The height-height correlation function for a fluctuating interface between two coexisting bulk phases is derived by means of general equilibrium properties of the corresponding density-density correlation function. A wavelength-dependent surface tension $γ(\mathbf{q})$ can be defined and expressed in terms of the direct correlation function $c(\mathbf{r},\mathbf{r}')$, the equilibrium density profile $ρ_{\circ}(\mathbf{r})$ and an operator which relates density to surface configurations. Neither the concept of an effective interface Hamiltonian nor the difference in pressure is needed to determine the general structure of the height-height correlations or $γ(\mathbf{q})$, respectively. This result generalizes the Mecke/Dietrich surface tension $\gmd$ (Phys. Rev. E {\bf 59}, p. 6766 (1999)) and modifies recently published criticism concerning $\gmd$ (P. Tarazona, R. Checa and, E.Chacón: Phys. Rev. Lett. {\bf 99}, p. 196101 (2007)).
We deploy linear stability analysis to find the threshold wavelength ($λ$) and surface tension ($γ$) of Rayleigh-Plateau type "peristaltic" instabilities in incompressible neo-Hookean solids in a range of cylindrical geometries with radius $R_0$. First we consider a solid cylinder, and recover the well-known, infinite wavelength instability for $γ\ge6 μR_0$, where $μ$ is the solid's shear modulus. Second, we consider a volume-conserving (e.g.\ fluid filled and sealed) cylindrical cavity through an infinite solid, and demonstrate infinite wavelength instability for $γ\ge 2 μR_0$. Third, we cons…
Dielectric elastomers have recently been proposed for various biologically-relevant applications, in which they may operate in fluidic environments where surface tension effects may have a significant effect on their stability and reliability. Here, we present a theoretical analysis coupled with computational modeling for a generalized electromechanical analysis of surface stability in dielectric elastomers accounting for surface tension effects. For mechanically deformed elastomers, significant increases in critical strain and instability wavelength are observed for small elastocapillary numb…
An adhesively stressed thin film of a soft hydrogel confined between two rigid flat substrates auto-roughens with its dominant wavelength exhibiting pronounced dependence on the film thickness (H). A linear stability analysis confirmed that this long wavelength instability (~7H) is due to an elasto-capillary effect, the implementation of which required direct measurements of the surface tension and the elasticity of the gel. The surface tension of the gel was estimated from the fundamental spherical harmonic of a hemispherical cap of the gel that was excited by an external noise. The shear mod…
Active fluctuations induce buckling of living surfaces
Ludwig-Maximilians-Universität München（慕尼黑大学）；Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München（慕尼黑大学物理系阿诺德·索末菲理论物理中心与纳米科学中心）；Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Helmholtz Centre for Infection Research（赫尔霍兹感染研究中心）；Technische Universität Braunschweig（布伦瑞克工业大学）；Max Planck School Matter to Life（马克斯·普朗克物质生命学院）
The existence and origin of line tension has remained controversial in literature. To address this issue we compute the shape of Lennard-Jones nanodrops using molecular dynamics and compare them to density functional theory in the approximation of the sharp kink interface. We show that the deviation from Young's law is very small and would correspond to a typical line tension length scale (defined as line tension divided by surface tension) similar to the molecular size and decreasing with Young's angle. We propose an alternative interpretation based on the geometry of the interface at the mol…
A theory is presented to account for the increase in surface tension of water in the presence of electrolyte. Unlike the original ``grand-canonical'' calculation of Onsager and Samaras, which relied on the Gibbs adsorption isotherm and lead to a result which could only be expressed as an infinite series, our approach is ``canonical'' and produces an analytic formula for the excess surface tension. For small concentrations of electrolyte, our result reduces to the Onsager-Samaras limiting law.
