An Immersed Interface Method for the Incompressible Navier-Stokes Equations in Irregular Domains

We present an immersed interface method for the incompressible Navier Stokes equations capable of handling rigid immersed boundaries. The immersed boundary is represented by a set of Lagrangian control points. In order to guarantee that the no-slip condition on the boundary is satisfied, singular forces are applied on the fluid at the immersed boundary. The forces are related to the jumps in pressure and the jumps in the derivatives of both pressure and velocity, and are interpolated using cubic splines. The strength of singular forces is determined by solving a small system of equations at each time step. The Navier-Stokes equations are discretized on a staggered Cartesian grid by a second order accurate projection method for pressure and velocity.

An augmented method for free boundary problems with moving contact lines

An augmented immersed interface method (IIM) is proposed for simulating one-phase moving contact line problems in which a liquid drop spreads or recoils on a solid substrate. While the present two-dimensional mathematical model is a free boundary problem, in our new numerical method, the fluid domain enclosed by the free boundary is embedded into a rectangular one so that the problem can be solved by a regular Cartesian grid method. We introduce an augmented variable along the free boundary so that the stress balancing boundary condition is satisfied. A hybrid time discretization is used in the projection method for better stability. The resultant Helmholtz/Poisson equations with interfaces then are solved by the IIM in an efficient way. Several numerical tests including an accuracy check, and the spreading and recoiling processes of a liquid drop are presented in detail. (C) 2010 Elsevier Ltd. All rights reserved.

La méthode IIM pour une membrane immergée dans un fluide incompressible

La méthode IIM (Immersed Interface Method) permet d'étendre certaines méthodes numériques à des problèmes présentant des discontinuités. Elle est utilisée ici pour étudier un fluide incompressible régi par les équations de Navier-Stokes, dans lequel est immergée une membrane exerçant une force singulière. Nous utilisons une méthode de projection dans une grille de différences finies de type MAC. Une dérivation très complète des conditions de saut dans le cas où la viscosité est continue est présentée en annexe. Deux exemples numériques sont présentés : l'un sans membrane, et l'un où la membrane est immobile. Le cas général d'une membrane mobile est aussi étudié en profondeur.

Une nouvelle mise en oeuvre de la méthode IIM pour les équations de Navier-Stokes en présence d'une force singulière

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal

An electrokinetic sensor for studying immersed surfaces, using focused ultrasound

A novel method for obtaining information on the charge density of an immersed surface is presented. The technique uses focused ultrasound to excite oscillatory fluid motion in the plane of the solid-liquid interface, over a localised area. The displacement current (resulting from the motion of fluid-borne ions in the outer double-layer) is detected by electrodes in the liquid. The method is demonstrated as a means for monitoring protein adsorption, and for monitoring interactions between two different proteins. A second electrokinetic effect at the interface is identified, isolated from the first, and shown to provide additional information on the compressibility and charge density of the double-layer. © 2001 Elsevier Science B.V. All rights reserved.

Charge transfer across the water/nitrobenzene interface by three-electrode system

A droplet of aqueous solution containing a certain molar ratio of redox couple is first attached onto a platinum electrode surface, then the resulting drop electrode is immersed into the organic solution containing very hydrophobic electrolyte. Combined with reference and counter electrodes, a classical three-electrode system has been constructed, Ion transfer (IT) and electron transfer (ET) are investigated systematically using three-electrode voltammetry. Potassium ion transfer and electron transfer between potassium ferricyanide in the aqueous phase and ferrocene in nitrobenzene are observed with potassium ferricyanide/potassium ferrocyanide as the redox couple. Meanwhile, the transfer reactions of lithium, sodium, potassium, proton and ammonium ions are obtained with ferric sulfate/ferrous sulfate as the redox couple. The formal transfer potentials and the standard Gibbs transfer energy of these ions are evaluated and consistent with the results obtained by a four-electrode system and other methods.

