Studies on diffusion in molten metals

Solute diffusion is an important process that determines the dendrite growth during solidification. The theoretical model generally simplifies the solute diffusion coefficient in liquid phase into a constant. Nevertheless, the composition of the boundary layer changes greatly in the solidification process, the diffusion coefficient will no longer be a constant and is dependent on concentration. In this paper, the quantitative phase field model is used to simulate the effect of concentration-dependent diffusion coefficient on dendrite growth in directional solidification. In the model, the concentration-dependent diffusion process is investigated by coupling the concentration-dependent diffusion coefficient in the liquid solute diffusion equation. A series of simulation results confirms that the concentration-dependent diffusion process has a significant effect on the dendrite growth. The results show that the increase of the coupling intensity of solute concentration will enhance the diffusion of solute in the mushy zone between primary dendrites to the dendrite tip, resulting in the increase of solute enrichment at the dendrite tip, thereby increasing the tip undercooling. The variation of diffusion coefficient in liquid phase has little effect on the tip radius of dendrite, and the simulation results are in good agreement with those from the theoretical model. Moreover, the amplitude of dendritic side branches decreases with the increase of solute diffusion coefficient. In the study of dendrite arrays, it is found that the concentration-dependent diffusion coefficient increases the primary spacing and reduce the tip position. The results of this study indicate that for a system with a concentration-dependent coefficient significantly, the effect of concentration-dependent diffusion on tip undercooling and side branches should be considered in the quantitative and experimental verification of the existing model.

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

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.

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

Transport through a slab membrane governed by a concentration-dependent diffusion coefficient: III. Numerical solution of the diffusion equation: ‘early-time’ and ‘ [formula omitted]’ procedures

Transport through a slab membrane governed by a concentration-dependent diffusion coefficient: Part V. Transient-state fluxes

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

Diffusion of polarizable colloids in electromagnetic fields

A linear stability analysis of a moving planar interface between the liquid and solid phases in an isothermal phase transformation is carried out with the diffusion coefficient assumed to be a slowly varying function of concentration. The results of this analysis show that for the precipitation system under consideration (one in which the distribution coefficient, a ratio of the equilibrium concentration of solute on the solid side of the interface to that on the liquid side, is greater than unity), there is a destabilizing influence if the diffusion coefficient is an increasing function of concentration and a stabilizing one if it is a decreasing function.

Study of transport of small molecules through ethylene- co-vinyl acetate copolymers films. Part A: Water molecules

Diffusion coefficients for the systems aqueous xylose solution and aqueous malotse solution at 25°C were measured by the Rayleigh interference method. Viscosities of these systems were also determined. The concentration dependence of diffusion coefficient for maltose solution is well described by the Gordon relation. For xylose solution, however, a small deviation from this relation is observed. The translational frictional coefficient of maltose was calculated by the shell model of Bloomfield et al. If the effect of the local viscosity around a molecule of the solute is corrected, the agreement between the calculated and the observed values is satifsactory.

Thermochemical surface engineering by nitriding/carburizing of stainless steel causes a surface zone of expanded austenite, which improves the wear resistance of the stainless steel while preserving the stainless behavior. As a consequence of the thermochemical surface engineering, huge residual stresses are introduced in the developing case, arising from the volume expansion that accompanies the dissolution of high interstitial contents in expanded austenite. Modelling of the composition and stress profiles developing during low temperature surface engineering from the processing parameters temperature, time and gas composition is a prerequisite for targeted process optimization. A realistic model to simulate the developing case has to take the following influences on composition and stress into account: - a concentration dependent diffusion coefficient - trapping of nitrogen by chromium atoms - the effect of residual stress on diffusive flux - the effect of residual stress on solubility of interstitials - plastic accommodation of residual stress. The effect of all these contributions on composition and stress profiles will be addressed.

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

A mathematical simulation carried out to study the physical mechanisms of moisture diffusion into hygroscopic fabrics during humidity transients is reported. On the basis of a mathematical model developed to describe the coupled heat and moisture transfer in wool fabric, the moisture-sorption mechanisms are investigated for fabrics made from fibers with different degrees of hygroscopicity. Theoretical predictions on the moisture uptake and temperature changes under humidity transients are compared with those measured previously in a sorption-cell experiment for fabrics made from wool, cotton, acrylic fiber, and polypropylene fiber. It is concluded that the physical mechanism of moisture diffusion into highly hygroscopic fibers such as wool and cotton can he described by a two-stage moisture-diffusion process: a fast Fickian diffusion with a concentration-dependent diffusion coefficient and a slow diffusion with a time-dependent diffusion coefficient. For weakly hygroscopic fibers such as polypropylene fiber, the moisture-sorption process can be described by a single Fickian diffusion with a constant diffusion coefficient. Through theoretical calculations of the distributions of moisture concentration in the air of fabric void space, fiber moisture content, and temperature through fabric thickness, we show that moisture diffusion into a fabric through air is a fast process for all the fabrics studied. Meanwhile, the moisture diffusion into fibers is coupled with the heat-transfer process, which is much slower and is dependent on the ability of fibers to absorb moisture. The strength of the coupling effect is a function of a number of fiber properties, such as the moisture-sorption isotherms, water-diffusion coefficient, fiber diameter, and heat of sorption.

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.