Modeling the diffusion of solid copper into liquid solder alloys

During the soldering process, the copper atoms diffuse into liquid solders. The diffusion process determines integrity and the reworking possibility of a solder joint. In order to capture the diffusion scenarios of solid copper into liquid Sn–Pb and Sn–Cu solders, a computer modeling has been performed for 10 s. An analytical model has also been proposed for calculating the diffusion coefficient of copper into liquid solders. It is found that the diffusion coefficient for Sn–Pb solder is 2.74 × 10− 10 m2/s and for Sn–Cu solder is 6.44 × 10−9 m2/s. The modeling results reveal that the diffusion coefficient is one of the major factors that govern the rate at which solid Cu dissolve in the molten solder. The predicted dissolved amounts of copper into solders have been validated with the help of scanning electron microscopic analysis.

Simultaneous monitoring of drug and solvent diffusion across a model membrane using ATR-FTIR spectroscopy

Attenuated total reflectance Fourier transform infrared (ATR-FTIR) spectroscopy has been used to simultaneously follow the diffusion of model drugs and solvent across polydimethylsiloxane (silicone) membrane. Three model drugs, cyanophenol (CNP), methyl nicotinate (MN) and butyl paraben (BP) were selected to cover a range of lipophilicities. Isostearyl isostearate (ISIS) was chosen as the solvent because its large molecular weight should facilitate observation of whether the drug molecules are able to diffuse through the membrane independently of the solvent. The diffusion of the three drugs and the solvent was successfully described by a Fickian model. The effects of parameters such as the absorption wavelength used to follow diffusion on the calculated diffusion coefficient were investigated. Absorption wavelength which affects the depth of penetration of the infrared radiation into the membrane did not significantly affect the calculated diffusion coefficient over the wavelength range tested. Each of the model drugs was observed to diffuse independently of the solvent across the membrane. The diffusion of a CNP-ISIS hydrogen bonded complex across the membrane was also monitored. The relative diffusion rates of the solute and solvent across the membrane can largely be accounted for by the molecular size of the permeant.

ATR-FTIR spectroscopy and spectroscopic imaging of solvent and permeant diffusion across model membranes

The uptake and diffusion of solvents across polymer membranes is important in controlled drug delivery, effects on drug uptake into, for example, infusion bags and containers, as well as transport across protective clothing. Attenuated Total Reflectance Fourier Transform Infrared (ATR-FTIR) spectroscopy has been used to monitor the effects of different solvents on the diffusion of a model compound, 4-cyanophenol (CNP) across silicone membrane and on the equilibrium concentration of CNP obtained in the membrane following diffusion. ATR-FTIR spectroscopic imaging of membrane diffusion was used to gain an understanding of when the boundary conditions applied to Fick's second law, used to model the diffusion of permeants across the silicone membrane do not hold. The imaging experiments indicated that when the solvent was not taken up appreciably into the membrane, the presence of discrete solvent pools between the ATR crystal and the silicone membrane can affect the diffusion profile of the permeant. This effect is more significant if the permeant has a high solubility in the solvent. In contrast, solvents that are taken up into the membrane to a greater extent, or those where the solubility of the permeant in the vehicle is relatively low, were found to show a good fit to the diffusion model. As such these systems allow the ATR-FTIR spectroscopic approach to give mechanistic insight into how the particular solvents enhance permeation. The solubility of CNP in the solvent and the uptake of the solvent into the membrane were found to be important influences on the equilibrium concentration of the permeant obtained in the membrane following diffusion. In general, solvents which were taken up to a significant extent into the membrane and which caused the membrane to swell increased the diffusion coefficient of the permeant in the membrane though other factors such as solvent viscosity may also be important.

Numerical simulation of vacuum dezincing of lead alloy

Removing zinc by distillation can leave the lead bullion virtually free of zinc and also produces pure zinc crystals. Batch distillation is considered in a hemispherical kettle with water-cooled lid, under high vacuum (50 Pa or less). Sufficient zinc concentration at the evaporating surface is achieved by means of a mechanical stirrer. The numerical model is based on the multiphysics simulation package PHYSICA. The fluid flow module of the code is used to simulate the action of the stirring impeller and to determine the temperature and concentration fields throughout the liquid volume including the evaporating surface. The rate of zinc evaporation and condensation is then modelled using Langmuir’s equations. Diffusion of the zinc vapour through the residual air in the vacuum gap is also taken into account. Computed results show that the mixing is sufficient and the rate-limiting step of the process is the surface evaporation driven by the difference of the equilibrium vapour pressure and the actual partial pressure of zinc vapour. However, at higher zinc concentrations, the heat transfer through the growing zinc crystal crust towards the cold steel lid may become the limiting factor because the crystallization front may reach the melting point. The computational model can be very useful in optimising the process within its safe limits.

Mutual information performance of differential MPSK detection over time-varying channels

This paper provides mutual information performance analysis of multiple-symbol differential WSK (M-phase shift keying) over time-correlated, time-varying flat-fading communication channels. A state space approach is used to model time correlation of time varying channel phase. This approach captures the dynamics of time correlated, time-varying channels and enables exploitation of the forward-backward algorithm for mutual information performance analysis. It is shown that the differential decoding implicitly uses a sequence of innovations of the channel process time correlation and this sequence is essentially uncorrelated. It enables utilization of multiple-symbol differential detection, as a form of block-by-block maximum likelihood sequence detection for capacity achieving mutual information performance. It is shown that multiple-symbol differential ML detection of BPSK and QPSK practically achieves the channel information capacity with observation times only on the order of a few symbol intervals

Probabilistic modeling of structural deterioration of reinforced concrete beams under saline environment corrosion

For existing reinforced concrete structures exposed to saline or marine conditions, there is an increasing engineering interest in their remaining safety and serviceability. A significant factor is the corrosion of steel reinforcement. At present there is little field experience and other data available. This limits the possibility for developing purely empirical models for strength and performance deterioration for use in structural safety and serviceability assessment. An alternative approach using theoretical concepts and probabilistic modeling is proposed herein. It is based on the evidence that the rate of diffusion of chlorides is influenced by internal damage to the concrete surrounding the reinforcement. This may be due to localized stresses resulting from external loading or through concrete shrinkage. Usually, the net effect is that the time to initiation of active corrosion is shortened, leading to greater localized corrosion and earlier reduction of ultimate capacity and structural stiffness. The proposed procedure is applied to an example beam and compared to experimental observations,including estimates of uncertainty in the remaining ultimate moment capacity and beam stiffness. Reasonably good agreement between the results of the proposed procedure and the experiment was found