Study of facilitated potassium ion transfer across a water vertical bar 1,2-dichloroethane interface using different phase volume ratio systems

A study of potassium ion transfer across a water \ 1,2-dichloroethane (W \ DCE) interface facilitated by dibenzo-18-crown-6 (DB18C6) with various phase volume ratio systems is presented. The key point was that a droplet of aqueous solution containing a redox couple, Fe(CN)(6)(3-)/Fe(CN)(6)(4-), with equal molar ratio, was first attached to a platinum electrode surface, and the resulting droplet electrode was then immersed into the organic solution containing a hydrophobic electrolyte to construct a platinum electrode/aqueous phase/organic phase system. The interfacial potential of the W \ DCE within the series could be externally controlled because the specific compositions in the aqueous droplet make the Pt electrode function like a reference electrode as long as the concentration ratio of Fe(CN)(6)(3-)/Fe(CN)(6)(4-) remains constant. In this way, a conventional three-electrode potentiostat can be used to study the ion transfer process at a liquid \ liquid (L \ L) interface facilitated by an ionophore with variable phase volume ratio (r = V-o/V-w). The effect of r on ion transfer and facilitated ion transfer was studied in detail experimentally. We also demonstrated that as low as 5 x 10(-8) M DB18C6 could be determined using this method due to the effect of the high phase volume ratio.

Study of electron-transfer reactions across an externally polarized water/1,2-dichloroethane interface by scanning electrochemical microscopy

A novel method to study electron-transfer (ET) reactions between ferrocene in 1,2-dichloroethane (DCE) and a redox couple of K3Fe(CN)(6) and K4Fe(CN)(6) in water using scanning electrochemical microscopy (SECM) with a three-electrode setup is reported. In this work, a water droplet that adheres to the Surface of a platinum disk electrode is immersed in a DCE solution. The aqueous redox couple serves both as a reference electrode on the platinum disk and as an electron donor/acceptor at the polarized liquid/liquid inter-face. With the present experimental approach, the liquid/liquid interface can be polarized externally, while the electron-transfer reactions between the two phases can be monitored independently by SECM. The apparent heterogeneous rate constants for the ET reactions were obtained by fitting the experimental approach curves to the theoretical values. These rate constants obey the Butler-Volmer theory i.e., them, are found to be potential dependent.

Reflection and Transmission at a Phase Discontinuous Interface

In this paper we extend the derivation of the modified form Snells's law that occurs when an additional phase profile is introduced at the material interface. We show that this permits electromagnetic (EM) beam steering, negative refraction and retrodirective action opportunities for such engineered surfaces even if they are immersed in a uniform dielectric. Simple expressions for the retrodirected and negatively refracted beams are derived along with the propagation conditions that occur at the boundary interface inside the critical angle range. It is also demonstrated how the transmission and reflected power levels are affected by the additional phase taper introduced at the surface.

Bacterial leakage along the implant-abutment interface of premachined or cast components

In recent clinical studies, contamination of the inner parts of dental implants through bacterial penetration along the implant components has been observed. The aim of the present in-vitro study was to investigate leakage of Fusobacterium. nucleatum through the interface between implants and premachined or cast abutments. Both premachined (n = 10) and cast (n = 10) implant abutment assemblies were inoculated with 3.0 mu L of microbial inoculum. The assemblies were completely immersed in 5.0 mL of tryptic soy broth culture medium to observe leakage at the implant-abutment interface after 14 days of anaerobic incubation. Bacterial growth in the medium, indicative of microbial leakage, was found only in 1 out of 9 samples (11.1%) in each group. Both premachined and cast abutments connected to external hexagonal implants provide low percentages of bacterial leakage through the interface in in vitro unloaded conditions if the manufacturer`s instructions and casting procedures are properly followed.

A discontinuous-Galerkin-based immersed boundary method

A numerical method to approximate partial differential equations on meshes that do not conform to the domain boundaries is introduced. The proposed method is conceptually simple and free of user-defined parameters. Starting with a conforming finite element mesh, the key ingredient is to switch those elements intersected by the Dirichlet boundary to a discontinuous-Galerkin approximation and impose the Dirichlet boundary conditions strongly. By virtue of relaxing the continuity constraint at those elements. boundary locking is avoided and optimal-order convergence is achieved. This is shown through numerical experiments in reaction-diffusion problems. Copyright (c) 2008 John Wiley & Sons, Ltd.

