Interface Boundary Conditions Research Articles

Acoustic Radiation Characteristics of a Forced Vibrating Elastic Panel Under Thermal Environments

This paper presents the thermo-acoustic frequency response of an un-baffled rectangular panel subjected to an external excitation load. A boundary element method BEM has been employed taking into account the Kirchhoff-Helmholtz K-H integral equation for the acoustic pressure and with the fluid-plate interface boundary condition the acoustic pressure jump over the panel is calculated. The thermal effects are considered regarding in the form of a uniform increment of temperature of the panel and are analysed in order to prevent the buckling phenomena. The excitation force considered is in the form of a concentrated load at some point of the panel and the deformation modes correspond to the vacuum case. Applying a collocation method for the panel equation, a frequency transfer function is obtained that relates the deflexion of the panel with the applied load. The effect of several geometric parameters, different thermal loads and location of the load applied on the acoustic radiated power and the acoustic efficiency spectrum are evaluated. Furthermore, the influence of the excitation frequency on the sound directivity is evaluated. The verification of the method is proven with other works.

Revealing molecular insights into surface charge and local viscosity in electroosmotic flows

The limitations of the continuum theory in predicting osmotic response at the nanoscale stem from its lack of molecular-level insight into local fluid properties and the interfacial structure of fluid and electrolyte solutions. To overcome this challenge, our study integrates molecular dynamics (MD) simulation with the continuum framework to explore how surface charge and various hydrodynamic properties impact electroosmotic flow (EOF). The failure of continuum theories to account for molecular interactions and geometric boundaries leads to significant disparities between MD simulations and continuum predictions, influenced by local fluid properties and the electric field. Emphasizing the importance of incorporating appropriate local hydrodynamic properties and atomic interface boundary conditions, our findings bridge the gap between MD simulations and continuum EOF predictions. Our computational results and theoretical model, considering surface charge, atomic interface boundaries, and dynamic structure-based hydrodynamic properties, provide crucial insights and guidance for EOF investigations.

A network model to predict ionic transport in porous materials

Understanding the dynamics of electric-double-layer (EDL) charging in porous media is essential for advancements in next-generation energy storage devices. Due to the high computational demands of direct numerical simulations and a lack of interfacial boundary conditions for reduced-order models, the current understanding of EDL charging is limited to simple geometries. Here, we present a network model to predict EDL charging in arbitrary networks of long pores in the Debye-Hückel limit without restrictions on EDL thickness and pore radii. We demonstrate that electrolyte transport is described by Kirchhoff's laws in terms of the electrochemical potential of charge (the valence-weighted average of the ion electrochemical potentials) instead of the electric potential. By employing the equivalent circuit representation suggested by these modified Kirchhoff's laws, our methodology accurately captures the spatial and temporal dependencies of charge density and electric potential, matching results obtained from computationally intensive direct numerical simulations. Our network model provides results up to six orders of magnitude faster, enabling the efficient simulation of a triangular lattice of five thousand pores in 6 min. We employ the framework to study the impact of pore connectivity and polydispersity on electrode charging dynamics for pore networks and discuss how these factors affect the time scale, energy density, and power density of capacitive charging. The scalability and versatility of our methodology make it a rational tool for designing 3D-printed electrodes and for interpreting geometric effects on electrode impedance spectroscopy measurements.

Numerical Reconstruction of Time-Dependent Boundary Conditions to 2D Heat Equation on Disjoint Rectangles at Integral Observations

In this paper, two-dimensional (2D) heat equations on disjoint rectangles are considered. The solutions are connected by interface Robin’s-type internal conditions. The problem has external Dirichlet boundary conditions that, in the forward (direct) formulation, are given functions. In the inverse problem formulation, the Dirichlet conditions are unknown functions, and the aim is to be reconstructed upon integral observations. Well-posedness both for direct and inverse problems is established. Using the given 2D integrals of the unknown solution on each of the domains and the specific interface boundary conditions, we reduce the 2D inverse problem to a forward heat 1D one. The resulting 1D problem is solved using the explicit Saul’yev finite difference method. Numerical test examples are discussed to illustrate the efficiency of the approach.

