Calculation Of Effective Diffusion Coefficient Research Articles

Multi-component sorption of Pb2+, Cu2+ and Ni2+ on PEI modified chitosan-based hybrid membranes

Novel poly(ethylene imine) (PEI) modified chitosan-based hybrid membranes (PMCHMs) were created via a soft chemistry method, in which unmodified chitosan (CS) firstly reacted with PEI to produce a CS-PEI precursor. Later, such CS-PEI precursor was blended with silicone to create the membrane solution of PMCHMs. Finally, PMCHMs could be obtained via phase-inversion process. Multi-component sorption of Pb2+, Cu2+ and Ni2+ on PMCHMs in metal mixed solutions, such as, Pb2+&Cu2+ and Pb2+&Ni2+ binary, Pb2+, Cu2+ and Ni2+ ternary, as well as Pb2+, Cu2+, Ni2+, Cd 2+ and Cr3+ quintuple mixed solutions, was inspected. The calculation of effective diffusion coefficients, distribution coefficients and selectivity coefficients showed that Pb2+ sorption on PMCHMs had excellent selectivity in these mixed multi-metal solutions. While, the calculation of activation energy proved that Pb2+, Cu2+ and Ni2+ sorption on PMCHMs was a physic-sorption process Also, mechanism insight reveals that Pb2+ sorption on PMCHMs could be depicted via Lagergren pseudo-2nd-order kinetic model and Langmuir or Freundlich isotherm equation. Exclusively, intra-particle diffusion process was discussed in detail. Desorption testing verified that HCl is a good desorbent for metals sorption on PMCHMs and the cycle time of membranes can arrive at 6 times. These results demonstrate that PMCHMs can be used to preferentially eradicate Pb2+ from metal mixture solutions, showing prospective applications in the treatment of metal mixture wastewater from waste vehicle power-battery and other various metal-bearing polluted water.

Calculation of effective diffusion coefficient in a colloidal crystal by the finite-element method

The work is devoted to the calculation of effective diffusion coefficient of ions from the bulk solution to the electrode through a mask and the calculation of the distribution of the limiting current density over the electrode surface. A colloidal crystal, which is formed by orderly arranged monodispersed spherical particles, serves as a mask. It is shown that the diffusion of electroactive ions in the pores between spherical particles can be simulated by unit cells with rhombic, rectangular, or triangular cross-section. In the latter case, the cell side surface has no periodical boundaries. This simplifies significantly the numerical solution of the Laplace’s equation by the finite-element method. The effective diffusion coefficient in the bulk colloidal crystal is calculated at various values of its porosity. The calculated results agree well with the literature data. It is found that, for close-packed spherical particles, the relative effective diffusion coefficient in the bulk colloidal crystal is 0.16. The thicknesses of transient zones adjacent to the electrode surface and outer boundary of colloidal crystal and the effective diffusion coefficients for these zones are determined. The dependence of effective diffusion coefficient on the number of spherical particle layers in the colloidal crystal is obtained. The distribution of the limiting current density over the electrode surface is analyzed at various numbers of particle layers.

Calculation of effective diffusion coefficient in even approximations of the surface pseudo source method

The preference of even approximations of the surface pseudo source method for calculation of the diffusion coefficient is substantiated. The homogenization limit for the G0 approximation in the case of the cell size tending to zero is analytically proved.

Classical diffusion in strong random media

We study classical diffusion of particles in random media. Although many of our results are general, we focus on the case of an ion in a three-dimensional medium with random, quenched charge centers obeying bulk charge neutrality. Within a functional-integral framework, we calculate the effective diffusion coefficients by first-order and second-order self-consistent perturbation theory (with a Gaussian reference in both cases). We also carry out a one-loop order momentum space renormalization group calculation. The self-consistent methods are complicated numerically and fail beyond intermediate disorder strengths. In contrast, the renormalization group calculation gives an analytical result that appears valid even to high disorder strengths. The methodology, generally applicable to a quantitative calculation of effective diffusion coefficients in disordered media, resolves deficiencies in self-consistent perturbation theory approaches to this class of problems.

Transmission of water through a biocompatible polyurethane: application to circulatory assist devices.

The permeability characteristics of a water-segmented polyurethane (Biomer) system under the conditions encountered in circulatory-assist devices were investigated. A diffusion cell and permeability system providing precise control of membrane boundary conditions and allowing continuous measurement of water vapor transmission was designed. Liquid water at 37 degrees C was used as the donor fluid and the system incorporated a constant-flow nitrogen carrier gas and an optical dew point sensor downstream to determine the water vapor mass flow rate as a function of time. The mass flow rate was then numerically integrated and plotted against time to allow calculation of effective diffusion coefficient (D) by the dynamic time lag method. Steady-state permeabilities were found to be insensitive to donor chamber hydrostatic pressure (50-200 mm Hg) indicating that bulk flow is not a transport mechanism in these membranes. The permeability coefficient (P) was independent of membrane thickness (H) over the four samples tested (0.0102, 0.0148, 0.0269, and 0.0366 cm), with an average value of 3.29 X 10(-4) cm2/s. Thus, diffusion was Fickian with negligible boundary layers. A plot of lag time versus H2 was linear (R = 0.98) yielding a value for D of 2.18 X 10(-7) cm2/s. A water-Biomer partition coefficient was determined for each sample with an average value of 1525, indicating a moderately hydrophilic membrane with a water sorption of 6.3% at 37 degrees C. Since water transport is by Fickian diffusion in the absence of bulk flow, liquid water cannot be expected to accumulate in circulatory-assist devices unless a condensing surface is maintained within the system.

Modified entrainment method for measuring vapour pressures and heterogeneous equilibrium constants. Part 3.—Measurement of diffusivity of hydrogen chloride in hydrogen and extension of the method to multicomponent diffusion at 700–1300 K

The binary diffusion coefficient of HCl in H2 may be represented by 0.54(T/273 K)1.85 cm2 S–1 over the temperature range 700–1300 K. We present a useful second-order approximation to multicomponent diffusion, which permits calculation of effective diffusion coefficients in multicomponent gas mixtures.

Diffusion in Inhomogeneous Media

Methods are given for the calculation of effective diffusion coefficients for inhomogeneous media in which the actual diffusion coefficient varies from point to point in a random manner. An exact result is obtained in the form of an infinite series involving correlations between diffusion coefficients at n different points. A procedure for deriving approximate expressions involving only two-point correlations is also developed, and applied, in particular, to the important special case of diffusion through a porous material.