Embedded interface method

Two-way embedded interfacing methods. These involve embedding an atomistic or CG model within a continuum representation. Implicit solvent models fall into this category. New multiscale methods, which capture hydrodynamic and mechanical effects have now also been developed. 

It is noticed that after some re-evaluation Tryggvason and co-workers [228, 222] classified their front tracking method [227] as an embedded interface method, since it is best described as a hybrid between a front tracking and a front capturing method. 

In this sub-section the embedded interface method (frequently referred to as a front tracking method) developed for direct numerical simulations of viscous multi-fluid flows is outlined and discussed. The unsteady model is based on the whole held formulation in which a sharp interface separates immiscible fluids, thus the different phases are treated as one fluid with variable material properties. Therefore, equations (3.14) and (3.15) account for both the differences in the material properties of the different phases as well as surface tension effects at the phase boundary. The bulk fluids are incompressible. The numerical surface tension force approximation used is consistent with the VOF and LS techniques [222] [32], hence the major novelty of the embedded interface method is in the way the density and viscosity fields are updated when the fluids and the interface evolve in time and space. 

Tryggvason G (1999) Embedded Interface Methods Applications. In Modelling and Computation of Multiphase Flows, Short Course, Zurich, Switzerland, March 8-12, 16B l-27. 

Now that the top-down internal state variable theory was established, the bottom-up simulations and experiments were required. At the atomic scale (nanometers), simulations were performed using Modified Embedded Atom Method, (MEAM) Baskes [176], potentials based upon interfacial atomistics of Baskes et al. [177] to determine the conditions when silicon fracture would occur versus silicon-interface debonding [156]. Atomistic simulations showed that a material with a pristine interface would incur interface debonding before silicon fracture. However, if a sufficient number of defects were present within the silicon, it would fracture before the interface would debond. Microstructural analysis of larger scale interrupted strain tests under tension revealed that both silicon fracture and debonding of the silicon-aluminum interface in the eutectic region would occur [290, 291]. 

Although a valence-type force field of the type illustrated by Eq. [1] is most suitable for modeling molecular systems, the electronegativity equalization approach to treating polarization can be coupled equally well to other types of potentials. Streitz and Mintmire used an EE-based model in conjunction with an embedded atom method (EAM) potential to treat polarization effects in bulk metals and oxides. The resulting ES + EAM model has been parameterized for aluminum and titanium oxides, and has been used to study both charge-transfer effects and reactivity at interfaces. 

Continuum models can be directly interfaced with atomistic or coarse grain models using a two-way embedded interface. In this scheme, the atomistic or CG model is embedded within a continuum model. Implicit solvent methods, in which an atomistic or CG model of a solute is embedded within a continuum model of the solvent, are popular and well-established examples of this type of interface. Implicit solvent models represent the solvent as a dielectric continuum, and allow the electrostatics of the atomistic or CG solute to polarise the continuum, which then results in an electrostatic reaction field that returns to interact with the solute. Implicit solvent models have been reviewed in detail many times before, and enable the dynamic transfer of electrostatic information across the atomistic/ continuum or CG/continuum interfaces. Recently, new multiscale continuum methods have been developed that allow for the dynamic transfer of mechanical and hydrodynamic information across these interfaces. One example is the work by Villa... 

Metal-solution interfaces are of obvious importance to corrosion, but they are particularly difficult to model. By definition, the interface comprises that part of the system in which the intensive variables of the two adjoining phases differ from their respective bulk values, and even in concentrated solutions this implies a thickness of the order of 15-20 A. This is too large to be modeled solely by density functional theory (DFT), which surface scientists often use as a panacea for the metal-gas interface. In addition, the two adjoining phases are of very different nature metals are usually solid at ambient temperatures, and their properties do not differ too much from those at 0 K, so that DFT, or semiempirical force fields like the embedded atom method, are good methods for their investigation. By contrast, the molecules in solutions are highly mobile, and thermal averaging is indispensable. Therefore, the two parts of the interface usually require different models, and an important part of the art consists in their combination. 

Several studies have focused on extensive MD simulations of Pt nanoparticles adsorbed on carbon in the presence or absence of ionomers [109-113]. Lamas and Balbuena performed classical molecular dynamics simulations on a simple model for the interface between graphite-supported Pt nanoparticles and hydrated Nation [113]. In MD studies of CLs, the equilibrium shape and structure of Pt clusters are usually simulated using the embedded atom method (EAM). Semi-empirical potentials such as the many-body Sutton-Chen potential (SC) [114] are popular choices for the close-packed metal clusters. Such potential models include the effect of the local electron density to account for many-body terms. The SC potential for Pt-Pt and Pt-C interactions provides a reasonable description of the properties of small Pt clusters. The potential energy in the SC potential is expressed by... 

Cammarata [14] has reviewed the subject of interface stress and presents theoretical values for several metal/metal interfaces, which were calculated using embedded-atom methods. The calculated interfacial stresses for (111)/(111) interfaces both for Ag/Cu and for Ag/Ni were tensile. The calculated value for Ag/Cu was 0.32 J/m, while the experimental value is -3.19 J/m. The cause of this discrepancy is not known but the experimental value should at worst be correct with regard to sign. 

Figure 1 schematically displays the coupling procedure. The system is subdivided into three zones the atomistic domain, modeled by an interatomic potential such as the embedded atom method (EAM) or Morse potential, the continumn domain, where an FE approach is used, and an interface domain, where atoms and FE meshes overlap. 

In this method [89], a single fiber is taken and partially embedded in a drop of uncured resin placed on a holder. The resin is then cured with the fiber held upright. The holder, with resin and fiber, is held in a grip attached to the crosshead and then pulled out from the resin. The force pulling the fiber out of the resin is balanced by shear stress at the resin-fiber interface holding the fiber in place. The maximum shear stress occurs as the embedded length tends to zero and is given by ... 

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