Efficient solutions to robust, semi-implicit discretizations of the immersed boundary method

The immersed boundary method is a versatile tool for the investigation of flow-structure interaction. In a large number of applications, the immersed boundaries or structures are very stiff and strong tangential forces on these interfaces induce a well-known, severe time-step restriction for explicit discretizations. This excessive stability constraint can be removed with fully implicit or suitable semi-implicit schemes but at a seemingly prohibitive computational cost. While economical alternatives have been proposed recently for some special cases, there is a practical need for a computationally efficient approach that can be applied more broadly. In this context, we revisit a robust semi-implicit discretization introduced by Peskin in the late 1970s which has received renewed attention recently. This discretization, in which the spreading and interpolation operators are lagged. leads to a linear system of equations for the inter-face configuration at the future time, when the interfacial force is linear. However, this linear system is large and dense and thus it is challenging to streamline its solution. Moreover, while the same linear system or one of similar structure could potentially be used in Newton-type iterations, nonlinear and highly stiff immersed structures pose additional challenges to iterative methods. In this work, we address these problems and propose cost-effective computational strategies for solving Peskin`s lagged-operators type of discretization. We do this by first constructing a sufficiently accurate approximation to the system`s matrix and we obtain a rigorous estimate for this approximation. This matrix is expeditiously computed by using a combination of pre-calculated values and interpolation. The availability of a matrix allows for more efficient matrix-vector products and facilitates the design of effective iterative schemes. We propose efficient iterative approaches to deal with both linear and nonlinear interfacial forces and simple or complex immersed structures with tethered or untethered points. One of these iterative approaches employs a splitting in which we first solve a linear problem for the interfacial force and then we use a nonlinear iteration to find the interface configuration corresponding to this force. We demonstrate that the proposed approach is several orders of magnitude more efficient than the standard explicit method. In addition to considering the standard elliptical drop test case, we show both the robustness and efficacy of the proposed methodology with a 2D model of a heart valve. (C) 2009 Elsevier Inc. All rights reserved.

Estudo das propriedades mecânicas da interface adesiva criada por sistemas adesivos convencional e autocondicionante, associados ou não ao laser Nd:YAG, utilizando a técnica da nanoindentação

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Produção do conhecimento em Serviço Social: análise das dissertações de mestrado defendidas no Programa de Pós-graduação em Serviço Social da Unesp - Campus Franca entre 1999 e 2009 e a interface com a indústria calçadista de Franca-SP

Pós-graduação em Serviço Social - FCHS

Avaliação do selamento de ápices radiculares retrobturados ou recobertos com diferentes materiais mediante infiltração marginal por corante e análise da interface em microscopia eletrônica de varredura

The purpose of this study was to evaluate the apical sealing ability and the marginal adaptation of five dental materials used in retrofillings or applied to the bevelled root surface. One hundred and forty extracted single rooted human teeth were used, divided into seven groups of twenty each. ln the first, second, third and fourth groups, the teeth were apicoectomized, submitted to cavity preparations and retrofilled with one of the following materiais: zinc free silver amalgam, a dentin bonding system plus composite resin, a glass ionomer cement ora compomer. In the fifth, sixth and seventh groups, the teeth were apicoectomized and capped on the bevelled root surface with one of the following materiais: a dentin bonding system plus composite resin, a glass ionomer cement or a compomer. Two specimens of each experimental group were evaluated for the marginal adaptation using scanning electron microscopy. The remaining 126 specimens were immersed in 2% methylene blue dye, stored for one week at 37ºC and the infiltration was evaluated with a stereomicroscope. The results showed that the glass ionomer cement presented the lowest values of marginal infiltration when used as retrofilling material, with a significant statistical difference when compared with the others tested materials. When used as apical capping, the glass ionomer cement and the compomer were equivalent and significantly better than the dentin bonding system plus composite resin. Using scanning electron microscopy, all the materials showed some slight adjustment problem. ln the retrofilling, the smallest marginal gaps were observed with the compomer and the dentin bonding system plus composite resin, while the largest were observed with the glass ionomer cement and zinc free silver amalgam. ln the apical capping, the smallest marginal gaps were observed with the compomer and the dentin bonding system plus composite resin and ...