Sharp Interface Model Research Articles

Shock-induced bubble collapse near a tissue-like material

In this study, we numerically investigate the shock-induced bubble collapse phenomenon near a tissue-like material. Here, a sharp-interface model is applied to represent a 3-material system containing the liquid, the air and the gelatin. We present the results of the complex interface dynamics and compare them with the experimental data. The goal of this study is to understand the mechanism of the shock wave–bubble interaction near tissues in a more accurate manner with advanced numerical methods.

An energy-stable finite element method for the simulation of moving contact lines in two-phase flows

We consider the dynamics of two-phase fluids, in particular the moving contact line, on a solid substrate. The dynamics are governed by the sharp-interface model consisting of the incompressible Navier-Stokes/Stokes equations with the classical interface conditions, the Navier boundary condition for the slip velocity along the wall and a contact line condition which relates the dynamic contact angle of the interface to the contact line velocity. We propose an efficient numerical method for the model. The method combines a finite element method for the Navier-Stokes/Stokes equations on a moving mesh with a parametric finite element method for the dynamics of the fluid interface. The contact line condition is formulated as a time-dependent Robin-type of boundary condition for the interface so it is naturally imposed in the weak form of the contact line model. For the Navier-Stokes equations, the numerical scheme obeys a similar energy law as in the continuum model but up to an error due to the interpolation of numerical solutions on the moving mesh. In contrast, for Stokes flows, the interpolation is not needed so we can prove the global unconditional stability of the numerical method in terms of the energy. Numerical examples are presented to demonstrate the convergence and accuracy of the numerical methods.

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.

Progress in Modeling Wetting Phenomena on Structured Substrates

Research on wetting phenomena aims to initially understand the underlying physics and then to fabricate smart, functional surfaces with desirable wetting properties. Special attention is given to micro- and nano-textured surfaces which are expected to benefit various technological applications (e.g. drag reduction in vessels, droplet manipulation in microfluidic devices). Realizing the above applications requires an efficient methodology for predicting the behavior of droplets on such structured surfaces. The conventional modeling approaches of wetting phenomena, however, are proven to have limited applicability since either they fail to adequately describe the complicated droplet motion on a complex substrate, or demand vast computational resources for real-life applications. In this review, we initially demonstrate the conventional models for describing static and dynamic wetting phenomena. Then we present a novel, continuum-level, sharp-interface modeling approach, which has been proven particularly efficient for simulating wetting phenomena on complex (geometrically or chemically textured) solid surfaces. The efficiency of the proposed method is demonstrated by performing realistic simulations of droplets spreading and sliding on geometrically patterned substrates.

Existence of weak solutions for a sharp interface model for phase separation on biological membranes

<p style='text-indent:20px;'>We prove existence of weak solutions of a Mullins-Sekerka equation on a surface that is coupled to diffusion equations in a bulk domain and on the boundary. This model arises as a sharp interface limit of a phase field model to describe the formation of liqid rafts on a cell membrane. The solutions are constructed with the aid of an implicit time discretization and tools from geometric measure theory to pass to the limit.

Modeling of dendritic growth using a quantitative nondiagonal phase field model

The phase field method has emerged as the tool of choice to simulate complex pattern formation processes in various domains of materials sciences. For the phase field model to faithfully reproduce the dynamics of a prescribed free-boundary problem with transport equations in the bulk and boundary conditions at the interfaces, the so-called thin-interface limit should be performed. For a phase transformation driven by diffusion, the kinetic cross-coupling between the phase field and the diffusion field has recently been introduced, allowing a control on interface boundary conditions in the general case where the diffusivity in the growing phase ${D}_{S}$ neither vanishes (one-sided model) nor equals the one of the disappearing phase ${D}_{L}$ (symmetric model). Here, we investigate the capabilities of this nondiagonal phase field model in the case of two-dimensional dendritic growth. We benchmark our model with Green's function calculations (sharp-interface model) for the symmetric and one-sided cases, and our results for arbitrary ${D}_{S}/{D}_{L}$ allow us to propose a generalization of the theory by Barbieri and Langer [Phys. Rev. A 39, 5314 (1989)] for finite anisotropy of interface energy. We also perform simulations that evidence the necessity of introducing the kinetic cross-coupling and of eliminating surface diffusion. Our work opens up the way for quantitative phase field simulations of phase transformations with diffusion in the growing phases playing an important role in the pattern and velocity selections.

