Effect of concentration-dependent diffusion coefficient on dendrite growth in directional solidification

Ray tracing method is used to study the propagation of collimated beams in a liquid–core cylindrical lens (LCL), which has dual functions of diffusion cell and image formation. The diffusion images on the focal plane of the used LCL are simulated by establishing and solving both linear and nonlinear ray equations, the calculated results indicate that the complex imaging results of LCL in inhomogeneous media can be treated by the law of ray propagation in homogeneous media under the condition of small refractive index gradient of diffusion solution. Guided by the calculation conditions, the diffusion process of triethylene glycol aqueous solution is experimentally studied at room temperature by using the LCL in this paper. The spatial and temporal concentration profile Ce(z, t) of diffusion solution is obtained by analyzing diffusion image appearing on the focal plane of the LCL; Then, the concentration-dependent diffusion coefficient is assumed to be a polynomial D(C) = D0 × (1 + α1C + α2C2 + α3C3 + ⋅). The finite difference method is used to solve the Fick diffusion equation for calculating numerically the concentration profiles Cn(z, t). The D(C)of triethylene glycol aqueous solution is obtained by comparing the Cn(z, t) with Ce(z,t). Finally, the obtained polynomial D(C) is used to calculate the refractive index profiles nn(z,t)s of diffusion solution in the used LCL. Based on the ray propagation law in inhomogeneous media and the calculated n(z,t), the ray tracing method is used again to simulate the dynamic images of the whole experimental diffusion process to varify the correctness of the calculated D(C). The method presented in this work opens up a new way for both measuring and verifying the concentration-dependent liquid diffusion coefficients.

One of the most effective energy saving technologies is the improvement of existing heat and mass exchange units. A stream-bubble contact device is designed to enhance the operation efficiency of heat and mass exchange units. The stages of the stream-bubble units that are proposed by the authors for the decarbonization process comprise contact devices with equivalent sizes, whose number is determined by the required performance of a unit. This approach to the structural design eliminates the problems that arise upon the transition from laboratory samples to industrial facilities and makes it possible to design the units of any required performance without a decrease in the effectiveness of mass exchange. To choose the optimal design that provides the maximum effectiveness of the mass-exchange processes in units and their intensification, the change of the mass-transfer coefficient is analyzed with the assumption of a number of parameters. The results of the study of the effect of various structural parameters of a stream-bubble contact device on the mass-transfer coefficient in the liquid phase are given. It is proven that the mass-transfer coefficient increases in the liquid phase, in the first place, with the growth of the level of liquid in the contact element, because the rate of the liquid run-off grows in this case and, consequently, the time of surface renewal is reduced; in the second place, with an increase in the slot diameter in the downpipe, because the jet diameter and, accordingly, their section perimeter and the area of the surface that is immersed in liquid increase; and, in the third place, with an increase in the number of slots in the downpipe, because the area of the surface that is immersed in the liquid of the contact element increases. Thus, in order to increase the mass-transfer coefficient in the liquid phase, it is necessary to design the contact elements with a minimum width and a large number of slots and their increased diameter; in this case, the filling degree of contact elements by the liquid must be maximum.

The dendritic growth patterns in directional solidification with different amplitudes of solid-liquid interface energy anisotropy were investigated using the two-dimensional cellular automata (CA) model. It is shown that when the preferred growth direction of the crystal was the same as the direction of thermal gradient, the solidification pattern would transform from seaweed to dendrite with the increase of amplitude of interface energy anisotropy. The amplitude of interface energy anisotropy could also influence the morphology of dendritic tips. As the amplitude of interface energy anisotropy increased, the dendritic tip radius, the liquid concentration ahead of the tip and the tip undercooling decreased. A power law relationship evisted between the stability parameter of dendritic tip and the amplitude of interface energy anisotropy in directional solidification. The primary arm spacing changed little with the increase of interface energy anisotropy. When the angle between the preferred growth direction of the crystals and the direction of thermal gradient was-40, and the amplitude of interface energy anisotropy increased, the solidification pattern would transform from seaweed to degenerated dendrite and finally to tilted dendrite.

