Finite volume schemes for multilayer diffusion

March, Nathan G.; Carr, Elliot J.

doi:10.1016/j.cam.2018.06.041

Cited by 15 publications

(13 citation statements)

References 27 publications

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“…The time‐dependent percentage change in resistance of the Mg test structure, Δ R = ( h 0 / h − 1) × 100%, depends on the initial thickness h 0 and remaining thickness h , as obtained in the same manner as in the single‐layer model (see Experimental Section). The film–Mg contact transfer coefficient (defined in Experimental Section), [ 34,35 ] H film‐Mg = (2.0 ± 0.3) × 10 −11 cm s −1 , follows from experimentally measured changes in the resistance of Mg structures protected by 1‐layer SiON‐PA films in PBS at 37 °C (Figure 4B). The SiON–SiON contact transfer coefficient, [ 34,35 ] H SiON‐SiON = (3.0 ± 0.2) × 10 −11 cm s −1 , follows from similar measurements of resistance but protected by 3‐layer SiON‐PA films (Figure 4C).…”

Section: Resultsmentioning

confidence: 99%

“…The film–Mg contact transfer coefficient (defined in Experimental Section), [ 34,35 ] H film‐Mg = (2.0 ± 0.3) × 10 −11 cm s −1 , follows from experimentally measured changes in the resistance of Mg structures protected by 1‐layer SiON‐PA films in PBS at 37 °C (Figure 4B). The SiON–SiON contact transfer coefficient, [ 34,35 ] H SiON‐SiON = (3.0 ± 0.2) × 10 −11 cm s −1 , follows from similar measurements of resistance but protected by 3‐layer SiON‐PA films (Figure 4C). With these parameters, the water concentration in 1‐layer (Figure 4D) and 3‐layer (Figure 4E) SiON‐PA films after soaking in PBS at 37 °C for 10, 30, and 60 days, can be calculated.…”

Section: Resultsmentioning

confidence: 99%

“…For SiON in this study, M H2O = 18 g mol −1 , 𝜌 SiON = 2.344 g cm −3 (Table S2, Supporting Information), M SiON = 1958 g mol −1 , and q SiON = 72. [34,35] : D i ∂w i ∕∂y i | yi = hi = H i (w i+1 | yi+1 = 0 -w i | yi = hi ), which reveals a flux-dependent water concentration difference across the interface, where H i is the interfacial contact transfer coefficient. The finite integral transform and Laplace transform methods are applied to give a theoretical solution of w (see Note S1, Supporting Information, for details).…”

Section: Methodsmentioning

confidence: 99%

“…The boundary conditions at the top and bottom surfaces of the multilayer film in the model correspond to a constant water concentration, w 0 = 1 g cm −3 , and zero water flux, respectively. Combined with the continuity condition of water flux at the interface between the i th and i +1 th layers ( i = 1, 2, 3, …, m ), D i ∂ w i ∕∂ y i | yi = hi = D i +1 ∂ w i +1 ∕∂ y i +1 | yi +1 = 0 , an interfacial jump condition is applied [ 34,35 ] : D i ∂ w i ∕∂ y i | yi = hi = H i ( w i +1 | yi +1 = 0 – w i | yi = hi ), which reveals a flux‐dependent water concentration difference across the interface, where H i is the interfacial contact transfer coefficient. The finite integral transform and Laplace transform methods are applied to give a theoretical solution of w (see Note S1, Supporting Information, for details).…”

Section: Methodsmentioning

confidence: 99%

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Bioresorbable Multilayer Organic–Inorganic Films for Bioelectronic Systems

Hu,

Guo,

et al. 2024

Advanced Materials

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Bioresorbable electronic devices as temporary biomedical implants represent an emerging class of technology relevant to a range of patient conditions currently addressed with technologies that require surgical explantation after a desired period of use. Obtaining reliable performance and favorable degradation behavior demands materials that can serve as biofluid barriers in encapsulating structures that avoid premature degradation of active electronic components. Here, we present a materials design that addresses this need, with properties in water impermeability, mechanical flexibility and processability that are superior to alternatives. The approach uses multilayer assemblies of alternating films of polyanhydride and silicon oxynitride formed by spin‐coating and plasma enhanced chemical vapor deposition, respectively. Experimental and theoretical studies investigate the effects of material composition and multilayer structure on water barrier performance, water distribution, and degradation behavior. Demonstrations with inductor‐capacitor circuits, wireless power transfer systems, and wireless optoelectronic devices illustrate the performance of this materials system as a bioresorbable encapsulating structure.This article is protected by copyright. All rights reserved