A New Solution of Drag for Newtonian Fluid Droplets in a Power-Law Fluid

Understanding flow behaviors of multiple droplets in complex non-Newtonian fluids is crucial in many science and engineering applications. In this study, a new and improved analytical solution is developed based on the free surface cell model for the flow drag of swamp of Newtonian fluid drops through a power-law fluid. The developed solution is accurate and compares well to the numerical solutions. The improvement involves a new quantification of shear stress boundary condition at the interface and a more consistent approximation in linearizing the power-law fluid flow governing equation. The Newtonian fluid solutions can be reasonably used to linearize the flow governing equation. The approximation of the boundary conditions at the interface, however, has a major impact on the model prediction. The main improvement in the new solution is observed under the condition of comparable viscosities of the Newtonian drops and the outside power-law fluid when the results are sensitive to the interface boundary condition. Under the two extreme conditions of high viscosity ratio (approaching particles) and low ratio (approaching bubbles), the present and existing solutions converge.

THE ANALYSIS OF THE FLOW OF BLOOD IN A STENOSED ARTERY THROUGH SIMULATION: A COMPARISON AMONG VARIOUS NON-NEWTONIAN MODELS

This paper focuses on the dual quality of blood, Newtonian and non-Newtonian, in particular by exploring the energy curves. Careful investigation of the dual property of blood has been made by considering two different geometries to represent a stenosed arterial segment. We present a cautious assessment of non-Newtonian blood rheology impacts in arterial stream simulations by coupling the Newtonian and non-Newtonian models. The flow of energy through the two flow dimensions is meticulously investigated using velocity (kinetic energy), pressure, and wall shear stress (pressure energy). Besides, the proper implementation of an interface boundary condition (IBC) was emphasized to ensure consistency with the flow conditions downstream of a backward-facing step. The integration of the Newtonian and non-Newtonian models adjoins the novelty of the current research. The energy curves are obtained by implementing five different non-Newtonian models to designate a suitable non-Newtonian model for blood flow investigations. The combination of the non-Newtonian models enforced in this research is novel and particular attention is paid to the energy curves obtained. The conclusion was to elect the Carreau model as a suitable non-Newtonian rheological model for the blood flow study. This study was able to finalize the fact that the coupling of Newtonian and non-Newtonian models is necessary to obtain accurate results. For the sinusoidal waveform considered for the velocity, Carreau and the Power law models yield better results, eliminating the other non-Newtonian models from the list. With a better inlet condition imposed in the form of the Fourier series for pressure and velocity, the Carreau model yields the best results.

The effect of shear rate and overconsolidation ratios on undrained clay–suction caisson interface behaviors

The interface resistance during installation is crucial for the stability and safety of suction caisson in offshore geotechnical engineering, which is strongly affected by the penetration rate and soil–structure interface mechanical properties. This research conducts a series of clay–structure interface shear tests using modified direct simple shear device to fully study the mechanical behavior of clay–suction caisson interface. The effect of shear rate, over consolidation ratios (OCRs), interface boundary conditions, stress levels, and interface roughness were considered. Results show that as the OCR increases, the strength of both the clay and interface increase but show distinct patterns under constant volume (CV) and constant normal load (CNL) boundary condition. It was found that the interface strength is positively related to interface roughness and shear rate impact both the clay and corresponding interface strength. Under CNL conditions, the strength of normally consolidated (NC) clay decreases with rising shear rate, while the over consolidated (OC) clay demonstrate a opposite trend. In contrast, the effect of shear rate on interface behavior gets complicated owing to the combination of roughness, stress levels, and OCRs. Under CV conditions, the shear strength of clay and interface exhibits a logarithmic growth relationship with shear rates. The result of this work can provide a basis for interface resistance evaluation for suction caisson installation in clay.

Air-water interface boundary condition for the numerical evaporation rate prediction of a horizontal water span under different convection regimes

This paper conducts a comprehensive analysis of the existing numerical models addressing the dynamics of water vapor flux across the air-water interface. Additionally, it introduces a novel model based on the empirical friction velocity of the air over a water surface. This new model is used to predict evaporation rates, especially in the context of wind tunnel experiments where water tanks are subjected to controlled drying conditions. Then, these predictions are compared to both the empirically measured evaporation rates and those generated by other numerical models. A wide range of configurations are simulated to cover the different convection regimes. Overall, these simulations show good agreement between the model's predictions and the observed experimental measurements of evaporation rates, underscoring its robustness and reliability. One notable advantage of this model is its remarkable independence from the convection regime, setting it apart from traditional empirical correlations that typically exhibit such dependencies.

