Anisotropic Surface Tension Research Articles

Modeling capillary flows by conservation of acceleration and surface energy

Modeling of capillary flows on a surface or at the interface of two fluids is approached from a formulation with two contributions, one described by the divergence of the normal to the surface and the second represented by its curl. These are the two curl-free and divergence-free components of a Helmholtz–Hodge decomposition of the capillary acceleration; the first is the gradient of the scalar potential of the acceleration and the second the dual curl of the vector potential. Proposed formulation is characterized by (i) definition of a directional curvature based on the dihedral angle instead of an average curvature, (ii) an intrinsic anisotropic surface tension per unit mass excluding the presence of density in the capillary terms of the equation of motion and (iii) introduction of a capillary potential, an energy per unit mass. This energetic approach leads to an equation of capillary motion of a surface without thickness; the same formalism can be integrated as a source in an equation of motion of immiscible fluids.

Medium effect on anisotropic surface tension of magnetized quark matter

The thermodynamics of finite size quark matter in the quasiparticle model is self-consistently constructed by an effective bag function, which presents the medium effect to the confinement. We obtained completely analytic surface tension in the strong magnetic field with the multiple reflection expansion. The anisotropic structure is demonstrated by the splitting of the longitudinal and transverse surface tensions. The anisotropy of the surface tension could be enhanced by an increase of the magnetic field. The analytical surface tension is modified by an additional term related to the bag function. For strong enough magnetic fields, the increase of the longitudinal surface tension is proportional to the magnetic field.On the contrary, the transverse component vanishes due to all quarks locating in the lowest landau level.

Tip Splitting Dynamics in Degenerate Seaweed Patterns of Aluminum Alloys Induced by Anisotropic Surface Tension

The formation of degenerate seaweed in Al-4.5 wt % Cu, Al-3 wt % Mg, and commercial A356 alloys during quasi-two-dimensional directional solidification is studied. By designing (100)[011]-and (−211)[111]-oriented planar-front seeds, the surface tension profiles are symmetrically arranged with respect to the temperature gradient direction. The results show that growth toward the surface tension maxima is preferred, and the tips tend to grow outward in both directions, leading to degenerate seaweed formation. The comparison of the degenerate seaweeds in the three Al alloys shows that the morphologic features are qualitatively similar. However, the anisotropic surface tension has a significant effect on the growth dynamics of the degenerate seaweed. This quantitatively indicates that Al alloys with a larger anisotropy tend to exhibit growth with a smaller tip spacing (λ) and a higher splitting frequency (f).

Selection Criterion of Stable Dendritic Growth for a Ternary (Multicomponent) Melt with a Forced Convective Flow

A stable growth mode of a single dendritic crystal solidifying in an undercooled ternary (multicomponent) melt is studied with allowance for a forced convective flow. The steady-state temperature, solute concentrations and fluid velocity components are found for two- and three-dimensional problems. The stability criterion and the total undercooling balance are derived accounting for surface tension anisotropy at the solid-melt interface. The theory under consideration is compared with experimental data and phase-field modeling for Ni98Zr1Al1 alloy.

Conformational entropy limits the transition from nucleation to elongation in amyloid aggregation

The formation of β-sheet-rich amyloid fibrils in Alzheimer’s disease and other neurodegenerative disorders is limited by a slow nucleation event. To understand the initial formation of β-sheets from disordered peptides, we used all-atom simulations to parameterize a lattice model that treats each amino acid as a binary variable with β- and non-β-sheet states. We show that translational and conformational entropy give the nascent β-sheet an anisotropic surface tension that can be used to describe the nucleus with 2D classical nucleation theory. Since translational entropy depends on concentration, the aspect ratio of the critical β-sheet changes with protein concentration. Our model explains the transition from the nucleation phase to elongation as the point where the β-sheet core becomes large enough to overcome the conformational entropy cost to straighten the terminal molecule. At this point the β-strands in the nucleus spontaneously elongate, which results in a larger binding surface to capture new molecules. These results suggest that nucleation is relatively insensitive to sequence differences in coaggregation experiments because the nucleus only involves a small portion of the peptide.

