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Amorphous polymer-derived Si-C-N ceramics can be doped with different elements (Al, B etc.) through various pre-ceramic polymer routes. Thus, controlling of the high temperature oxidation resistance can be achieved on an atomic level. An important factor for silica layer growth is oxygen diffusion in protective thermally grown layers. In order to get insight of the oxygen diffusion mechanism, analysis should include both, bulk and short-circuit diffusion. XRD measurements of oxidized Si-C-N and SiC revealed the possibility that oxide layers were fully crystallized and are composed of nano-sized cristobalite-like grains. Secondary ion mass spectrometry depth profile analysis after ¹⁸O₂-¹⁶O₂ isotope exchange experiments on oxidized SiC indicated that short-circuit diffusion is probably grain boundary diffusion of molecular oxygen.

An original approach for accurately measuring the mass transfer of a single bubble rising in a liquid is reported. The approach consists in using PLIF technique (Planar Laser Induced Fluorescence) at micro-scale to capture images of the released oxygen concentration field in the bubble wake. The applicability of the technique for determining mass transfer coefficients in different fluids (1 < Re < 100) is demonstrated and the relevance of the results is corroborated by established correlations. This direct and non-intrusive technique could be a promising tool to enrich the understanding of mass transfer phenomena.

Diffusion is an essential component of gas exchange at the cellular and tissue level, and a mathematical analysis of diffusion is therefore important to model biological processes in many systems. When several factors affect diffusion, finding an explicit non-steady-state equation can be difficult or impossible. In an earlier work (J Biol Systems15:63–72), we described such a function for a system where oxygen diffuses from the air into a body that consumes oxygen, assuming that the exchange surface is flat. Here, an explicit solution is limited to the case where tissue oxygen consumption decreases linearly with oxygen concentration and reaches 0 only when all oxygen has been consumed. The objective of this article is the analysis of gas diffusion into a respiring tissue that is cylindrical, which applies to tree stems and is a more realistic approximation for many other organs. This approach differs from diffusion along a flat surface, resulting in formally completely different explicit solutions, and is more flexible allowing for different relationships between oxygen concentration and tissue oxygen consumption.

The goal of this article is to find a correct approximated solution using a polynomial of sixth degree for the free boundary problem corresponding to the diffusion of oxygen in a spherical medium with simultaneous absorption at a constant rate, and to show some mistakes in previously published solutions.

Oxygen diffusion in porous media (ODPM) with rough surfaces (RS) under dry and wet conditions is of great interest. In this work, a novel fractal model for the oxygen effective diffusivity of porous media with RS under dry and wet conditions is proposed. The proposed fractal model is expressed in terms of relative roughness, the water saturation, fractal dimension for tortuosity of tortuous capillaries, fractal dimension for pores, and porosity. It is observed that the normalized oxygen diffusivity decreases with increasing relative roughness and fractal dimension for capillary tortuosity. It is found that the normalized oxygen diffusivity increases with porosity and fractal dimension for pore area. Besides, it is seen that that the normalized oxygen diffusivity under wet condition decreases with increasing water saturation. The determined normalized oxygen diffusivity is in good agreement with experimental data and existing models reported in the literature. With the proposed analytical fractal model, the physical mechanisms of oxygen diffusion through porous media with RS under dry and wet conditions are better elucidated. Every parameter in the proposed fractal model has clear physical meaning, with no empirical constant.

Manganese porphyrins are of interest due to the optical, electronic and magnetic properties of the central metal ion, coupled to the low bandgap of the polyaromatic ring. These attractive characteristics are harnessed in solutions or in ultra-thin films, such as, for example, self-assembled monolayers. However, for devices, thicker films deposited using a controlled and reproducible method are required. Here we present the morphological, structural, chemical and optical properties of manganese(III) tetraphenylporphyrin chloride (MnTPPCl) thin films deposited using organic molecular beam deposition, typically employed to process analogue molecules for applications such as organic photovoltaics. We find, using a combination of UV-vis and X-ray photoelectron spectroscopies, that the sublimation process leads to the scission of the Mn–Cl bond. The resultant film is a Mn(II)TPP:Mn(III)TPPCl blend where approximately half the molecules have been reduced. Following growth, exposure to air oxidizes the Mn(II)TPP molecule. Through quantitative analysis of the time-dependent optical properties, the oxygen diffusion coefficient (D) $\sim 1.9\times 10^{-17}{\mathrm{\text{cm}}}^2/\mathrm{\text{s}}$ is obtained, corresponding to a slow bulk oxidation following fast oxidation of a 8-nm-thick surface layer. The bulk diffusion D is lower than for analogous polycrystalline films, suggestion that grain boundaries, rather than molecular packing, are the rate-limiting steps in oxidation of molecular films. Our results highlight that the stability of the axial ligands should be considered when depositing metal porphyrins from the vapor phase, and offer a solvent-free route to obtain reproducible and smooth thin films of complex materials for engineering film functionalities.

