces between the fluids and above the upper fluid are free to move. The fluids are acted on by gravity in the bulk, and at the free interfaces we consider both the case of surface tension and the case of no surface forces. We establish a sharp nonlinear global-in-time stability criterion and give the explicit decay rates to the equilibrium. When the upper fluid is heavier than the lower fluid along the equilibrium interface, we characterize the set of surface tension values in which the equilibrium is nonlinearly stable. Remarkably, this set is non-empty, i.e., sufficiently large surface tension can prevent the onset of the Rayleigh-Taylor instability. When the lower fluid is heavier than the upper fluid, we show that the equilibrium is stable for all non-negative surface tensions and we establish the zero surface tension limit.     

Attainable superheating of solutions of cryogenic liquids

The kinetics of spontaneous boiling-up of superheated binary solutions of cryogenic liquids is studied. Within the framework of the Kramers-Zeldovich method, an expression is obtained for the steady state rate of homogeneous nucleation in a solution that takes into account free-molecular and diffusion regimes of the substance supply to a growing bubble. Viscous and inertial forces are also taken into account in the study of the nucleus growth dynamics. The work of critical nucleus formation is determined within the framework of the Gibbs and van der Waals capillarity theories. The dependence of the surface tension of critical bubbles in the solution on their size is investigated. The temperature of attainable superheating and nucleation rates in superheated solutions of cryogenic liquids with complete or partial solubility of the components are determined by a method of lifetime measurement. The experiments were conducted in a wide range of pressures and solution concentrations. The measurement results are compared with the theory of homogeneous nucleation taking or not taking into account the size effect in nucleation. It has been found that, by taking into account the size dependence of the surface tension of a nucleus, better agreement between the theory and experiment is obtained. The boundary of essential instability of the solution, that is, the diffusion spinodal, is computed.     

Turbulent propagation of premixed flames in the presence of Darrieus–Landau instability

We investigate the role played by hydrodynamic instability in the wrinkled flamelet regime of turbulent combustion, where the intensity of turbulence is small compared to the laminar flame speed and the scale large compared to the flame thickness. To this end the Michelson–Sivashinsky (MS) equation for flame front propagation in one and two spatial dimensions is studied in the presence of uncorrelated and correlated noise representing a turbulent flow field. The combined effect of turbulence intensity, integral scale, and an instability parameter related to the Markstein length are examined and turbulent propagation speed monitored for both stable planar flames and corrugated flames for which the planar conformation is unstable. For planar flames a particularly simple scaling law emerges, involving quadratic dependence on intensity and a linear dependence on the degree of instability. For corrugated flames we find the dependence on intensity to be substantially weaker than quadratic, revealing that corrugated flames are more resilient to turbulence than planar flames. The existence of a threshold turbulence intensity is also observed, below which the corrugated flame in the presence of turbulence behaves like a laminar flame. We also analyze the conformation of the flame surface in the presence of turbulence, revealing primary, large-scale wrinkles of a size comparable to the main corrugation. When the integral scale is much smaller than the characteristic corrugation length we observe, in addition to primary wrinkles, secondary small-scale wrinkles contaminating the surface. The flame then acquires a multi-scale, self-similar conformation, with a fractal dimension, for one-dimensional flames, plateauing at 1.23 for large intensities. The existence of an intermediate integral scale is also found at which the turbulent speed is maximized. When two-dimensional flames are subject to turbulence, the primary wrinkling patterns give rise to polyhedral-cellular structures which bear a very close resemblance to those observed in experiments on hydrodynamically unstable expanding spherical flames.     