We show that the electric field driven surface instability of visco-elastic films has two distinct regimes: (1) The visco-elastic films behaving like a liquid display long wavelengths governed by applied voltage and surface tension, independent of its elastic storage and viscous loss moduli, and (2) the films behaving like a solid require a threshold voltage for the instability whose wavelength always scales as ~ 4 x film thickness, independent of its surface tension, applied voltage, loss and storage moduli. Wavelength in a narrow transition zone between these regimes depends on the storage m…
We study the shapes of elastic membranes under the simultaneous exertion of tensile and compressive forces when the translational symmetry along the tension direction is broken. We predict a multitude of novel morphological phases in various regimes of a 2-dimensional parameter space $(ε,ν)$ that defines the relevant mechanical and geometrical conditions. Theses parameters are, respectively, the ratio between compression and tension, and the wavelength contrast along the tension direction. In particular, our theory associates the repetitive increase of pattern periodicity, recently observed on…
We model the elasticity of the cerebral cortex as a layered material with bending energy along the layers and elastic energy between them in both planar and polar geometries. The cortex is also subjected to axons pulling from the underlying white matter. Above a critical threshold force, a "flat" cortex configuration becomes unstable and periodic unduluations emerge, i.e. a buckling instability occurs. These undulations may indeed initiate folds in the cortex. We identify analytically the critical force and the critical wavelength of the undulations. Both quantities are physiologically relevan…
We investigate the effect of an applied electric potential on the mechanics of a coarse grained POPC bilayer under tension. The size and duration of our simulations allow for a detailed and accurate study of the fluctuations. Effects on the fluctuation spectrum, tension, bending rigidity, and bilayer thickness are investigated in detail. In particular, the least square fitting technique is used to calculate the fluctuation spectra. The simulations confirm a recently proposed theory that the effect of an applied electric potential on the membrane will be moderated by the elastic properties of t…
We use computer simulations and a simple free energy model to study the response of a bilayer membrane to the application of a negative (compressive) mechanical tension. Such a tension destabilizes the long wavelength undulation modes of giant vesicles, but it can be sustained when small membranes and vesicles are considered. Our negative tension simulation results reveal two regimes - (i) a weak negative tension regime characterized by stretching-dominated elasticity, and (ii) a strong negative tension regime featuring bending-dominated elastic behavior. This resembles the findings of the cla…
Attempts to extend the capillary-wave theory of fluid interfacial fluctuations to microscopic wavelengths, by introducing an effective wave-vector ($q$) dependent surface tension $σ_\text{eff}(q)$, have encountered difficulties. There is no consensus as to even the shape of $σ_\text{eff}(q)$. By analysing a simple density functional model of the liquid-gas interface, we identify different schemes for separating microscopic observables into background and interfacial contributions. In order for the backgrounds of the density-density correlation function and local structure factor to have a cons…
Wrinkling of stretched elastic sheets is widely observed, and the scaling relations between the amplitude and wavelength of the wrinkles have been proposed by Cerda and Mahadevan. However, the surface effects should be taken into account when the sheet is even thinner. The surface energy was considered in this work, and the discrepancies with the classical theory has been discussed. A dimensionless parameter has been proposed to represent the size-dependence. A method of characterizing mechanical properties of thin film using wrinkles considering surface effects has also been proposed.
The unique pressure exerted by active particles -- the "swim" pressure -- has proven to be a useful quantity in explaining many of the seemingly confounding behaviors of active particles. However, its use has also resulted in some puzzling findings including an \textit{extremely negative} surface tension between phase separated active particles. Here, we demonstrate that this contradiction stems from the fact that the swim pressure \textit{is not a true pressure}. At a boundary or interface, the reduction in particle swimming generates a net active force density -- an entirely \textit{self-gen…
Two different tensions can be defined for a fluid membrane: the internal tension, $γ$, conjugated to the real membrane area in the Hamiltonian, and the frame tension, $τ$, conjugated to the projected (or frame) area. According to the standard statistical description of a membrane, the fluctuation spectrum is governed by $γ$. However, using rotational invariance arguments, several studies argued that fluctuation spectrum must be governed by the frame tension $τ$ instead. These studies disagree on the origin of the result obtained with the standard description yet: either a miscounting of config…
The surface tension of living cells and tissues originates from the generation of nonequilibrium active stresses within the cell cytoskeleton. Here, using laser ablation, we generate gradients in the surface tension of cellular aggregates as models of simple tissues. These gradients of active surface stress drive large-scale and rapid toroidal motion. Subsequently, the motions spontaneously reverse as stresses reaccumulate and cells return to their original positions. Both forward and reverse motions resemble Marangoni flows in viscous fluids. However, the motions are faster than the timescale…
We review recent computer simulation studies of undulating lipid bilayers. Theoretical interpretations of such fluctuating membranes are most commonly based on generalized Helfrich-type elastic models, with additional contributions of local "protrusions" and/or density fluctuations. Such models provide an excellent basis for describing the fluctuations of tensionless bilayers in the fluid phase at a quantitative level. However, this description is found to fail for membranes in the gel phase and for membranes subject to high tensions. The fluctuations of tilted gel membranes show a signature o…
Recent measurements of the short-wavelength (~ 1--100 nm) fluctuations in stacks of lipid membranes have revealed two distinct relaxations: a fast one (decay rate of ~ 0.1 ns^{-1}), which fits the known baroclinic mode of bulk lamellar phases, and a slower one (~ 1--10 μs^{-1}) of unknown origin. We show that the latter is accounted for by an overdamped capillary mode, depending on the surface tension of the stack and its anisotropic viscosity. We thereby demonstrate how the dynamic surface tension of membrane stacks could be extracted from such measurements.