Photosynthetically-powered phototactic active nematic liquid crystal fluids and gels

One of the most ancient forms of life dating to ~3.5 billion years ago, cyanobacteria are highly abundant organisms that convert light into energy and motion, often within conjoined filaments and larger colonies that attract a great deal of interest but their active nematic behavior remained unexplored. Here we demonstrate how light causes a spontaneous self-assembly of two- and three-dimensional active nematic states of cyanobacterial filaments, with a plethora of topological defects. We quantify light-controlled evolutions of orientational and velocity order parameters during the transition between disordered and orientationally ordered states of photosynthetic active matter, as well as the subsequent active nematic’s fluid-gel transformation. Patterned illumination and foreign inclusions with different shapes interact with cyanobacterial active nematics in nontrivial ways while inducing interfacial boundary conditions and fractional boojum defects. Our phototactic model system promises opportunities to systematically explore fundamental properties and technological utility of the liquid crystalline active matter.

Multi-species kinetic-fluid coupling for high-energy density simulations

Many physics problems are subject to a mix of continuum and non-equilibrium flows or conditions where one transition into the other, as a function of time and/or space. Numerically, such flows could be described with a purely kinetic method which, in the limit of small particle mean free paths, reproduces a continuum regime. However, from a computational perspective, such approaches are usually very expensive or simply not feasible, even on modern computational architectures. A solution is the construction of hybrid methods which connect the kinetic and hydrodynamic system of evolution equations. Such coupling usually requires specific boundary conditions between non-equilibrium and continuum regimes which come with their own numerical challenges and can introduce unphysical effects. Here, we present a hybrid model which uses a buffer region to transition from a kinetic into a fluid description following the original work of Degond et al. [1]. In the buffer region, both, the kinetic and hydrodynamic equations are solved simultaneously while being coupled via a so-called transition function. The latter also ensures a smooth conversion from the coupled model to either the kinetic or continuum approach at the interfaces of the buffer region. With that, the method avoids the need to find direct interface boundary conditions and allows one to localize the use of a high dimensional kinetic model only where it is needed. In our work, we extend the original method of Degond to flows with multiple particle species in 3D. We derive the coupled equations for the multispecies Vlasov-Bhatnagar-Gross-Krook (VBGK) model and its limiting Euler or Navier-Stokes hydrodynamic equations. To validate our model numerically, we simulate a Sod shock problem and study the effect of kinetic multi-species mixing in the preheat phase of a high energy-density plasma physics experiment.

Influence of hydrophobic particles on the film drainage during bubble–solid interaction

In this article, we investigate the complex drainage behavior of liquid (“dimple”) films entrapped between hydrophilic glass substrates and air bubbles in water and aqueous suspensions of polystyrene (PS) particles. The film drainage was monitored by capturing the evolution of spatial-temporal thicknesses using interferometry. Faster drainage of the entrapped film is observed in the PS colloid suspensions compared to the water. The film drainage strongly depends on the interface boundary conditions. Our experiments reveal that the air–liquid interface of the entrapped film becomes partially mobile in the PS suspensions, which results in faster drainage. The hydrophobic PS particles tend to migrate toward the air–water interface and form an ordered layer. We argue that the adsorbed layer of PS particles makes the bubble surface elastic, delaying the formation of the immobile interface.

Application of rigorous interface boundary conditions in mesoscale plasticity simulations

The interactions between dislocations and interface/grain boundaries, including dislocation absorption, transmission, and reflection, have garnered significant attention from the research community for their impact on the mechanical properties of materials. However, the traditional approaches used to simulate grain boundaries lack physical fidelity and are often incompatible across different simulation methods. We review a new mesoscale interface boundary condition based on Burgers vector conservation and kinetic dislocation reaction processes. The main focus of the paper is to demonstrate how to unify this boundary condition with different plasticity simulation approaches such as the crystal plasticity finite element (CPFEM), continuum dislocation dynamics (CDD), and discrete dislocation dynamics (DDD) methods. In DDD and CDD, plasticity is simulated based on dislocation activity; in the former, dislocations are described as discrete lines while in the latter in terms of dislocation density. CPFEM simulates plasticity in terms of slip on each slip system, without explicit treatment of dislocations; it is suitable for larger scale simulations. To validate our interface boundary condition, we implemented simulations using both the CPFEM method and a two-dimensional CDD model. Our results show that our compact and physically realistic interface boundary condition can be easily integrated into multiscale simulation methods and yield novel results consistent with experimental observations.