Correlation of diffusion coefficients for naphthalene and dimethylnaphthalene isomers in supercritical carbon dioxide

Drying kinetic measurements of polymer nanolayers – Experimental results with a model-based validation and interpretation of solvent diffusion

Intrinsic diffusion coefficients have been calculated for a solid solution binary fcc metal alloy with vacancies using grand canonical and kinetic Monte Carlo (MC) methods for a variety of model Hamiltonians. Model Hamiltonians include a kinetically and thermodynamically ideal case, solute-vacancy attraction and repulsion, and solute-solute attraction and repulsion. These model Hamiltonians are chosen to have constant average activation energies in order to focus on contributions from other thermodynamic and kinetic factors. The thermodynamic factor calculated using MC is compared to a mean-field regular solution model. It is shown that the mean-field model accurately predicts the thermodynamic factors for each model alloy Hamiltonian except for the alloys with a solute-solute interaction and concentration that are in the spinodal region (as predicted by the regular solution model). The MC determined concentration-dependent intrinsic diffusion coefficients are compared to values determined from the dilute five-frequency model and Darken and Manning analytical approximations. The results indicate that for a solid solution with known average barriers and vacancy concentration, Darken and Manning approximation-based analytic expressions and mean-field theory can be used to predict concentration-dependent diffusion coefficients within a factor of approximately three, provided the system is outside of the spinodal region. The good accuracy of this approximate approach follows from the fact that the thermodynamic factor is the main contribution to the concentration dependence of the diffusion constants, and that this thermodynamic factor is well described by mean-field theory.

The inverse gas chromatography (IGC) method has been evaluated as a method to determine diffusion coefficients in polymer–solvent systems near the glass transition temperature. The poly(vinyl acetate)–toluene system was used for this purpose. Diffusion and partition coefficients were measured over a wide range of temperature. At temperatures significantly above the glass transition of the polymer, the capillary column model developed by Pawlisch and co-workers1,2 was used. At temperatures near the glass transition temperature, the modification of the capillary column model, proposed by Vrentas et al.3 was used. A sensitivity analysis of the capillary column model was made to delineate the range of applicability of the model. The diffusion coefficients obtained from IGC were compared with those extrapolated from the gravimetric sorption technique. The values agree within the expected range of error. Finally, free-volume theory was evaluated for its ability to predict the temperature and concentration dependencies of diffusion coefficients at temperatures near the glass transition from high temperature IGC data. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1233–1240, 1997

Recent predictive equations for evaluating the value of diffusion coefficients, developed for two hard sphere−solvent systems, have been extended to n-hard-sphere−solvent systems. This model has been used to predict the diffusion behavior of nonionic polymer−solvent mixtures as a first-order function of volume fraction from the knowledge of the distribution function. Hence, the entire diffusion matrix for polydisperse systems, which include both main- and cross-term diffusion coefficients, has been built up for the first time. The main-terms diffusion coefficients Dii are mostly affected by the variation in viscosity. The magnitude of the cross-term diffusion coefficients Dij is strictly related to the abundance and diffusivity of solute i and to the molecular volume corresponding to solute j. The predicted diffusion coefficients have been used to calculate the apparent, average diffusion coefficients, which are compared with the experimental values measured by the Gouy interferometry method in the case of the poly(ethylene glycol) homologous series. The agreement between the calculated and experimental Gouy parameters is good. The cross-term diffusion coefficients are found to be significant in the calculation of the apparent diffusion coefficient for a polydisperse solute. Some comments on the study of ternary systems containing a polydisperse solute are done.

In this paper, we consider the problem of the stability of an isothermal system of two miscible fluids in a gravity field. Fluids are aqueous solutions of non-reacting substances with different diffusion coefficients. At the very beginning, the solutions uniformly fill half-spaces, which are separated from each other by an infinitely thin horizontal contact surface. Such a configuration can be easily realized experimentally, although it is more difficult for theoretical analysis. We assume that the initial configuration of the system is statically stable. After the start of evolution, the solutions begin to mix, penetrating each other, and creating conditions for the development of the convective instability of double diffusion. An important complicating factor of the problem is the functional dependence of the diffusion coefficients of solutions on their concentration. In recent years, this effect has been actively studied, since its significant influence on convective stability has been proven experimentally. For simplicity, we assume that the diffusion coefficients of solutions depend linearly on concentration. The problem of the stability of a mixture includes the equation of motion in the Darcy and Boussinesq approximation, the continuity equation, and two transport equations for the concentrations. The solution to this problem in the absence of the effect of concentration-dependent diffusion is well known from the literature. If we take into accountsuch a dependence, then we have to deal with the problem of nonlinear diffusion, which can only be solved numerically. To find an analytical solution to the problem, we propose to apply the method of preliminary linearization of Wiedeburg (1890). The method is well known in the theory of thermal conductivity, although it was originally developed specifically for solutions of substances. In our case, we demonstrate that the conditions for convective stability of the base state can be obtained analytically. The comparative analysis of the discrepancy between the Wiedeburg solution and the numerical solution is given. Based on the closed-form analytical solution, we obtain a stability map for the problem under the consideration. We show how the effect of concentration-dependent diffusion affects stability.

