scholarly journals Computational Modelling of Biosensors with an Outer Perforated Membrane

2009 ◽  
Vol 14 (1) ◽  
pp. 85-102 ◽  
Author(s):  
K. Petrauskas ◽  
R. Baronas
Keyword(s):  
Diffusion Coefficient ◽  
Effective Diffusion Coefficient ◽  
Effective Diffusion ◽  
Enzymatic Reaction ◽  
Computational Modelling ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
D Model ◽  
Kinetics Of ◽  
Biosensor Response

This paper presents one-dimensional (1-D) and two-dimensional (2-D) in-space mathematical models for amperometric biosensors with an outer perforated membrane. The biosensor action was modelled by reaction-diffusion equations with a nonlinear term representing the Michaelis-Menten kinetics of an enzymatic reaction. The conditions at which the 1-D model can be applied to simulate the biosensor response accurately were investigated numerically. The accuracy of the biosensor response simulated by using 1-D model was evaluated by the response simulated with the corresponding 2-D model. A procedure for a numerical evaluation of the effective diffusion coefficient to be used in 1-D model was proposed. The numerically calculated effective diffusion coefficient was compared with the corresponding coefficients derived analytically. The numerical simulation was carried out using the finite difference technique.

scholarly journals Drying Kinetics of Noni Seeds

2019 ◽  
Vol 11 (5) ◽  
pp. 250 ◽  
Author(s):  
Wellytton Darci Quequeto ◽  
Osvaldo Resende ◽  
Patrícia Cardoso Silva ◽  
Fábio Adriano Santos e Silva ◽  
Lígia Campos de Moura Silva
Keyword(s):  
Experimental Data ◽  
Activation Energy ◽  
Diffusion Coefficient ◽  
Moisture Content ◽  
Mathematical Models ◽  
Effective Diffusion Coefficient ◽  
Effective Diffusion ◽  
Information Criterion ◽  
Drying Kinetics ◽  
Kinetics Of

Noni seeds have been used for years as an important medicinal source, with wide use in the pharmaceutical and food industry. Drying is a fundamental process in the post-harvest stages, where it enables the safe storage of the product. Therefore, the present study aimed to fit different mathematical models to experimental data of drying kinetics of noni seeds, determine the effective diffusion coefficient and obtain the activation energy for the process during drying under different conditions of air temperature. The experiment used noni seeds with initial moisture content of 0.46 (decimal, d.b.) and dehydrated up to equilibrium moisture content. Drying was conducted under different controlled conditions of temperature, 40; 50; 60; 70 and 80 ºC and relative humidity, 24.4; 16.0; 9.9; 5.7 and 3.3%, respectively. Eleven mathematical models were fitted to the experimental data. The parameters to evaluate the fitting of the mathematical models were mean relative error (P), mean estimated error (SE), coefficient of determination (R2), Chi-square test (c2), Akaike Information Criterion (AIC) and Schwarz’s Bayesian Information Criterion (BIC). Considering the fitting criteria, the model Two Terms was selected to describe the drying kinetics of noni seeds. Effective diffusion coefficient ranged from 8.70 to 23.71 × 10-10 m2 s-1 and its relationship with drying temperature can be described by the Arrhenius equation. The activation energy for noni seeds drying was 24.20 kJ mol-1 for the studied temperature range.

Apparent Parameters of Enzymatic Plate-Gap Electrode

2005 ◽  
Vol 10 (3) ◽  
pp. 211-211 ◽  
Author(s):  
I. Kaunietis ◽  
R. Šimkus ◽  
V. Laurinavičius ◽  
F. Ivanauskas
Keyword(s):  
Enzymatic Reaction ◽  
Reaction Diffusion ◽  
Wide Range ◽  
Steady State Current ◽  
Substrate Diffusion ◽  
Michaelis Constants ◽  
Complete Set ◽  
Kinetics Of ◽  
Substrate Concentrations ◽  
Biosensor Response

It was suggested that reaction-diffusion conditions in pores of bulk enzymatic electrode resemble particular conditions in thin enzyme filled gap between parallel conducting plates. The plate-gap model of porous enzymatic electrode is based on the diffusion equations containing a nonlinear term related to the Michaelis-Menten kinetics of the enzymatic reaction inside the gap. Steady state current was calculated for the wide range of given values of substrate diffusion coefficient, depth of the gap and substrate concentrations. Simple approximate relationships between “apparent” parameters of amperometric biosensor (maximal currents and apparent Michaelis constants) and given values of diffusion characterising parameters were derived. Association of these dependences with previously reported relationships led to derive approximate formulae that bind apparent parameters with the complete set of given parameters of the plate-gap enzymatic electrode. The limit case of slow diffusion into deep gap was also characterised. In this specific case, the highest numerical values of the apparent parameters were obtained. However, this gain is achievable at the expense of biosensor response time.