In-situ comparison of interface instability of basal and edge planes during unidirectional growth of sea ice

The evolutions of water/ice interface with distinct ice orientations are one of the central problems in sea ice growth. Some misunderstandings prevailed in previous hypothesis on morphological evolution of sea ice, which need the validation with carefully designed experiments. Up to now, there is no in-situ comparison of unidirectional freezing behavior between distinct ice orientations, which makes the previous hypothesis on sea ice growth skeptical about its physical basis. The aim of this paper is to provide an in-situ comparison of unidirectional growth behavior of lamellar sea ice between basal and edge planes. Our experiment is realized by a delicate design of parallel freezing samples with two specified ice orientations in a modeled sea water under an imposed thermal gradient. The planar instability as well as the unidirectional cellular/dendritic growth patterns of water/ice interfaces of basal and edge plane ice are compared. It is found that the instability grows faster for edge plane ice, which is addressed by an incubation time coupled with the surface tension anisotropy. In addition, two types of tilted growth patterns of sea ice after planar instability are observed simultaneously, which are suggested to stem from distinct physical origins and provide a new insight into the tilted growth of cellular/dendritic ice. Collectively, these experimental results are suggested to promote our understanding of morphological evolution of unidirectional growth of sea ice, as well as its diverse relevance to many other areas involving ice growth.

Complex Nanowrinkling in Chiral Liquid Crystal Surfaces: From Shaping Mechanisms to Geometric Statistics.

Surface wrinkling is closely linked to a significant number of surface functionalities such as wetting, structural colour, tribology, frictions, biological growth and more. Given its ubiquity in nature’s surfaces and that most material formation processes are driven by self-assembly and self-organization and many are formed by fibrous composites or analogues of liquid crystals, in this work, we extend our previous theory and modeling work on in silico biomimicking nanowrinkling using chiral liquid crystal surface physics by including higher-order anisotropic surface tension nonlinearities. The modeling is based on a compact liquid crystal shape equation containing anisotropic capillary pressures, whose solution predicts a superposition of uniaxial, equibiaxial and biaxial egg carton surfaces with amplitudes dictated by material anchoring energy parameters and by the symmetry of the liquid crystal orientation field. The numerical solutions are validated by analytical solutions. The blending and interaction of egg carton surfaces create surface reliefs whose amplitudes depend on the highest nonlinearity and whose morphology depends on the anchoring coefficient ratio. Targeting specific wrinkling patterns is realized by selecting trajectories on an appropriate parametric space. Finally, given its importance in surface functionalities and applications, the geometric statistics of the patterns up to the fourth order are characterized and connected to the parametric anchoring energy space. We show how to minimize and/or maximize skewness and kurtosis by specific changes in the surface energy anisotropy. Taken together, this paper presents a theory and simulation platform for the design of nano-wrinkled surfaces with targeted surface roughness metrics generated by internal capillary pressures, of interest in the development of biomimetic multifunctional surfaces.

Anisotropic surface tensions for phase transitions in periodic media

This paper establishes bounds on the homogenized surface tension for a heterogeneous Allen-Cahn energy functional in a periodic medium. The approach is based on relating the homogenized energy to a purely geometric variational problem involving the large scale behaviour of the signed distance function to a hyperplane in periodic media. Motivated by this, a homogenization result for the signed distance function to a hyperplane in both periodic and almost periodic media is proven.

Wrinkling pattern formation with periodic nematic orientation: From egg cartons to corrugated surfaces.