In this paper we propose an analytic expression for surface tension of organic compounds. This new expression, originally derived from the statistical-mechanics is shown to represent the experimental surface tension data of 94 different organic compounds within 1.05 AAD%. We also propose another simpler expression. When this generalized expression is used surface tensions for all the 94 compounds can be predicted within 2.57 AAD% for all temperatures investigated.
Recent experiments by Kantsler et. al. (2007) have shown that the relaxational dynamics of a vesicle in external elongation flow is accompanied by the formation of wrinkles on a membrane. Motivated by these experiments we present a theory describing the dynamics of a wrinkled membrane. Formation of wrinkles is related to the dynamical instability induced by negative surface tension of the membrane. For quasi-spherical vesicles we perform analytical study of the wrinkle structure dynamics. We derive the expression for the instability threshold and identify three stages of the dynamics. The scal…
In this paper, we examine the emergence of cell flow induced by a tension gradient on a tissue interface as in the case of the Marangoni flow on liquid interface. We consider the molecule density polarity of the heterophilic adhesion between tissues as the origin of the tension gradient. By applying the cellular Potts model, we demonstrate that polarization in concentration (i.e., intracellular localization) of heterophilic adhesion molecules can induce a cell flow similar to the Marangoni flow. In contrast to the ordinary Marangoni flow, this flow is oriented in the opposite direction to that…
Recently Escobedo and Mansoori (AIChE J. 42(5): 1425, 1996) proposed a new expression, originally derived from statistical mechanics, for the surface tension prediction of pure fluids. In this report, the same theory is extended to the case of mixtures of organic liquids. Using the proposed equation surface tensions of 55 binary mixtures are predicted within an overall 0.50 AAD% which is better than the other available prediction methods. Using a corresponding states expression the surface tension of all the 55 binary mixtures are predicted within an overall 2.10 AAD%. The proposed model is al…
Formulas, analogous to the Triezenberg-Zwanzig expression for the surface tension of a planar interface, are presented for the Tolman length, the bending rigidity, and the rigidity constant associated with Gaussian curvature. These expressions feature the Ornstein-Zernike direct correlation function and are derived from considering the deformation of a liquid drop in the presence of an external field. This approach is in line with the original analysis by Yvon in 1948. It is shown that our expressions reduce to previous results from density functional theory when a mean-field approximation is …
Surface tension plays a ubiquitous role in phase transitions including condensation or evaporation of atmospheric liquid droplets. Especially, understanding of interfacial thermodynamics of the critical nucleus of 1 nm scale is important for molecular characterization of the activation energy barrier of nucleation. Here, we investigate surface tension of spherical nanodroplets with both molecular dynamics and density functional theory, and find that surface tension decreases appreciably below 1 nm radius, whose analytic expression is consistently derived from the classic Tolman's equation. In …
We calculate the fluctuation spectrum of the shape of a lipid vesicle or cell exposed to a nonthermal source of noise. In particular we take into account constraints on the membrane area and the volume of fluid that it encapsulates when obtaining expressions for the dependency of the membrane tension on the noise. We then investigate three possible origins of the non-thermal noise taken from the literature: A direct force, which models an external medium pushing on the membrane. A curvature force, which models a fluctuating spontaneous curvature, and a permeation force coming from an active tr…
We review and compare recent work on the properties of fluctuating interfaces between nematic and isotropic liquid-crystalline phases. Molecular dynamics and Monte Carlo simulations have been carried out for systems of ellipsoids and hard rods with aspect ratio 15:1, and the fluctuation spectrum of interface positions (the capillary wave spectrum) has been analyzed. In addition, the capillary wave spectrum has been calculated analytically within the Landau-de Gennes theory. The theory predicts that the interfacial fluctuations can be described in terms of a wave vector dependent interfacial te…
In 1966 Pelofsky proposed an empirical linear correlation between the natural logarithm of the surface tension and the reciprocal viscosity, which seems to work adequately for a wide range of fluids. In particular, it has been shown that it is useful in the case of n-alkanes and their binary and ternary mixtures. More recently however, it has been found not to work for several ionic liquids unless the reciprocal viscosity is raised to a power. The exponent of this power was fixed to be 0.3, at least for the studied ionic fluids. In the present work, the performance and accuracy of both the ori…