scholarly journals A Comparison of Finite Difference Schemes for Computational Modelling of Biosensors

2007 ◽  
Vol 12 (3) ◽  
pp. 359-369 ◽  
Author(s):  
E. Gaidamauskaitė ◽  
R. Baronas
Keyword(s):  
Finite Difference ◽  
Computational Modelling ◽  
Computation Time ◽  
Reaction Diffusion ◽  
Difference Schemes ◽  
Reaction Diffusion Equations ◽  
Finite Difference Schemes ◽  
Enzymatic Reactions ◽  
Calculation Results ◽  
Kinetics Of

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.

Influence of Diffusion through a Porous Film under Electrode Surface in Chronoamperometry Problems

2021 ◽  
Vol 413 ◽  
pp. 84-90
Author(s):  
Daniil Bograchev
Keyword(s):  
Diffusion Coefficient ◽  
Electrode Surface ◽  
Effective Diffusion Coefficient ◽  
Effective Diffusion ◽  
Electrode Reaction ◽  
Direct Numerical Simulations ◽  
High Porosity ◽  
Kinetics Of ◽  
Stationary Approximation ◽  
Good Agreement

In the presented work on chronoamperometry, the Cottrell model has been generalized by taking into account a thin porosity layer covering the surface of the electrode and Tafel kinetics of an electrode reaction. The effective diffusion coefficient inside a porosity layer is calculated by Bruggeman’s law. It is shown that in the quasi-stationary approximation of diffusion inside a thin porous layer, the chronoamperometry problem can be solved analytically. The obtained solution has been compared with the results of direct numerical simulations and a good agreement is shown. Limiting cases of the solution related to low and high porosity are considered.

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

2004 ◽  
Vol 9 (3) ◽  
pp. 203-218 ◽  
Author(s):  
R. Baronas ◽  
F. Ivanauskas ◽  
J. Kulys ◽  
M. Sapagovas
Keyword(s):  
Digital Simulation ◽  
Enzymatic Reaction ◽  
Computational Modelling ◽  
Enzyme Reaction ◽  
Diffusion Region ◽  
Two Dimensional ◽  
Analyte Concentration ◽  
Finite Difference Technique ◽  
Kinetics Of ◽  
Biosensor Response

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.

scholarly journals Drying kinetics of blackberry leaves

2018 ◽  
Vol 22 (8) ◽  
pp. 570-576 ◽  
Author(s):  
Elton A. S. Martins ◽  
André L. D. Goneli ◽  
Alexandre A. Goncalves ◽  
Cesar P. Hartmann Filho ◽  
Valdiney C. Siqueira ◽  
...  
Keyword(s):  
Activation Energy ◽  
Diffusion Coefficient ◽  
Effective Diffusion Coefficient ◽  
Effective Diffusion ◽  
Fixed Bed ◽  
Drying Kinetics ◽  
Drying Time ◽  
Thin Layer Drying ◽  
Air Speed ◽  
Kinetics Of

ABSTRACT Blackberry leaves have some pharmacological properties and one of the most widespread and studied uses is to relieve symptoms of the climacteric and other symptoms during the premenstrual period. Thus, drying becomes important for the conservation and storage of the product until its use or processing. The present study aimed to evaluate the drying kinetics of blackberry leaves, as well as to determine the effective diffusion coefficient and the activation energy during the drying process. Blackberry leaves were dried in an experimental fixed-bed dryer under four controlled temperature conditions (40, 50, 60 and 70 °C) and two drying air speeds (0.4 and 0.8 m s-1). With the experimental data of moisture ratio, eight mathematical models were fitted to represent the process of thin-layer drying of agricultural products. Based on the obtained results, it was found that the Midilli model represented best the phenomenon of drying of blackberry leaves. The increase in temperature and air speed reduced the drying time of blackberry leaves and increased the values of the effective diffusion coefficient. This relation can be described by the Arrhenius equation, which has an activation energy for the liquid diffusion during drying of 65.94 and 66.08 kJ mol-1, for drying air speeds of 0.4 and 0.8 m s-1, respectively.