Microfluidics to determine the diffusive mass transfer of a low viscosity solvent into a high viscosity hydrocarbon

Diffusion of polarizable colloids in electromagnetic fields

Brownian dynamics (BD) has been applied as a comprehensive tool to model sedimentation and diffusion of nanoparticles in analytical ultracentrifugation (AUC) experiments. In this article, we extend the BD algorithm by considering space-dependent diffusion and solvent compressibility. With this, the changes in the sedimentation and diffusion coefficient from altered solvent properties at increased pressures are accurately taken into account. Moreover, it is demonstrated how the concept of space-dependent diffusion is employed to describe concentration-dependent sedimentation and diffusion coefficients, in particular, through the Gralen coefficient and the second virial coefficient. The influence of thermodynamic nonideality on diffusional properties can be accurately simulated and agree with well-known evaluation tools. BD simulations for sedimentation equilibrium and sedimentation velocity (SV) AUC experiments including effects of hydrodynamic and thermodynamic nonideality are validated by global evaluation in SEDANAL. The interplay of solvent compressibility and retrieved nonideality parameters can be studied utilizing BD. Finally, the second virial coefficient is determined for lysozyme from SV AUC experiments and BD simulations and compared to membrane osmometry. These results are in line with DLVO theory. In summary, BD simulations are established for the validation of nonideal sedimentation in AUC providing a sound basis for the evaluation of complex interactions even in polydisperse systems.

The gradient of Bicoid (Bcd) is key for the establishment of the anterior-posterior axis in Drosophila embryos. The gradient properties are compatible with the SDD model in which Bcd is synthesized at the anterior pole and then diffuses into the embryo and is degraded with a characteristic time. Within this model, the Bcd diffusion coefficient is critical to set the timescale of gradient formation. This coefficient has been measured using two optical techniques, Fluorescence Recovery After Photobleaching (FRAP) and Fluorescence Correlation Spectroscopy (FCS), obtaining estimates in which the FCS value is an order of magnitude larger than the FRAP one. This discrepancy raises the following questions: which estimate is "correct''; what is the reason for the disparity; and can the SDD model explain Bcd gradient formation within the experimentally observed times? In this paper, we use a simple biophysical model in which Bcd diffuses and interacts with binding sites to show that both the FRAP and the FCS estimates may be correct and compatible with the observed timescale of gradient formation. The discrepancy arises from the fact that FCS and FRAP report on different effective (concentration dependent) diffusion coefficients, one of which describes the spreading rate of the individual Bcd molecules (the messengers) and the other one that of their concentration (the message). The latter is the one that is more relevant for the gradient establishment and is compatible with its formation within the experimentally observed times.

ABSTRACTThe effects of the implantation parameters (dose and energy) on the Arsenic redistribution and outdiffusion rate in (100) p-type silicon, after 7–12 s Rapid Thermal Annealing in the 1100–1200°C temperature range have been investigated. Four doses ranging from 2×1014 to l×1016 cm−2, and As+ energies between 70 and 170 keV, have been studied. The experimental diffusion profiles obtained from the SIMS measurements, in complement with the RBS results, were modelled using the one dimensional Fick's equation with semi-infinite boundary conditions, using a concentration and temperature dependent diffusion coefficient D(C, T). The As diffusivity was classically attributed to As+V0, As+V−, and As+V − pairs with the related diffusion coefficients taken from the literature. A relatively good description of the As redistribution was obtained without introducing any transient or SPE effects.

A computational assessment of water and salt transport parameters describing the coupled moisture and chloride transport in porous media is presented in this paper.The experimentally determined moisture profiles, chloride concentration profiles and chloride binding isotherm are subjected to inverse analysis where three different modes of salt solution transport are assumed.On the basis of this analysis, moisture dependent moisture diffusivity and salt concentration dependent chloride diffusion coefficient are calculated.The obtained results can find use in computational modelling of salt transport in porous building materials which is currently a very important topic, particularly from the point of view of durability of building materials and service life of building structures exposed to salt attack.