Point-vortex cluster formation in the plane and on the sphere: an energy bifurcation condition

The dynamics of a system of point vortices is considered in the plane and on the sphere. Particular attention is given to the formation of vortex clusters and to global vortex dynamics, especially in the spherical case. For integrable systems and systems with given symmetries, we show the existence of a critical energy above or below which (depending on the geometry of the surface) the system splits into clusters and vortex dynamics is confined to a particular region. The case of nonidentical vortices is of particular interest since we observe quite different global dynamics depending on the energy and the initial conditions. Furthermore we identify all the relative equilibria configurations as critical points of the reduced energy and we give an instability criterion to deduce instability for certain configurations.     

Buckling resistance of solid shell bubbles under ultrasound

Thin solid shell contrast agents bubbles are expected to undergo different volume oscillating behaviors when the acoustic power is increased: small oscillations when the shell remains spherical, and large oscillations when the shell buckles. Contrary to bubbles covered with thin lipidic monolayers that buckle as soon as compressed: the solid shell bubbles resist compression, making the buckling transition abrupt. Numerical simulations that explicitly incorporate a shell bending modulus give the critical buckling pressure and post-buckling shape, and show the appearance of a finite number of wrinkles. These findings are incorporated in a model based on the concept of effective surface tension. This model compares favorably to experiments when adjusting two main parameters: the buckling tension and the rupture shell tension. The buckling tension provides a direct estimation of the acoustic pressure threshold at which buckling occurs.     

黏性、表面张力和磁场对Rayleigh-Taylor不稳定性气泡演化影响的理论分析

采用理论分析的方法考察了磁场中非理想流体中Rayleigh-Taylor(RT)不稳定性气泡的演化过程,在与磁场垂直的平面中,综合考虑流体黏性和表面张力的影响,推导了二维非理想磁流体RT不稳定性气泡运动的控制方程组,给出了不同情况下气泡速度的渐近解和数值解,分析了流体黏性、表面张力和磁场对气泡发展的影响,分析结果表明:流体黏性和表面张力能够降低气泡速度和振幅,即能够抑制RT不稳定性;而磁场对RT不稳定性的影响是由非线性部分引起的,并且磁场非线性部分的方向决定了磁场是促进还是抑制RT不稳定性的发展,     

Effect of the configuration of a wrinklon on the distributions of the energy and elastic strain in a graphene nanoribbon

The formation of wrinkles in thin membranes is a widespread phenomenon. In particular, wrinkles can appear in graphene, which is the thinnest natural membrane, and affect its properties. A region where wrinkles with different wavelengths are linked is called wrinklon. Conditions of the fixing of an elastically deformed graphene sheet dictate a certain wavelength of wrinkles near the fixed edge. Wrinkles with a longer wavelength become more energetically favorable with an increase in the distance from the edge. As a result, wrinklons appear and reduce the potential energy of the system by uniting wrinkles into larger wrinkles with an increase in the distance from the edge. The possibility of implementing various equilibrium configurations of wrinklons at given plane strains in graphene has been demonstrated by the molecular quasistatic method. The distributions of the energy and elastic strain components in wrinklons with various configurations for nanoribbons with different widths have been calculated.     

化学气相沉积法制备的石墨烯晶畴的氢气刻蚀

利用化学气相沉积法在抛光铜衬底上制备出六角形石墨烯晶畴, 并且在高温条件下对石墨烯晶畴进行氢气刻蚀, 利用光学显微镜和扫描电子显微镜对石墨烯晶畴进行观测, 发现高温条件下石墨烯晶畴表面能够被氢气刻蚀出网络状和线状结构的刻蚀条纹. 通过电子背散射衍射测试证明了刻蚀条纹的形态、密度与铜衬底的晶向有密切关系. 通过对比实验证明了石墨烯表面上的刻蚀条纹是由于石墨烯和铜衬底的热膨胀系数不同, 在降温过程中, 石墨烯表面形成了褶皱, 褶皱在高温氢气气氛下发生氢化反应形成的. 对转移到二氧化硅衬底的石墨烯晶畴进行原子力显微镜测试, 测试结果表明刻蚀条纹的形貌、密度与石墨烯表面褶皱的形貌、密度十分相似. 进一步证明了刻蚀条纹是由于褶皱结构被氢气刻蚀引起的. 实验结果表明, 即使在六角形石墨烯晶畴表面也存在褶皱和点缺陷. 本文提供了一种便捷的方法来观察铜衬底上石墨烯褶皱的分布与形态; 同时, 为进一步提高化学气相沉积法制备石墨烯的质量提供了更多参考.     