Egg cartons, known as doubly sinusoidal surfaces, display a rich variety of saddles-cylinder-spherical patches organized with different spatial symmetries and connectivities. Egg carton surfaces, rich in functionalities, are observed in synthetic and biological materials, as well as across atomic and macroscopic scales. In this work we use the liquid crystal shape equationin the absence of elastic effects and normal stress jumps to predict and classify a family of uniaxial, equibiaxial, and biaxial egg cartons, according to the periodicities of the surface director field in nematic (N) and cholesteric (N*) liquid crystals under the presence of anisotropic surface tension (anchoring). Egg carton surface shape periodic solutions to the nonlinear and linearized liquid crystal shape equationspredict that the mean curvature is a linear function of the orthogonal (along the surface normal) splay and bend contributions. Mixtures of egg carton surfaces (uniaxial, equibiaxial, and biaxial) emerge according to the symmetries of the nonsingular director field, and the spatial distributions of the director escape into the third dimension; pure uniaxial egg cartons emerge when the director escape has linelike geometries and mixtures of egg cartons arise under source or sink orientation lattices. Orientation symmetry and permutation analysis are incorporated into a full curvature (Casorati, shape parameter, mean curvature, and Gaussian curvature) characterization. Under a fixed anchoring parameter, conditions for maximal nanoscale curvedness and microscale maximal shape gradient diversity are identified. The present results contribute to various pathways to surface pattern formation using intrinsic anisotropic interfacial tension.

Nonlinear Phase-Field Modeling of Lithium Dendritic Growth during Electrodeposition

Lithium batteries have been widely used, but the growth of lithium dendrites does lead to some hazards, such as internal short circuit, thermal runaway and even explosion. In paper, a nonlinear phase field model combined with Butler-Volmer expression was developed to study dendrite growth during electrodeposition. Two types of initial electrode-electrolyte interface are applied in numerical simulations. Results show that the cation concentration enrichment occurs near the dendritic tip due to the electromigration, and the curve of the growth velocity versus time follows a simple power law relation, indicating that the stability of the dendritic array originating from initial electrode-electrolyte interface can be broken with the applied electrical potential increasing. Moreover, we found that applied electric potential gradient can strongly influence the dendritic growth velocity and the dendritic growth during electrodeposition is less relative to the surface tension anisotropy.

Modeling ice crystal growth using the lattice Boltzmann method

Given the multitude of growth habits, pronounced sensitivity to ambient conditions and wide range of scales involved, snowflake crystals are particularly challenging systems to simulate. Only a few models are able to reproduce the diversity observed regarding snowflake morphology. It is particularly difficult to perform reliable numerical simulations of snow crystals. Here, we present a modified phase-field model that describes vapor-ice phase transition through anisotropic surface tension, surface diffusion, condensation, and water molecule depletion rate. The present work focuses on the development and validation of such a coupled flow/species/phase solver in two spatial dimensions based on the lattice Boltzmann method. It is first shown that the model is able to correctly capture species and phase growth coupling. Furthermore, through a study of crystal growth subject to ventilation effects, it is shown that the model correctly captures hydrodynamics-induced asymmetrical growth. The validated solver is then used to model snowflake growth under different ambient conditions with respect to humidity and temperature in the plate-growth regime section of the Nakaya diagram. The resulting crystal habits are compared to both numerical and experimental reference data available in the literature. The overall agreement with experimental data shows that the proposed algorithm correctly captures both the crystal shape and the onset of primary and secondary branching instabilities. As a final part of the study, the effects of forced convection on snowflake growth are studied. It is shown, in agreement with observations in the literature, that under such conditions the crystal exhibits nonsymmetrical growth. The non-uniform humidity around the crystal due to forced convection can even result in the coexistence of different growth modes on different sides of the same crystal.

H^1 solutions for a Kuramoto–Sinelshchikov–Cahn–Hilliard type equation

The Kuramoto–Sinelshchikov–Cahn–Hilliard equation models the spinodal decomposition of phase separating systems in an external field, the spatiotemporal evolution of the morphology of steps on crystal surfaces and the growth of thermodynamically unstable crystal surfaces with strongly anisotropic surface tension. In this paper, we prove the well-posedness of the Cauchy problem, associated with this equation.