A sharp-interface Cartesian grid method for time-domain acoustic scattering from complex geometries

This paper is concerned with the development of a Cartesian grid method for predicting the acoustic field scattered by complex geometries immersed in an infinite fluid. The sound wave in the fluid is formulated by the linearized Euler equations (LEEs), which are computed on a fixed Cartesian grid by using a fourth-order dispersion-relation-preserving (DRP) scheme. The solid object naturally cuts the underlying Cartesian grid with its geometrical boundary, which is modeled by the Lagrangian method. A sharp-interface Cartesian grid model based on the ghost-cell immersed boundary method is established to impose the non-penetrating conditions on the complex boundary of the solid. The values of the acoustic variables at the ghost points are constructed by a linear extrapolation in conjunction with a constrained moving least-squares (CMLS) interpolation method. The interpolation method is capable of eliminating the numerical instability encountered in the conventional moving least-squares (MLS) formulation. The perfectly matched layers are adopted to absorb the out-going sound waves without any reflections from the computational boundary to the interior domain. The proposed method is verified by several benchmark problems in computational aeroacoustics, including the initial value problem of a pressure perturbation scattered by a rigid cylinder, and Gaussian distributed acoustic sources scattered by a single cylinder or two cylinders. Application of the proposed method to the problem of acoustic waves scattered by solids with complex geometries is also presented to demonstrate the effectiveness and robustness of the method.

Lattice-Boltzmann simulations of the dynamics of liquid barrels

We study the relaxation towards equilibrium of a liquid barrel—a partially wetting droplet in a wedge geometry—using a diffuse-interface approach. We formulate a hydrodynamic model of the motion of the barrel in the framework of the Navier–Stokes and Cahn–Hilliard equations of motion. We present a lattice-Boltzmann method to integrate the diffuse-interface equations, where we introduce an algorithm to model the dynamic wetting of the liquid on smooth solid boundaries. We present simulation results of the over-damped dynamics of the liquid barrel. We find that the relaxation of the droplets is driven by capillary forces and damped by friction forces. We show that the friction is determined by the contribution of the bulk flow, the corner flow near the contact lines and the motion of the contact lines by comparing simulation results for the relaxation time of the barrel. Our results are in broad agreement with previous analytical predictions based on a sharp interface model.

Modeling of dendrite growth from undercooled nickel melt: sharp interface model versus enthalpy method

The dendritic growth of pure materials in undercooled melts is critical to understanding the fundamentals of solidification. This work investigates two new insights, the first is an advanced definition for the two-dimensional stability criterion of dendritic growth and the second is the viability of the enthalpy method as a numerical model. In both cases, the aim is to accurately predict dendritic growth behavior over a wide range of undercooling. An adaptive cell size method is introduced into the enthalpy method to mitigate against ‘narrow-band features’ that can introduce significant error. By using this technique an excellent agreement is found between the enthalpy method and the analytic theory for solidification of pure nickel.

Two-well rigidity and multidimensional sharp-interface limits for solid–solid phase transitions

We establish a quantitative rigidity estimate for two-well frame-indifferent nonlinear energies, in the case in which the two wells have exactly one rank-one connection. Building upon this novel rigidity result, we then analyze solid–solid phase transitions in arbitrary space dimensions, under a suitable anisotropic penalization of second variations. By means of $$\Gamma $$-convergence, we show that, as the size of transition layers tends to zero, singularly perturbed two-well problems approach an effective sharp-interface model. The limiting energy is finite only for deformations which have the structure of a laminate. In this case, it is proportional to the total length of the interfaces between the two phases.

Effect of tiny amount of impurity and convective transport on dendrite growth kinetics

Using the developed sharp-interface model of solidification we quantitatively estimate influence of tiny amount of impurity and forced convection on kinetics of dendritic growth. As tested systems, we choose Ni and Ni–Zr dendrites which are growing into a stagnant undercooled melt, the melt with incoming forced flow and with/without impurity (that is small amount of Zr diluted in a pure Ni). The model predictions and comparisons allow us to quantitatively estimate predominant influence of impurity (chemical segregation), thermal influence (due to temperature inhomogeneity) and hydrodynamic effects (due to investigated laminar and forced melt flow) on the dendrite growth kinetics.

