Solution Of Mass Transport Equations Research Articles

Absolute Analysis of Nanoparticle Suspension with Surface Plasmon Microscopy.

The recently developed surface plasmon microscopy of single nanoparticles offers a powerful tool for monitoring particle transfer from bulk solution to the adsorbing surface. In the present work, the possibility of absolute analysis of suspension, based on particle transfer observation, was examined. A model based on particle diffusion in a laminar flow, which allows analytical solution of mass transport equation, was considered. It was demonstrated that direct determination of particle concentration, based on counting the particles that bind to the sensor surface, is possible. The model contains only independent, easy to determine parameters: flow cell geometry, flow rate, particle size, and liquid viscosity. For applicability of the model, particles should be irreversibly bound when touching the sensor surface. It was demonstrated that the required "perfect binding" is provided in certain electrolyte concentration range because even particles oppositely charged to the surface do not bind in pure water. If the binding probability is less than 100%, "absoluteness" of the method is not violated. It will require the extension of the transport model with the sticking coefficient, which can be also measured by the surface plasmon microscopy directly. The present work shows the feasibility of the absolute analysis. It demonstrates the great potential of the method toward the comprehensive nanoparticle analytics and investigation of binding processes.

Simulation study of tertiary current distributions on rotating electrodes

The tertiary current distributions on rotating electrodes have been studied by using the numerical simulation method. An acid copper sulphate electrolyte composed of 0·3M CuSO4 and 1·9M H2SO4 was used within an electrochemical cell of practical dimensions. The rotating disc had a diameter of 6 mm, within which the working electrode with diameter of 3 mm was located at the bottom centre of the disc. The distributions of ion concentrations were obtained by two-dimensional fluid flow simulation and the solution of mass transport equations based on axial symmetry. The calculated concentration boundary layer thicknesses agree well with those obtained from the Levich equation. It is found that the tertiary current distribution on the working electrode is affected by the rotating velocity of the electrode, even if currents are considerably below the limiting current. The effect disappears with the increase in rotating velocity up to 1000 rev min−1 in comparison with the secondary current distribution. The tertiary current distributions for three types of working electrode have been calculated and an improved shape of working electrode is proposed. Since the working electrode is normally used for electrochemical measurements, e.g. polarisation characteristics, which are applied for the calculation of current distribution in the present work, the present study would provide beneficial results to improve the accuracy of measurements.

Modelling the crack propagation rate for corrosion fatigue at high frequency of applied stress

The application of standard mathematical techniques for the solution of mass transport equations, in the case of advection that is caused by the pulsating movement of crack walls in the case of corrosion fatigue, can be very time consuming. This problem arises, due to the requirement that the time step that must be employed, when solving the non-stationary equations numerically, must be significantly smaller than the period of oscillation. For overcoming these time-consuming limitations, a simple algorithm, which is based on eliminating the convective term from the equations of mass transfer in the pulsating slab by a suitable change of variables, was developed. The estimation of the advection effect on the rate of corrosion fatigue has been performed for the cases of diffusion and mixed kinetic control at high frequencies of applied stress. It is shown that, in many cases, it is possible to use codes that were developed for describing stress corrosion cracking, i.e. for the case of mass transfer without advection at zero loading frequency, to predict corrosion fatigue crack propagation rate, by simply substituting an effective crack length. Numerical calculations that have been performed in this work also show that the method developed here yields results that are applicable not only to the elevated frequencies, but to the any arbitrary frequency from 0 to ∞ for estimating corrosion fatigue crack propagation rate.

Numerical solution of mass transport equations in concrete structures

To calculate the service life of reinforced concrete (RC) structures, the process of reinforcement corrosion was modeled using a numerical formulation of the associated mass transport partial differential equations. Migration of chlorides, moisture and heat transfer within concrete, resulting from seasonal variations in the surface conditions of the RC member, form a coupled boundary-value problem, which was solved in space using a finite element formulation and in time using a finite difference marching scheme. The stage of active corrosion was modeled by including in the numerical algorithm of the FE formulation the mass conservation equation that describes diffusion of oxygen in the concrete cover. The paper presents details of the FE formulation and computed results from selected case studies.