Modeling and numerical analysis of counter-current dialyzer at steady state

A mathematical model of a continuous counter-current dialyzer in the case of the transport of one component, which is based on the mass balance and balance of transported component, has been presented. It enables users to calculate the component recovery yield if parameters of the dialyzer (height, dimensions of compartments), parameters of the membrane (thickness, partition coefficients, diffusivity of the component in the membrane, flux of solution through the membrane), parameters of liquids in both the compartments (density, viscosity, diffusivity of the component) and parameters of streams entering the dialyzer (component concentration, volumetric liquid flow rate) are specified.     

Semi-empirical model of toluene transport in polyethylene membranes based on the data using a new type of apparatus for determining gas permeability, diffusivity and solubility

Solubility, diffusivity and permeability of toluene vapors in low-density polyethylene (LDPE) membranes of various thicknesses (approximately 48, 93, 138 and 187 μm) at different temperatures 30, 40 and 50 °C in the range of relative vapor pressure p/p⁰=(0.05; 0.95) were measured using new type of permeation apparatus. Moreover, special construction of the new cell enables determination of the permeant amount sorbed in the membrane in the steady state operation of vapor permeation.The simple semi-empirical model of toluene transport in a polyethylene membrane based on relation between experimentally obtained effective diffusion coefficients and concentration dependent diffusion coefficients evaluated from experiments on a new permeation apparatus was proposed. The model enables estimation of toluene fluxes, sorption in the steady state of vapor permeation and concentration profiles in a polyethylene membrane from equilibrium sorption isotherms and effective diffusion coefficients. Very good agreement between experimental and calculated values from the proposed model was obtained.     

Dialysis of aqueous solutions of nitric acid and ferric nitrate

The separation of an HNO₃ + Fe(NO₃)₃ mixture using an anion-exchange membrane Neosepta-AFN has been investigated in a two-compartment dialysis cell with stirrers. The experiments have proved that this membrane is a very good separator for this mixture, because nitric acid permeates well through the membrane and ferric nitrate is efficiently rejected. The separation is very efficient at high acid concentrations or low content of the salt in the mixture to be dialyzed.     

Transport of nitric acid through the anion-exchange membrane NEOSEPTA-AFN

The paper presents the determination of mobility of H₃O⁺ and NO₃⁻ ions and diffusivity of the non-dissociated form of acid on the basis of experiments with nitric acid carried out in a batch mixed cell with an anion-exchange membrane NEOSEPTA-AFN, which have been completed by measurements of membrane conductivity. The dependencies of mobility of H₃O⁺ and NO₃⁻ ions upon the acid concentration in the membrane were approximated by the second degree polynomial, whose coefficients were determined by the numerical integration of the differential equation describing the time dependence of nitric acid in the cell followed by an optimizing procedure. Diffusivity of the non-dissociated form was calculated from mobilities of H₃O⁺ and NO₃⁻ ions. The model used is based on the Nernst-Planck electro-diffusion equation and takes into account ionic equilibrium between the species. Using all the experimental data obtained at various acid concentrations and rotational speeds ofthe stirrers, it was found that the transport characteristics mentioned above (except for mobility of H₃O⁺ ions) were affected by the nitric acid concentration in the membrane.     

Using Numerical Dissipation Rate and Viscosity to Assess Turbulence-Related Data Accuracy – Part 1: Experimental Setup

This is the first part of a two-part paper focusing on the assessment of accuracy of turbulence-related data from computational fluid dynamics (CFD) simulations using effective numerical dissipation rate and effective numerical viscosity. Setup of the CFD cases replicating a swirling pipe flow experiment from literature, for which turbulence-related data measured via laser Doppler anemometry (LDA) had been reported, is presented. The way effective numerical dissipation rate and effective numerical viscosity were obtained for each mesh cell is also discussed. The results of the study are presented in the second part of this series.     

Macroscopic fracture characteristics of random particle systems

This paper deals with determination of macroscopic fracture characteristics of random particle systems, which represents a fundamental but little explored problem of micromechanics of quasibrittle materials. The particle locations are randomly generated and the mechanical properties are characterized by a triangular softening force-displacement diagram for the interparticle links. An efficient algorithm, which is used to repetitively solve large systems, is developed. This algorithm is based on the replacement of stiffness changes by inelastic forces applied as external loads. It makes it possible to calculate the exact displacement increments in each step without iterations and using only the elastic stiffness matrix. The size effect method is used to determine the dependence of the mean macroscopic fracture energy and the mean effective process zone size of two-dimensional particle systems on the basic microscopic characteristics such as the microscopic fracture energy, the dominant inhomogeneity spacing (particle size) and the coefficients of variation of the microstrength and the microductility. Some general trends are revealed and discussed.Walter P. Murphy Professor of Civil Engineering and Materials Science.     

Choice of standard fracture test for concrete and its statistical evaluation

The main characteristics of the cohesive (or fictitious) crack model, which is now generally accepted as the best simple fracture model for concrete, are (aside from tensile strength) the fracture energies G _F and G _f corresponding to the areas under the complete softening stress-separation curve and under the initial tangent of this curve. Although these are two independent fracture characteristics which both should be measured, the basic (level I) standard test is supposed to measure only one. First, it is argued that the level I test should measure G _f, for statistical reasons and because of relevance to prediction of maximum loads of structures. Second, various methods for measuring G _f (or the corresponding fracture toughness), including the size effect method, the Jenq-Shah method (TPFM), and the Guinea et al. method, are discussed. The last is clearly the most robust and optimal because: (1) it is based on the exact solution of the bilinear cohesive crack model and (2) necessitates nothing more than measurement of the maximum loads of notched specimens of one size, supplemented by tensile strength measurements. Since the identification of material fracture parameters from test data involves two random variables, f_t (tensile strength) and G _f, statistical regression should be applied. But regression is not feasible in the original Guinea et al.'s method. The present study proposes an improved version of Guinea et al.'s method which reduces the statistical problem to linear regression thanks to exploiting the systematic trend of size effect. This is made possible by noting that, according to the cohesive (or fictitious) crack model, the zero-size limit _N0 of nominal strength _N of a notched specimen is independent of F _f and thus can be easily calculated from the measured f_t. Then, the values of _N0 obtained from the measured f_t values, together with the measured _N-values of notched specimens, are used in statistical regression based on the exact size effect curve calculated in advance from the cohesive crack model for the chosen specimen geometry. This has several advantages: (1) the linear regression is the most robust statistical approach; (2) the difficult question of statistical correlation between measured f_t and the nominal strength of notched specimens is bypassed, by virtue of knowing the size effect trend; (3) the resulting coefficient of variation of mean G _f is very different and much more realistic than in the original version; (4) the coefficient of variation of the deviations of individual data from the regression line is very different from the coefficient of variation of individual notched test data and represents a much more realistic measure of scatter; and (5) possible accuracy improvements through the testing of notched specimens with different notch lengths and the same size, or notched specimens of different sizes, are in the regression setting straightforward. For engineering purposes where high accuracy is not needed, the simplest approach is the previously proposed zero-brittleness method, which can be regarded as a simplification of Guinea et al.' method. Finally, the errors of TPFM due to random variability of unloading-reloading properties from one concrete to another are quantitatively estimated.     

Thermodynamic Properties of He@C60

Abstract

Contributions to thermodynamic properties of the endohedral He@C₆₀, resulting from motion of He inside the cage, are calculated. The contribution to C _v shows a maximum at low temperatures. The maxima for ³He@C₆₀ and ⁴He@C₆₀ are at about 41 K and 30 K, respectively.