Sharp-Interface Model for Simulating Solid-State Dewetting in Three Dimensions

The problem of simulating solid-state dewetting of thin films in three dimensions (3D) by using a sharp-interface approach is considered in this paper. Based on the thermodynamic variation, a speed method is used for calculating the first variation to the total surface energy functional. The speed method shares more advantages than the traditional use of parameterized curves (or surfaces), e.g., it is more intrinsic and its variational structure (related with Cahn-Hoffman $\boldsymbol{\xi}$-vector) is clearer and more direct. By making use of the first variation, necessary conditions for the equilibrium shape of the solid-state dewetting problem is given, and a kinetic sharp-interface model which includes the surface energy anisotropy is also proposed. This sharp-interface model describes the interface evolution in 3D which occurs through surface diffusion and contact line migration. By solving the proposed model, we perform lots of numerical simulations to investigate the evolution of patterned films, e.g., the evolution of a short cuboid and pinch-off of a long cuboid. Numerical simulations in 3D demonstrate the accuracy and efficacy of the sharp-interface approach to capture many of the complexities observed in solid-state dewetting experiments.

A Parametric Finite Element Method for Solid-State Dewetting Problems in Three Dimensions

We propose a parametric finite element method (PFEM) for efficiently solving the morphological evolution of solid-state dewetting of thin films on a flat rigid substrate in three dimensions (3D). The interface evolution of the dewetting problem in 3D is described by a sharp-interface model, which includes surface diffusion coupled with contact line migration. A variational formulation of the sharp-interface model is presented, and a PFEM is proposed for spatial discretization. For temporal discretization, at each time step, we first update the position of the contact line according to the relaxed contact angle condition; then, by using the position of the new contact line as the boundary condition, we solve a linear algebra system resulted from the discretization of PFEM to obtain the new interface surface for the next step. The well-posedness of the solution of the PFEM is also established. Extensive numerical results are reported to demonstrate the accuracy and efficiency of the proposed PFEM and to show the complexities of the dewetting morphology evolution observed in solid-state dewetting experiments.

Regional and well-scale indicators for assessing the sustainability of small island fresh groundwater lenses under future climate conditions

Salinization of the freshwater lens and well fields under future climate and groundwater demands threaten the sustainability of groundwater abstraction in small islands. In this paper, two simple indices are proposed for a comprehensive assessment of freshwater salinization in small islands. Values of these indices are computed based on a sharp-interface finite element numerical model with the interface matched to the lower limit of freshwater. The first index relates rainfall percentiles with the computed freshwater volume and provides regional assessment of changes in the volume stored in the freshwater lens over time. The second is a sustainability index, based on computed saltwater ratios in pumping wells as the performance indicator, which represents the well salinization risk at a spatial scale. The proposed methodology is illustrated with the example of Tongatapu Island. Freshwater lens dynamics and well salinization under various scenarios of dry, median, and wet general circulation model predictions-based unsteady recharge, sea level rise, and pumping demands were evaluated for the period 2010–2099. The freshwater lens of Tongatapu is dependent on rainfall, and the 60-month rainfall percentile is highly correlated with the total freshwater volume. Public well field indicates sustainability indexes of 45% and 100% under the current pumping conditions for the driest and the wettest scenarios, and with increased pumping and sea level rise, they reduce to 30% and 90%, respectively. Thus, management of pumping rates is essential for future freshwater sustainability. This methodology can be used for first-hand temporal and spatial estimations of small island freshwater lens salinization considering both the regional and well scales.

Consistent, essentially conservative and balanced-force Phase-Field method to model incompressible two-phase flows

In the present work, the Cahn-Hilliard Phase-Field model of incompressible two-phase flows is considered. Conditions needed for consistency of reduction, consistency of mass and momentum transport, and consistency of mass conservation are proposed. The mass flux in the Navier-Stokes equations is defined such that it satisfies the proposed consistency conditions. The analysis in both continuous and discrete levels shows that violation of the consistency conditions result in unphysical solutions and the inconsistent errors are proportional to the density contrast of the fluids. After considering the conservative form of the inertial term, a consistent and conservative scheme for momentum transport is developed. The balanced-force algorithm for the sharp interface model is extended to the surface force derived from the Cahn-Hilliard model. The proposed scheme is formally 2nd-order accurate in both time and space, satisfies the consistency conditions, conserves mass globally and momentum essentially, and is balanced-force, in the discrete level. Its convergence to the sharp interface solution is systematically discussed in cases including large density and viscosity ratios, surface tension, and gravity. Various two-phase flow problems with large density ratios are performed to validate and verify the proposed scheme and excellent agreements with published numerical and/or experimental results are achieved. The proposed scheme is a practical and accurate tool to study two-phase flows, especially for those including large density ratios.