In this paper, we investigate the diffusion of oxygen in a spherical cell including nonlinear uptake kinetics. The Lane–Emden boundary value problem with Michaelis–Menten kinetics is used to model the dimensionless oxygen concentration in our analysis. We first convert the Lane–Emden equation to the equivalent Volterra integral form that incorporates the boundary condition at the cell's center, but which still leaves one unknown constant of integration, as an intermediate step. Next we evaluate the Volterra integral form of the concentration and its flux at the cell membrane and substitute them into the remaining boundary condition to determine the unknown constant of integration by appropriate algebraic manipulations. Upon substitution we have converted the equivalent Volterra integral form to the equivalent Fredholm–Volterra integral form, and use the Duan–Rach modified recursion scheme to effectively decompose the unknown constant of integration by formula. The Adomian decomposition method is then applied to solve the equivalent nonlinear Fredholm–Volterra integral representation of the Lane–Emden model for the concentration of oxygen within the spherical cell. Our approach shows enhancements over existing techniques.

Bioconvection has shown significant promise for environmentally friendly, sustainable “green” fuel cell technologies. The improved design of such systems requires continuous refinements in biomathematical modeling in conjunction with laboratory and field testing. Motivated by exploring deeper the near-wall transport phenomena involved in bio-inspired fuel cells, in the present paper, we examine analytically and numerically the combined free-forced convective steady boundary layer flow from a solid vertical flat plate embedded in a Darcian porous medium containing gyrotactic microorganisms. Gyrotaxis is one of the many taxes exhibited in biological microscale transport, and other examples include magneto-taxis, photo-taxis, chemotaxis and geo-taxis (reflecting the response of microorganisms to magnetic field, light, chemical concentration or gravity, respectively). The bioconvection fuel cell also contains diffusing oxygen species which mimics the cathodic behavior in a proton exchange membrane (PEM) system. The vertical wall is maintained at iso-solutal (constant oxygen volume fraction and motile microorganism density) and iso-thermal conditions. Wall values of these quantities are sustained at higher values than the ambient temperature and concentration of oxygen and biological microorganism species. Similarity transformations are applied to render the governing partial differential equations for mass, momentum, energy, oxygen species and microorganism species density into a system of ordinary differential equations. The emerging eight order nonlinear coupled, ordinary differential boundary value problem features several important dimensionless control parameters, namely Lewis number (Le), buoyancy ratio parameter i.e. ratio of oxygen species buoyancy force to thermal buoyancy force (Nr), bioconvection Rayleigh number (Rb), bioconvection Lewis number (Lb), bioconvection Péclet number (Pe) and the mixed convection parameter ($𝜀)$ spanning the entire range of free and forced convection. The transformed nonlinear system of equations with boundary conditions is solved numerically by a finite difference method with central differencing, tridiagonal matrix manipulation and an iterative procedure. Computations are validated with the symbolic Maple 14.0 software. The influence of buoyancy and bioconvection parameters on the dimensionless temperature, velocity, oxygen concentration and motile microorganism density distribution, Nusselt, Sherwood and gradient of motile microorganism density are studied. The work clearly shows the benefit of utilizing biological organisms in fuel cell design and presents a logical biomathematical modeling framework for simulating such systems. In particular, the deployment of gyrotactic microorganisms is shown to stimulate improved transport characteristics in heat and momentum at the fuel cell wall.

In vitro tools, which can enable development of models that replicate the cell microenvironment associated with complex diseases such as osteoarthritis (OA), are critically needed. In OA, catabolic and inflammatory processes orchestrated by multiple cell types lead to the eventual destruction of articular cartilage. To address this need, our group developed a device that will enable investigation of complex cell systems. Our stackable tissue culture insert was fabricated and characterized with respect to biocompatibility, ease of use, and potential for tissue culture applications. The stackable tissue culture inserts can be easily modified, fabricated, and assembled into commercially available multi-well plates. In vitro studies conducted with three different cell types demonstrated high cell viability and functional secretion when cultured in the stackable inserts. Furthermore, synergistic effects when the three cell types were cultured together were observed. This demonstrates the need to more fully interrogate in vitro culture systems, and this stackable insert can provide a tool to fill the current technological void to do so.

Manganese porphyrins are of interest due to the optical, electronic and magnetic properties of the central metal ion, coupled to the low bandgap of the polyaromatic ring. These attractive characteristics are harnessed in solutions or in ultra-thin films, such as, for example, self-assembled monolayers. However, for devices, thicker films deposited using a controlled and reproducible method are required. Here we present the morphological, structural, chemical and optical properties of manganese(III) tetraphenylporphyrin chloride (MnTPPCl) thin films deposited using organic molecular beam deposition, typically employed to process analogue molecules for applications such as organic photovoltaics. We find, using a combination of UV-vis and X-ray photoelectron spectroscopies, that the sublimation process leads to the scission of the Mn–Cl bond. The resultant film is a Mn(II)TPP:Mn(III)TPPCl blend where approximately half the molecules have been reduced. Following growth, exposure to air oxidizes the Mn(II)TPP molecule. Through quantitative analysis of the time-dependent optical properties, the oxygen diffusion coefficient (D) ~1.9 × 10^-17 cm²/s is obtained, corresponding to a slow bulk oxidation following fast oxidation of a 8-nm-thick surface layer. The bulk diffusion D is lower than for analogous polycrystalline films, suggestion that grain boundaries, rather than molecular packing, are the rate-limiting steps in oxidation of molecular films. Our results highlight that the stability of the axial ligands should be considered when depositing metal porphyrins from the vapor phase, and offer a solvent-free route to obtain reproducible and smooth thin films of complex materials for engineering film functionalities.