scholarly journals Drying kinetics of sunflower grains

2017 ◽  
Vol 21 (3) ◽  
pp. 203-208 ◽  
Author(s):  
Thaís A. de S. Smaniotto ◽  
Osvaldo Resende ◽  
Kelly A. de Sousa ◽  
Daniel E. C. de Oliveira ◽  
Rafael C. Campos
Keyword(s):  
Activation Energy ◽  
Diffusion Coefficient ◽  
Moisture Content ◽  
Effective Diffusion Coefficient ◽  
Effective Diffusion ◽  
Initial Moisture Content ◽  
Air Ventilation ◽  
Forced Air ◽  
Kinetics Of ◽  
Best Fit

ABSTRACT The objectives of this study were to fit different mathematical models to experimental data of drying of sunflower grains, determine and evaluate the effective diffusion coefficient and obtain the activation energy for the process during the drying under various conditions of air. The sunflower grains were collected with an initial moisture content of 0.5267 dry basis (d.b.) and dried in an oven with forced air ventilation under five temperature conditions: 35, 50, 65, 80 and 95 °C, until reaching the moisture content of 0.0934 ± 0.0061 (d.b.). Among the analyzed models, Wang and Singh showed the best fit to describe the drying phenomenon. The effective diffusion coefficient of sunflower grains increased with the increment in air temperature and has activation energy for liquid diffusion in the sunflower drying of 29.55 kJ mol-1.

scholarly journals Mathematical Modeling of Thin-Layer Drying Kinetics of Piper aduncum L. Leaves

2019 ◽  
Vol 11 (8) ◽  
pp. 225
Author(s):  
Wellytton Darci Quequeto ◽  
Valdiney Cambuy Siqueira ◽  
Geraldo Acácio Mabasso ◽  
Eder Pedroza Isquierdo ◽  
Rafael Araujo Leite ◽  
...  
Keyword(s):  
Activation Energy ◽  
Free Energy ◽  
Diffusion Coefficient ◽  
Gibbs Free Energy ◽  
Effective Diffusion Coefficient ◽  
Effective Diffusion ◽  
Drying Kinetics ◽  
Thin Layer Drying ◽  
Piper Aduncum ◽  
Kinetics Of

As well as most agricultural products, some medicinal plants need to go through a drying process to ensure quality maintenance, however each product behaves differently. Therefore, the present study aimed to evaluate the drying kinetics of spiked pepper (Piper aduncum L.) leaves and determine their thermodynamic properties at different drying temperatures in laboratory scale. Leaves with initial moisture content of 78% w.b. (wet basis) were subjected to drying at temperatures of 40, 50, 60 and 70 ºC and air speed of 0.85 m s-1 in an experimental fixed bed dryer. The drying kinetics of the leaves was described by statistical fitting of mathematical models and determination of effective diffusion coefficient and activation energy. Enthalpy, entropy and Gibbs free energy were also evaluated for all drying conditions. It was concluded that, among the models evaluated, only Midilli and Valcam can be used to represent the drying of Piper aduncum leaves; the first for the two highest temperatures (60 and 70 ºC) and the second for 40 and 50 ºC. The activation energy was approximately 55.64 kJ mol-1, and the effective diffusion coefficient increase with the elevation of temperature. The same occurs with the values of Gibbs free energy, whereas the specific enthalpy and entropy decrease.

scholarly journals Computational modelling of the biosensor acting under parallel substrates conversion with dialysis membrane

2012 ◽  
Vol 53 ◽  
Author(s):  
Vytautas Ašeris
Keyword(s):  
Mathematical Model ◽  
Dimensional Space ◽  
Effective Diffusion ◽  
Computational Modelling ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Dialysis Membrane ◽  
Layered Model ◽  
Diffusion Layers ◽  
Model Response

A mathematical model of biosensor acting under parallel substrates conversion is investigated in this paper. Model consists of reaction-diffusion equations with non-linear terms, which in general case are solved numericaly. The mathematical model describes biosensor action in one-dimensional space, which consists of enzymatic, dialysis and diffusion layers. The purpose of this work was to define for which parameter values the layers of diffusion and dialysis membrane can be replaced by one external layer, described by the effective diffusion coefficient. The simulation error of two-layered model response was investigated by comparing it to the values of three-layered model response. 

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