Phase diagrams of honeycomb and square nanocrystal superlattices from the nanocrystal's surface chemistry at the dispersion-air interface.

In this work, we theoretically investigate the conditions favoring the interfacial self-assembly of PbSe nanocrystals (NCs) resulting in silicene-honeycomb superstructures. Using a coarse-grained molecular dynamics model, we study the NCs' self-assembly at the dispersion-air interface with respect to the input parameters regulating the various forces experienced by the NCs at the interface. From these results, we extrapolate detailed assembled-phase diagrams showing which ranges of the input parameters promote the formation of silicene-honeycomb superstructures and which regimes result in square geometries. Then, we use a sharp-interface numerical model to compute the energy landscape experienced by each NC at the dispersion-air interface with respect to the NC's surface chemistry. From such an energy landscape, we fit the parameters regulating the interface-adsorption forces experienced by the NCs at the interface. Combining these findings with the results presented in our assembled-phase diagrams, we find out which surface-chemistry properties of the NCs better promote the interfacial self-assembly in silicene-honeycomb superstructures, and we speculate on some experimental strategies to reach an improved control on the synthesis of PbSe silicene-honeycomb superstructures.

Phase field modeling of rapid resolidification of Al-Cu thin films

Abstract A binary alloy multi-order parameter phase field model is used to study rapid solidification in Al-Cu under conditions corresponding to recent dynamic transmission electron microscopy (DTEM) experiments. The phase field model’s sharp interface limit is set through a recent matched asymptotic analysis to follow the solute trapping and interface undercooling kinetics of the Continuous Growth Model (CGM). The phase field model convergence to the CGM sharp interface model is investigated, and based on this an optimal interface width is chosen to simulate the DTEM experimental conditions. The temperature distribution used in the phase field simulations is taken from an analytic expression extracted from experiments. Simulated solidification structures are compared to experiments, including time-resolved DTEM images and post-mortem TEM-based image quality and orientation maps. We find that the large scale morphological features of the simulated microstructures are in good agreement with the experiments, and the corresponding concentration profiles that emerge are in qualitative agreement with experiments. These results show that phase field simulations, informed with DTEM experiments, provides a promising framework to investigate rapidly solidified microstructure evolution and solute segregation, and to calibrate hard-to-determine solidification parameters.

P.827 Have the TRP channels a role in MPP+ neurotoxicity?

This article presents a sharp-interface model for solving solid-liquid phase change of pure materials. An interface capturing method combining VOF and level set, VOSET, is employed to track the moving interface during phase change, and the level-set function generated in VOSET is used to consider the effect of the phase boundary when solving the fields of temperature and velocity. In order to deal with the interaction between the solid and liquid phases, an immersed boundary method (IBM) is incorporated into SIMPLER algorithm. The fundamental numerical approaches presented in this article were individually assessed by test problems, all showing good agreements with benchmark solutions. The established sharp-interface model was then applied in simulating melting and solidification without and with fluid flow, where competitive performance in accuracy was demonstrated by the numerical results.

On the approximation of surface elasticity theory by means of phase‐field theory

AbstractWithin surface elasticity theory originally proposed by Gurtin and co‐workers ( [1]), effects associated with surface tension are naturally captured. In this paper, surface elasticity theory is approximated by means of phase field theory, cf. [4] and [5]. The resulting approximation is employed in order to analyze the size effects induced by the coupling of bulk and surface energies. For that purpose, the phase field framework is compared to the underlying sharp interface model proposed in [2].

A review on recent development of theoretical modeling of hydrogel phase behavior subject to mechanics and multiphysics coupled effects

Hydrogel is a class of hydrophilic crosslinked polymeric network filled with interstitial fluid. The specified composition and network structure enable the soft material to exhibit different mechanical properties, ranging from elastic solid to viscous liquid, subject to environmental stimuli. In this process, they are able to imbibe a large amount of water or other biological fluid, and thus solid-solid or solid-liquid phase transition may occur due to discontinuous changes of certain properties, where large elongation and nonlinear deformation are coupled with multiphysics changes, such as mass diffusion, heat conduction, and crosslinks forming/breaking. This paper reviews the recent development of theoretical modeling and simulation work for the soft materials, with emphasis on the phase behavior subject to mechanics and multiphysics coupled effects. Discussions cover bulk phase modeling for equilibrium states and critical conditions, two-phase modeling for gel-gel and gel-sol phase transitions, as well as simulation for interface behavior during phase transition with both sharp and diffuse interface models.