EFFECT OF ANISOTROPIC SURFACE TENSION ON THE GROWTH OF COLUMNAR CRYSTALS IN TERNARY UNDERCOOLED MELTS

The effect of anisotropic surface tension on the growth of columnar crystals in ternary melt is studied, and the approximate analytical solution of the growth morphology of columnar crystals is given. It is found that in the initial stage of growth, some parts of the interface grow outward, while some parts first grow inward, and grow outward together with other parts after reaching a certain depth, which makes the columnar crystal interface form a remarkable concave and convex formation. Compared with the case in the pure melt and ternary alloy melt, the component added in the ternary alloy melt decreases the effect of the anisotropic surface tension.

Well-posedness of the classical solution for the Kuramto\u2013Sivashinsky equation with anisotropy effects

The Kuramto–Sivashinsky equation with anisotropy effects models the spinodal decomposition of phase separating systems in an external field, the spatiotemporal evolution of the morphology of steps on crystal surfaces and the growth of thermodynamically unstable crystal surfaces with strongly anisotropic surface tension. Written in terms of the step slope, it can be represented in a form similar to a convective Cahn–Hilliard equation. In this paper, we prove the well-posedness of the classical solutions for the Cauchy problem, associated with this equation.

Biaxial nanowrinkling in cholesteric surfaces: Egg carton surfaces through chiral anchoring

Periodic micro and nano-structured surfaces in nature are responsible for functionalities including structural colour, superhydrophobicity, where wrinkling plays a significant role. The Bouligand architecture of fibrous composites such as insect exoskeleton and plant cell walls has been shown to generate uniaxial single and multiscale nanowrinkling through the chiral capillarity effect due to anisotropic surface tension and the helical fibre arrangement. The helical arrangement in Bouligand structures is a solid analogue of a cholesteric liquid crystal, which is an intermediate stage in the self-assembly formation process of fibrous composites. We extend uniaxial wrinkling predictions to biaxial wrinkling and show, using the liquid crystal shape equation, how and why egg carton surfaces with orthogonal patterning arise, since a planar helix tangential to a surface is unstable to oblique wrinkling modes. Taken together this work contributes to novel surface pattern formation and engineering principles to study surfaces of biological materials.

Rayleigh–Plateau instability of anisotropic interfaces. Part 1. An analytical and numerical study of fluid interfaces

Abstract

A semi-implicit conservative sharp-interface method for liquid-solid phase transition

The solidification of an undercooled liquid is physically unstable. The dominating instability modes are affected by both the evolving temperature field in the solid and liquid phases, and characteristics of the phase interface such as the curvature and the propagation velocity. To capture the instability mode, therefore both the temperature field and the interface have to be represented accurately in a numerical model of the phase-change process. In this work, we develop conservative interface exchange terms for a sharp-interface formulation of liquid-solid phase transition. Conservation at the interface is maintained by explicit formulation of interface fluxes into both solid and liquid phases. We propose a semi-implicit level-set formulation to evolve the phase interface. A new formulation for the interface surface in a cut cell is derived, which includes the Stefan condition. We achieve low numerical dissipation by an explicit third-order Runge-Kutta scheme for time discretization, and a novel WENO-like (Weighted Essentially Non-Oscillatory) interface-gradient reconstruction. This distinguishes our level-set based sharp-interface model from previous level-set based approaches, which rely on finite-difference based interface treatment, and thus do not ensure discrete conservation at the interface. The flux terms in our approach take into account surface-tension and kinetic effects on the interface temperature (Gibbs-Thomson relation). The Stefan condition provides a relation between interface fluxes of mass and energy, and the interface-propagation velocity. Computational efficiency is maintained by a multiresolution approach for local mesh adaptation, and an adaptive local time-stepping scheme.We present one- and two-dimensional simulation results for the growth of a planar solidification front and a single parabolic dendrite affected by surface tension. The results agree well with experimental and analytical reference data, showing that the model is capable to capture both stable (planar) and unstable (dendritic-like) growth processes in the heat-diffusion dominated regime. The convergence order for successively finer meshes in the one-dimensional case is one for the interface location and the temperature field, outperforming previously reported level-set based approaches. We present numerical data of a growing crystal with four-fold symmetry. Our results indicate that the artificial dissipation of the underlying numerical scheme affects its capability to reproduce consistently physical tip-splitting instabilities. The proposed low-dissipation scheme is able to resolve such instabilities. Finally, we demonstrate the capability of the method to simulate multiple growing crystals with anisotropic surface-tension and kinetic effects.