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

See 2 more Smart Citations

Bioresorbable Multilayer Organic–Inorganic Films for Bioelectronic Systems

Hu,

Guo,

et al. 2024

Advanced Materials

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“…As Eqs. → 0) [4,13,21], we consider only Type A conditions in the analysis presented in this section.…”

Section: Characteristic Timescales For Multilayer Diffusionmentioning

confidence: 99%

Characteristic time scales for diffusion processes through layers and across interfaces

Carr

2018

Phys. Rev. E

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This paper presents a simple tool for characterizing the time scale for continuum diffusion processes through layered heterogeneous media. This mathematical problem is motivated by several practical applications such as heat transport in composite materials, flow in layered aquifers, and drug diffusion through the layers of the skin. In such processes, the physical properties of the medium vary across layers and internal boundary conditions apply at the interfaces between adjacent layers. To characterize the time scale, we use the concept of mean action time, which provides the mean time scale at each position in the medium by utilizing the fact that the transition of the transient solution of the underlying partial differential equation model, from initial state to steady state, can be represented as a cumulative distribution function of time. Using this concept, we define the characteristic time scale for a multilayer diffusion process as the maximum value of the mean action time across the layered medium. For given initial conditions and internal and external boundary conditions, this approach leads to simple algebraic expressions for characterizing the time scale that depend on the physical and geometrical properties of the medium, such as the diffusivities and lengths of the layers. Numerical examples demonstrate that these expressions provide useful insight into explaining how the parameters in the model affect the time it takes for a multilayer diffusion process to reach steady state.

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Image-based mesh generation for constructing a virtual representation of engineered wood product samples

Grant,

Psaltis,

Shirmohammadi

et al. 2024

Eur. J. Wood Prod.

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The complex structure of timber has traditionally been difficult to model as it is a highly heterogeneous material. The density and material properties for structural species such as Pinus radiata (radiata pine) can vary greatly across the growth rings. Numerical simulation methods are becoming more prevalent as a method of predicting moisture migration, stress and strain distributions, and fungal/rot intrusion in engineered wood products (EWPs). All these applications require a computational mesh that captures the growth ring structure to facilitate an accurate assessment of the performance of EWPs. In this work, a low-cost image-based algorithm is developed for generating a virtual representation of a small cross laminated timber panel sample. Specifically, the proposed method results in a virtual description of an EWP sample comprised of a triangular prismatic mesh where the nodes are aligned on the growth rings of each individual timber component of the EWP, with specific wood material properties allocated to each mesh element. Each small component is treated individually and we assume there is no longitudinal variation in the density, pith location, and pith angle within the mesh structure. The initial step involves analysing an image of the end grain pattern of a single clear wood sample to identify the growth rings using a spectral clustering algorithm. Next, the centre of the tree (pith) is located through an iterative constrained least-squares algorithm to determine the pith angle. Image analysis of an anatomical image combined with the pith location allows for a constant density value to be assigned to each mesh element. The capability of this framework is then demonstrated by simulating the moisture migration and heat transfer throughout a CLT sample under atmospheric and saturating boundary conditions. Furthermore, the virtual representation provides the basis for simulating additional physical and biological phenomena, such as moisture-induced swelling, decay and fungal growth.

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Finite volume schemes for multilayer diffusion

Cited by 15 publications

References 27 publications

Bioresorbable Multilayer Organic–Inorganic Films for Bioelectronic Systems

Bioresorbable Multilayer Organic–Inorganic Films for Bioelectronic Systems

Characteristic time scales for diffusion processes through layers and across interfaces

Image-based mesh generation for constructing a virtual representation of engineered wood product samples

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