A Comparison of Finite Difference Schemes for Computational Modelling of Biosensors

This paper presents a one-dimensional-in-space mathematical model of an amperometric biosensor. The model is based on the reaction-diffusion equations containing a non-linear term related to Michaelis-Menten kinetics of the enzymatic reactions. The stated problem is solved numerically by applying the finite difference method. Several types of finite difference schemes are used. The numerical results for the schemes and couple mathematical software packages are compared and verified against known analytical solutions. Calculation results are compared in terms of the precision and computation time

Modelling of wood drying and an influence of lumber geometry on drying dynamics

Modelling of wood drying is analyzed. Wood drying involves moisture transfer from the interior of the wood to the surface, then from the wood surface to the surrounding air. These processes can be characterized by the internal and surface moisture transfer coefficients. A model of the two-dimensional moisture transfer is suggested to determine these coefficients in contrast to the one-dimensional model which was proposed in [12]. The model is based on a diffusion equation with a variable diffusion coefficient. The insufficiency of the one-dimensional model is considered. The influence of the geometry of a lumber on determination of the surface emission and diffusion coefficients and on the dynamics of drying is investigated

Modelling of a microreactor on heterogeneous surface and an influence of microreactor geometry

A model of an action of the amperometric biosensors based on carbon paste electrodes encrusted with single microreactor is analyzed. The model is based on non stationary diffusion equations containing non-linear term related to the enzymatic reaction. The biosensors current, which is a function of the concentration gradient of the reaction product on the electrodes, is used for analyzing of dynamics of the reaction. An influence of a size of microreactor, a geometrical form of microreactor and a position of microreactor on the biosensors action is investigated

Further Comparisons of Finite Difference Schemes for Computational Modelling of Biosensors

Simulations are presented for a reaction-diffusion system within a thin layer containing an enzyme, fed with a substrate from the surrounding electrolyte. The chemical term is of the nonlinear Michaelis-Menten type and requires a technique such as Newton iteration for solution. It is shown that approximating the nonlinear chemical term in these systems by a linearised form reduces both the accuracy and, in the case of second-order methods such as Crank-Nicolson, reduces the global error order from O(δT2) to O(δT). The first-order methods plain backwards implicit with and without linearisation, and Crank-Nicolson with linearisation are all of O(δT) and very similar in performance, requiring, for a given accuracy target, an order of magnitude more CPU time than the efficient methods backward implicit with extrapolation and Crank-Nicolson, both with Newton iteration to handle the nonlinearity. Steady state computations agree with expectations, tending to the known solutions for limiting cases. The Crank-Nicolson method shows some concentration oscillations close to the outer layer boundary but this does not propagate to the inner boundary at the electrode. The backward implicit methods do not result in such oscillations and if concentration profiles are of interest, may be preferred

Computer Simulation of Amperometric Biosensor Response to Mixtures of Compounds

A mathematical model of amperometric biosensors has been developed. The model bases on non-stationary diffusion equations containing a non-linear term related to Michaelis-Menten kinetic of the enzymatic reaction. The model describes the biosensor response to mixtures of multiple compounds in two regimes of analysis: batch and flow injection. Using computer simulation, large amount of biosensor response data were synthesised for calibration of a biosensor array to be used for characterization of wastewater. The computer simulation was carried out using the finite difference technique

Modelling of Moisture Movement in Wood during Outdoor Storage

A model of moisture movement in wood is presented in this paper in a two-dimensional-in-space formulation. The finite-difference technique has been used in order to obtain the solution of the problem. The model was applied to predict the moisture content in sawn boards from pine during long term storage under outdoor climatic conditions. The satisfactory agreement between the numerical solution and experimental data was obtained

Computational Modelling of a Sensor Based on an Array of Enzyme Microreactors

This paper presents a two-dimensional-in-space mathematical model of a sensor system based an array of enzyme microreactors immobilised on a single electrode. The system acts under amperometric conditions. The model is based on the diffusion equations containing a non-linear term related to the Michaelis-Menten kinetics of the enzymatic reaction. The model involves three regions: an array of enzyme microreactors (cells) where enzyme reaction as well as mass transport by diffusion takes place, a diffusion limiting region where only the diffusion takes place, and a convective region, where the analyte concentration is maintained constant. Using computer simulation the influence of the geometry of the enzyme cells and the diffusion region on the biosensor response was investigated. The digital simulation was carried out using the finite difference technique

Distribution of extracellular flavins in a coastal marine basin and their relationship to redox gradients and microbial community members

The flavins (including flavin mononucleotide (FMN) and riboflavin (RF)) are a class of organic compounds synthesized by organisms to assist in critical redox reactions. While known to be secreted extracellularly by some species in laboratory-based cultures, flavin concentrations are largely unreported in the natural environment. Here, we present pore water and water column profiles of extracellular flavins (FMN and RF) and two degradation products (lumiflavin and lumichrome) from a coastal marine basin in the Southern California Bight alongside ancillary geochemical and 16S rRNA microbial community data. Flavins were detectable at picomolar concentrations in the water column (93–300 pM FMN, 14–40 pM RF) and low nanomolar concentrations in pore waters (250–2070 pM FMN, 11–210 pM RF). Elevated pore water flavin concentrations displayed an increasing trend with sediment depth and were significantly correlated with the total dissolved Fe (negative) and Mn (positive) concentrations. Network analysis revealed a positive relationship between flavins and the relative abundance of Dehalococcoidia and the MSBL9 clade of Planctomycetes, indicating possible secretion by members of these lineages. These results suggest that flavins are a common component of the so-called shared extracellular metabolite pool, especially in anoxic marine sediments where they exist at physiologically relevant concentrations for metal oxide reduction

Global silicate weathering flux over-estimated because of sediment-water cation exchange

Rivers carry the dissolved and solid products of silicate mineral weathering, a process that removes CO2 from the atmosphere and provides a key negative climate feedback over geological timescales. Here we show that in some river systems, a reactive exchange pool on river suspended particulate matter, bonded weakly to mineral surfaces, increases the mobile cation flux by 50%. The chemistry of both river waters and the exchange pool demonstrate exchange equilibrium, confirmed by Sr isotopes. Global silicate weathering fluxes are calculated based on riverine dissolved sodium (Na+) from silicate minerals. The large exchange pool supplies Na+ of non- silicate origin to the dissolved load, especially in catchments with widespread marine sediments, or where rocks have equilibrated with saline basement fluids. We quantify this by comparing the riverine sediment exchange pool and river water chemistry. In some basins, cation exchange could account for the majority of sodium in the river water, significantly reducing estimates of silicate weathering. At a global scale, we demonstrate that silicate weathering fluxes are over-estimated by 12-28%. This over-estimation is greatest in regions of high erosion and high sediment loads where the negative climate feedback has a maximum sensitivity to chemical weathering reactions. In the context of other recent findings that reduce the net CO2 consumption through chemical weathering, the magnitude of the continental silicate weathering fluxes and its implications for solid Earth CO2 degassing fluxes needs to be further investigated.NER