Multi-scale simulation of grain/sub-grain structure evolution during solidification in laser welding of aluminum alloys

This work developed a multi-scale model, combining the macro-scale model for heat transfer and fluid flow with the micro-scale phase-field model for polycrystalline alloy solidification, to investigate the grain/sub-grain structure evolution during solidification in laser welding of 5083 Al sheets. Special attentions were paid to the planar to cellular and dendritic growth. Results demonstrated that, during planar-to-cellular transition, the initial planar instability primarily resulted from the rapid change in growth rate. The surface tension anisotropy can significantly affect the initial planar instability. With the increase of misorientation angle, the interfacial stiffness tended to increase, which enhanced the stabilizing effects of surface tension and thus made the S/L interface more and more stable. Furthermore, Results elucidated how solidification morphology develops during cellular-to-dendritic transition. Two important phenomena, namely, tertiary branching and tip-splitting, which were responsible for the decrease in primary dendritic arm spacing, were discovered. Finally, results illustrated how multiple grains with various orientations grow in competition in laser weld pool. Two competitive mechanisms of grain growth were revealed, namely, lateral expansion of favorably-oriented (FO) grain and blocking its unfavorably-oriented (UO) grain neighbors, and the elimination of UO grain by FO grain at the converging grain boundary.

Non-axially oriented dendritic microstructures and their mechanical characteristics of single-crystal Al-4.5%Cu alloy

This study investigated microstructure formation as a function of orientation-dependent surface tension anisotropy during directional solidification of Al-4.5%Cu alloy. Axial dendrites (AD), tilted dendrite (TD), and degenerate pattern (DP) were identified in the solidified microstructures of the single crystals. A single-crystal specimen with a stable DP, which was characterized by successive splitting tips, was carefully prepared and specifically investigated. The corresponding mechanical properties were compared with those of single-crystal AD and TD specimens. The ductility and toughness of the single-crystal specimen with a DP were approximately 91% and 87% higher than those of the other specimens, respectively. Moreover, the DP specimen showed a stronger work hardening effect than the other specimens, and the tip splitting in this specimen gave rise to refined θ′ precipitates. Field emission scanning electron microscopy (FESEM) and transmission electron microscopy (TEM) characterizations uncovered the underlying mechanisms associated with this enhancement. This study provides insightful knowledge regarding microstructure control and enriches the understanding of mechanical properties for different dendritic patterns.

THE EFFECT OF ANISOTROPIC SURFACE TENSION ON THE LAMELLAR EUTECTIC GROWTH IN DIRECTIONAL SOLIDIFICATION

For the case of small interlamellar spacing relative to the solute diffusion length, the steady spatially periodic lamellar eutectic growth with the anisotropic effect of surface tension in directional solidification is studied by the approach of the interfacial wave (IFW) theory. The anisotropic surface tension is expressed as the fourfold symmetric function. We obtained a family of the uniformly valid asymptotic solutions for the steady lamellar eutectic growth and determined the corresponding interfacial patterns affected by anisotropic surface tension. The analytical solution reveals the anisotropic effect of surface tension on the interface shape of lamellar eutectic growth near the triple point. The temperature distribution at the interface shows a noticeable nonuniformity and there is a thin boundary layer for temperature and concentration near the triple point. As the anisotropic surface tension increases, the interface temperature away from the triple-point increases, whereas near the triple point the interface temperature decreases. Compared with the lamellar eutectic growth with isotropic surface tension, the anisotropic surface tension changes the position of the triple point and accelerates the growth of the lamellar eutectic. The theoretical prediction shows quantitatively consistent with recent experimental data without making any artificial adjustments to parameters.