Examinando por Materia "Effective time constant"
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Ítem Dynamics of an Electrochemical Biosensor for the Detection of Toxic Substances in Water(SPIE-INT SOC OPTICAL ENGINEERING, 2016-01-01) Simon, L.; Ospina, J.; Simon, L.; Ospina, J.; Universidad EAFIT. Departamento de Ciencias; Lógica y ComputaciónA proposed analytical method focuses on electrolyte transport to the electrode of an electrochemical cell. The recombinant Escherichia coli whole-cell biosensor detects toxicity in water based on a set of biochemical reactors. Previous contributions elucidated the kinetics of product formation and validated a mathematical model for its diffusion in the chamber. This work introduces an approach to investigate the dynamics of the probe using Laplace transforms and an effective time constant. The transfer function between the electrolyte production and the total current revealed a faster response for larger electrode radii. Both the first-order and effective time constants increased with the chamber height and radius. Separation of variables yields closed-form solutions and helps estimate the kinetics of p-aminophenol generation. When the bacteria were exposed to phenol concentrations of 1.6, 8.3 and 16 ppm, the corresponding overall rate constants were 5.11x10(-7), 1.13x10(-6) and 1.99x10(-6) (product concentration unit/s(2)), respectively. In addition to parameter estimation, the method can be applied to perform sensitivity analysis and aid manufacturers in meeting design specifications of biosensors.Ítem The dynamics of shrinking and expanding drug-loaded microspheres: A semi-empirical approach(ELSEVIER SCIENCE BV, 2014-07-16) Simon L; Ospina J; Willits RK; Simon L; Ospina J; Willits RK; Universidad EAFIT. Departamento de Ciencias; Lógica y ComputaciónThe dynamics of shrinking and expanding drug-loaded microspheres were studied using a diffusion equation in spherical coordinates. A movable boundary condition was incorporated as a convection term in the original model. The resulting convective-diffusive problem was solved using Laplace transform techniques with the Bromwich integral and the residue theorem. Analytical solutions were derived for the general case of shrinking or expanding microspheres and three particular kinetics expressions: linear growth, exponential swelling and exponential shrinking. Simulations show that microspheres with fast-swelling kinetics released their therapeutic cargo at a relatively slow rate in the first two cases. Ninety-nine percent of the medication was delivered at four times the effective time constant. In line with laboratory studies using bovine serum albumin, an increase in the shrinking rate led to a fast release of the medication from its carrier. The method was applied to analyze insulin transport through spherical Ca-alginate beads. A good agreement was noted between predicted and experimental data. The theoretical effective time constant was 114.0 min.Ítem A FIRST-ORDER TIME CONSTANT ESTIMATION FOR NONLINEAR DIFFUSION PROBLEMS(TAYLOR & FRANCIS INC, 2014-06-03) Simon, Laurent; Ospina, Juan; Simon, Laurent; Ospina, Juan; Universidad EAFIT. Departamento de Ciencias; Lógica y ComputaciónA Laplace transform-based procedure was proposed to calculate the effective time constant for a class of nonlinear diffusion problems. The governing mathematical representation was first estimated with a linear model by omitting the nonlinear term. The solution to this problem was later introduced into the original equation, which was solved with Laplace transforms, resulting in a first-order approximation of the real system's behavior. A time constant was calculated using frequency-domain expressions. Two case studies were considered to illustrate the methodology. As the rate of heat supplied to a rod is raised, the speed at which the temperature reached an equilibrium value decreased. Increasing the maximum velocity in reaction-diffusion transport by a factor of three lowered the time constant by only 1.7%. The applications of this method range from biosensor dynamics to process control. © 2014 Copyright Taylor and Francis Group, LLC.Ítem On the effusion time of drugs from the open pore of a spherical vesicle(ELSEVIER SCIENCE BV, 2016-06-01) Simon, L.; Ospina, J.; Simon, L.; Ospina, J.; Universidad EAFIT. Departamento de Ciencias; Lógica y ComputaciónSolute permeation through a spherical liposomal vesicle was analyzed using Fick's second law and a mixed Neumann-Dirichlet boundary condition. The first-principles approach was necessary to help calculate the effusion time of a medication through a pore located on the surface of the device. An infinite series of Bessel functions represented the concentration in the Laplace domain. This method yielded closed-form expressions for the characteristic time and the Laplace-transformed fraction of drug released, which was approximated by the first term of the series. The time constant was inversely proportional to the diffusion coefficient in the system and decreased as the pore size increased. It took 4 times the effusion time to unload nearly ninety-eight percent of the pharmaceutical ingredient. (C) 2016 Elsevier B.V. All rights reserved.Ítem Three-dimensional analyses of a perforated cylindrical drug delivery device(ELSEVIER SCIENCE BV, 2015-03-15) Simon L; Ospina J; Simon L; Ospina J; Universidad EAFIT. Departamento de Ciencias; Lógica y ComputaciónA closed-formed solution of a perforated drug-delivery model was developed. Laplace transforms were applied to the governing equation, which included diffusion through the tubular device and mass transfer across a rectangular cut. A first-order estimate for the fraction of drug released, in terms of the Laplace variable, was derived after employing suitable boundary and initial conditions. The effective time constant for the process was calculated. The residue theorem and the Zakian method were proposed as two reliable approaches to recover the solution in the time domain. Simulations show that the drug was released faster at higher Sherwood numbers. Ninety-eight percent (98%) of the loading dose was delivered after a period corresponding to four time constants. This analytical platform can aid in the design of implants for long-term delivery applications. (C) 2015 Elsevier B.V. All rights reserved.Ítem A three-dimensional semi-analytical solution for predicting drug release through the orifice of a spherical device(ELSEVIER SCIENCE BV, 2016-07-25) Simon, L.; Ospina, J.; Simon, L.; Ospina, J.; Universidad EAFIT. Departamento de Ciencias; Lógica y ComputaciónThree-dimensional solute transport was investigated for a spherical device with a release hole. The governing equation was derived using the Fick's second law. A mixed Neumann-Dirichlet condition was imposed at the boundary to represent diffusion through a small region on the surface of the device. The cumulative percentage of drug released was calculated in the Laplace domain and represented by the first term of an infinite series of Legendre and modified Bessel functions of the first kind. Application of the Zakian algorithm yielded the time-domain closed-form expression. The first-order solution closely matched a numerical solution generated by Mathematica (R). The proposed method allowed computation of the characteristic time. A larger surface pore resulted in a smaller effective time constant. The agreement between the numerical solution and the semi-analytical method improved noticeably as the size of the orifice increased. It took four time constants for the device to release approximately ninety-eight of its drug content. © 2016 Elsevier B.V. All rights reserved.