柔性基周期性厚度梯度薄膜的应变效应

可控的表面微结构在柔性电子、仿生器件和能源材料等方面均具有重要的应用价值.本文采用编织铜网作为掩模板,利用磁控溅射技术在柔性聚二甲基硅氧烷(PDMS)基底上制备具有周期分布的厚度梯度金属银薄膜,研究了薄膜在单轴压缩/拉伸过程中的形貌演化规律.实验发现,在单轴机械载荷作用下,银薄膜表面将形成相互垂直的条纹褶皱和多重裂纹.膜厚的梯度变化调制了薄膜的面内应力分布,导致褶皱在膜厚较小处率先形成,并逐渐扩展到膜厚较大区域,而裂纹则基本限定在膜厚较小区域.基于应力理论和有限元计算,对周期性厚度梯度薄膜的褶皱和裂纹的形貌特征、演化行为和物理机制进行了深入分析.该研究将有助于加深对非均匀薄膜体系的应变效应的理解,并有望通过梯度薄膜的结构设计在柔性电子等领域获得应用.     

Shear instabilities in granular mixtures

Dynamical instabilities in fluid mechanics are responsible for a variety of important common phenomena, such as waves on the sea surface or Taylor vortices in Couette flow. In granular media dynamical instabilities have just begun to be discovered. Here we show by means of molecular dynamics simulation the existence of a new dynamical instability of a granular mixture under oscillating horizontal shear, which leads to the formation of a striped pattern where the components are segregated. We investigate the properties of such a Kelvin-Helmholtz-like instability and show how it is connected to pattern formation in granular flow and segregation.     

各向异性表面张力对深胞晶界面形态稳定性的影响

应用匹配渐近展开法和多变量展开法研究各向异性表面张力对定向凝固中深胞晶界面形态稳定性的影响, 通过寻找定向凝固系统的模式解获得了深胞晶界面形态满足的量子化条件. 结果表明, 与各向同性的定向凝固系统中深胞晶界面形态稳定性比较, 考虑各向异性表面张力的定向凝固中深胞晶生长界面形态也有两种整体不稳定性机制: 整体波动不稳定性和低频不稳定性. 随着各向异性表面张力的增加, 中性模式产生强振荡的枝晶结构的整体波动不稳定性的不稳定区域减小, 中性模式产生弱振荡的胞晶结构的低频不稳定性的不稳定区域增加.     

Crumpling of a stiff tethered membrane

A first-principles numerical model for crumpling of a stiff tethered membrane is introduced. This model displays wrinkles, ridge formation, ridge collapse, and initiation of stiffness divergence. The amplitude and wavelength of the wrinkles and the scaling exponent of the stiffness divergence are consistent with both theory and experiment. Close to the stiffness divergence further buckling is hindered by the nonzero thickness of the membrane, and its elastic behavior becomes similar to that of dry granular media. No change in the distribution of contact forces can be observed at the crossover, implying that the network of ridges is then simultaneously a granular force-chain network.     

Friction of wrinkles

Sufficiently thin elastic sheets wrinkle when they are in contact with a small adhesive counterbody. Despite significant progress on the dynamics of wrinkle formation and morphology, little is known about how wrinkles impede the relative sliding motion of the counterbody. Using molecular dynamics we demonstrate that instabilities are likely to occur during sliding when the wrinkle pattern has asymmetries not present in the counterbody. The instabilities then cause Coulomb's friction law. The behavior can be rationalized in terms of simple models for multistable elastic manifolds.