Small Darcy number limit of the Navier–Stokes–Darcy system

We study the small Darcy number behavior of the Navier–Stokes–Darcy system with the conservation of mass, Beavers–Joseph–Saffman–Jones condition, and the Lions balance of the normal-force interface boundary conditions imposed on the interface separating the Navier–Stokes flow and Darcy flow. We show that the asymptotic behavior of the coupled system, at small Darcy number, can be captured by two semi-decoupled Darcy number independent sequences: a sequence of (linearized) Navier–Stokes equations, and a sequence of Darcy equations with appropriate initial and boundary data. Approximate solutions to any order of the small parameter (Darcy number) can be constructed via the two sequences. The local in time validity of the asymptotic expansion up to second order is presented. And the global in time convergence is derived under the assumption that the Reynolds number is below a threshold value.

An approach to the global well-posedness of a coupled 3-dimensional Navier-Stokes-Darcy model with Beavers-Joseph-Saffman-Jones interface boundary condition

<abstract><p>This study focused on investigating the global well-posedness of a coupled Navier-Stokes-Darcy model with the Beavers-Joseph-Saffman-Jones interface boundary condition in the three-dimensional Euclidean space. By utilizing this approach, we successfully obtained the global strong solution of the system in the three-dimensional space. Furthermore, we demonstrated the exponential stability of this strong solution. The significance of such coupled systems lies in their pivotal role in the analysis of subsurface flow problems, particularly in the context of karst aquifers.</p></abstract>

Terminal-coupling induced critical eigenspectrum transition in closed non-Hermitian loops

A hallmark feature of non-Hermitian (NH) systems is the non-Hermitian skin effect (NHSE), in which the eigenenergy spectra of the system under open boundary conditions (OBC) and periodic boundary conditions (PBC) differ markedly from each other. In particular, the critical NHSE occurs in systems consisting of multiple non-Hermitian chains coupled in parallel where even an infinitesimally small inter-chain coupling can cause the thermodynamic-limit eigenenergy spectrum of the system to deviate significantly from the OBC spectra of the individual component chains. We overturn the conventional wisdom that multiple chains are required for such critical transitions by showing that such a critical effect can also be induced in a single finite-length non-Hermitian chain where its two ends are connected together by a weak terminal coupling to form a closed loop. An infinitesimally small terminal coupling can induce the thermodynamic-limit energy spectrum of the closed loop to switch from the OBC to the PBC spectrum of the chain. Similar to the critical NHSE, this switch occurs abruptly when the chain length exceeds a critical size limit. We explain analytically the underlying origin of the effect in a Hatano–Nelson chain system, and demonstrate its generality in more complex one-dimensional non-Hermitian chains. Our findings illustrate the generality of critical size-dependent effects in finite NH systems that arise from the interplay between the interfacial boundary conditions and the influence of edge localization.

Shear rate effect on clay-structure interface strength properties in various interface boundary conditions

Based on the modified simple direct shear device which can directly measure the interface pore pressure and interface shear displacement, a series of interface shear tests and corresponding pure clay shear tests were conducted at an undrained state in constant normal load (CNL) boundary conditions or equivalent undrained state in constant volume (CV) boundary conditions. The clay-structure interfaces, consisting of seabed clay and Speswhite kaolin clay with overconsolidation ratios (OCR) of 1 and 3, were tested at three shear rates, respectively V1 = 0.0002 mm/s, V2 = 0.001 mm/s, and V3 = 0.01 mm/s. The results demonstrated that the shear strength of the clay-structure interface is lower than that of pure clay, and this difference is more pronounced under CV boundary conditions. In CNL condition, though the pure clay strength decreases with increasing shear rate at OCR = 1 and increases with increasing shear rate at OCR = 3, the shear rate effect on clay-structure interface strength is not obvious. In CV condition, the strength of the interface with the normally consolidated (NC) and over consolidated (OC) clay increases approximately linearly with the shear rate on the semi-logarithmic scale. the shear rate parameter ρ is used to describe the growth rate of pure clay or clay-structure interface shear strength with a tenfold increase in shear rate. As for normally consolidated clay, in CV condition, the corresponding shear rate parameter satisfies that ρ (with R1 roughness)> ρ (pure clay)> ρ (with R2 roughness). The rate parameter corresponding to NC seabed clay is significantly higher than the rate parameter corresponding to NC Speswhite kaolin clay. For OC clay, the shear rate parameter for interface strength is higher than that for pure clay, meeting with the relationship that ρ (with R1 roughness)> ρ (with R2 roughness)> ρ (pure clay).

Lattice Boltzmann simulations for the drying of porous media with gas–side convection–diffusion boundary

One of the most significant challenges in describing the drying of porous materials is the realistic integration of internal transport phenomena into mathematical models, coupled with the external free flow. However, the intricacies of pore-scale geometry make experimentation and observation very difficult in practice, thereby making modeling techniques a useful tool for the analysis of the drying process. Among the many modeling techniques developed for drying, the lattice Boltzmann method (LBM)-based modeling approach has gained favor in recent years due to its ability to incorporate realistic geometry and transport at the pore scale. Our previous works on Shan–Chen LBM for drying of capillary porous media were based on the Bhatnagar–Gross–Krook collision operator and diffusion interface boundary conditions. This study elucidates the drying of a capillary porous medium under the influence of convection–diffusion boundary conditions at the gas side, using Shan–Chen LBM. The pore-scale effects of convection–diffusion conditions during the drying process are presented in relation to the macroscale drying kinetics. Moreover, the differences between the convection–diffusion kinetics and purely diffusion–dominated kinetics of the drying process are also presented here. This work also aims to incorporate the convection–diffusion transport phenomena into the drying process of a porous medium under the influence of an imposed thermal gradient, establishing and studying the phenomena of stabilization and destabilization of the drying front under the influence of a temperature gradient, thereby extending the lattice Boltzmann method of modeling for the simulation of convection–diffusion drying, both for the isothermal case and the imposition of a thermal gradient.

Numerically efficient full-vectorial rational Chebyshev pseudo-spectral modal analysis for optical Waveguides

In this paper, an efficient full-vectorial modal analysis based on the rational Chebyshev pseudo-spectral method (V-RCPSM) is introduced to analyze 3 dimensional (3D) structures that are invariant along one spatial variable. Such structures are essential in silicon photonics and plasmonics applications where permittivity profiles with high-index contrast need precise treatment of the interface boundary conditions. Besides, such structures are open in general. Hence, good domain truncation is important. Our method handles these challenges via hybrid usage of the domain decomposition technique where the electromagnetic field is expanded in terms of Chebyshev functions in homogeneous regions, while the rational Chebyshev functions are used for semi-infinite homogeneous domains. The boundary conditions are rigorously imposed along the interfaces, a step that maintains the known exponential convergence rate of Chebyshev functions. Chebyshev functions have the ability to capture the correct rapid variation of the electromagnetic fields at the interfaces of the high-index-contrast waveguides using only a few basis functions; a critical feature for accurate mode computation. To show the accuracy and efficiency of our new approach, we studied rib and plasmonic waveguides and compared the results with those obtained using other full-vectorial approaches such as the finite elements method (FEM). Our developed approach has achieved a huge reduction in computational resources over the FEM.

Uniform approximations and effective boundary conditions for a high-contrast elastic interface

A difficulty in the theory of a thin elastic interface is that series expansions in its thickness become disordered in the high-contrast limit, i.e. when the interface is much softer or much stiffer than the media on either side. We provide a mathematical analysis of such series for an annular coating around a cylindrical fibre embedded in an elastic matrix subject to biaxial forcing. We determine the order of magnitude of successive terms in the series, and hence the terms that need to be retained in order to ensure that every neglected term is smaller in order of magnitude than at least one retained term. In this way, we obtain uniform approximations for quantities such as the jump in the displacement and stress across the coating, and explain some peculiarities that have been observed in numerical work. A key finding is that it is essential to distinguish three types of boundary-value problem, corresponding to ‘distant forcing’, ‘localized forcing’ and ‘the homogeneous problem’, since they give different patterns of disorder in the corresponding series expansions. This provides a meaningful correspondence between physical principles and our mathematical results.

Drug delivery to the anterior segment of the eye enhanced by ultrasound - modeling and simulation

Transcorneal drug delivery has been used to treat eye diseases of both segments of the eye: anterior and posterior segments. Due to the low corneal permeability, this drug administration route has been shown to be very ineffective. Ultrasound has been used to increase the corneal drug transport. In this paper we consider a system of partial differential equations (PDEs) defined by a wave equation to describe the propagation of the pressure wave generated by a transducer, a convection-diffusion-reaction equation for the drug transport in each layer of the cornea - epithelium, stroma and endothelium. The last equations are linked with the acoustic pressure through the diffusion coefficient and the convective velocity. The system of PDEs is completed with convenient interface conditions, initial and boundary conditions. The initial boundary value problem is studied from analytical point of view and the qualitative behavior is numerically illustrated. The results confirm the effectiveness of ultrasound as enhancer of the drug delivery through the cornea.