Mass Exchange Coefficient Research Articles

Theory of adsorption rate from a restricted volume in the case of sharply convex isotherms and finite external mass-exchange coefficient

1. The problem of the adsorption rate from a constant restricted volume for a granule of a monoporous adsorbent as a sheet is discussed for the case of a sharply convex isotherm, which is characteristic for microporous adsorbents. 2. Gases of both infinitely large and finite mass-exchange coefficient were analyzed. 3. A quite simple approximate analytical solution of this problem was obtained, which can be used to interpret experiments on the sorption rate on microporous adsorbents employing the gravimetric method and the method of x-raying a granule of the sorbent during the sorption of x-ray contrast materials.

A Model of Countercurrent Steam-Water Flow in Large Horizontal Pipes

AbstractA numerical study was performed to derive a model of countercurrent steam-water flow in large horizontal pipes, with application to the emergency core cooling (ECC) system of a pressurized water reactor. The purpose of the study was to provide data from which simple correlations could be obtained to describe mass, momentum, and energy exchange between the phases during hot leg ECC injection. It was assumed that steam, driven by a pressure drop from the upper plenum to the ECC injection port, flows counter to the subcooled ECC water. Several series of calculations were performed to determine the sensitivity of the ECC flow velocity at the entrance to the reactor vessel to the pressure drop, for several values of the mass and momentum exchange coefficients used in the numerical method. The results were consistent with those obtained from solution of the mixture equation, which did not involve interfacial drag or condensation.

Mixing effect on irreversible second order reaction in batch stirred tank reactor.

The mass exchange type micromixing model in a flow system is extended to batch mixing rate process accompanying a second-order reaction between miscible reactive fluids A and B. The performance of batch mixing rate process accompanied by reaction and the dimensionless parameter q=krCb0/km are obtained from theoretical analysis of the model. When the value of q becomes less than about 0.1, the mixing effect is negligible on the course of reaction. Through analysis of the mixing characteristics of the model, the mass exchange coefficient km can be correlated with mixing time as follows. km=ln(l/δ)/t(δ)M:δ=1-F=√IS¥=ΔC/ΔC0Theoretical studies mentioned above are confirmed through experimental studies of the alkaline hydrolysis of ethyl chloroacetate, for which the reaction rate is comparable to the rate of mixing and the infinitely rapid reaction of ammonium hydroxide and acetic acid. The experimental values of km determined in each experiment show that macromixing due to circulation of the fluid element has a dominant effect on the course of reaction in the experimental condition of 300 < Re < 5000.

Heterovalent Cation Exchange Equilibria in Soils with Variable and Heterogeneous Charge

AbstractDivalent cations were incrementally displaced, from limed and unlimed samples of three soils, by suspending the soils in increasing volumes of 2mM KCl. Mass action coefficients for exchange between Ca and Mg were constant. But for the exchange of divalent cations by K, the exchange coefficients of Kerr, Vanselow, Gapon, Krishnamoorthy and Overstreet, and Gaines and Thomas increased markedly as potassium saturation or pH increased.For each cation species, separate fractions which were relatively tightly or relatively loosely adsorbed could be estimated by a simple regression analysis. The loosely adsorbed Ca, which may control Ca availability to plants, could be independently estimated by a leaching procedure. Mass action exchange coefficients for the loosely adsorbed cations were approximately constant under all conditions tested.The variable charge mobilized by liming differed from the fixed charge in having a slightly higher proportion of sites with high divalent affinity, in an Oxisol, and a much lower proportion in a Vertisol and a Mollisol.

Diffusion to a particle at large péclet numbers in the case of arbitrary axisymmetric flow over a viscous fluid: PMM vol. 40, n≗ 5, 1976, pp. 941–945

An expression for a diffusive flux of matter onto a surface of a solid or liquid particle is obtained for the case of an arbitrary axisymmetric flow-over, containing an arbitrary number of critical lines. This is a generalization of results obtained in [1, 2] where various type constraints were imposed on the field of flow. The formulas obtained make it possible to compute the; distribution of the concentration and mass exchange coefficients, from the data on the velocity field near the particle. Formulas for computing the diffusive mass exchange of a rigid spherical particle in a flow with a parabolic velocity profile, and of an ellipsoid of revolution in an uniform translational flow are given.

Mass transfer in a moving drop when it periodically collides with a hard surface

The article describes an experimental study of mass transfer in a moving drop which periodically collides with a hard surface. An empirical formula for calculating the coefficients of mass exchange within the drop is obtained.

Hydraulic resistance and heat and mass exchange during turbulent flow over surfaces with slight roughness

Flow over a surface with slight roughness is examined. It is established that at high Prandtl or Schmidt numbers such roughness can markedly increase the coefficients of heat and mass exchange.

Determination of the relative heat and mass exchange coefficients and the critical separation parameters for a turbulent boundary layer under inhomogeneous blowing in conditions of nonisothermy

Results of a determination of the relative limit laws of heat exchange and the separation parameters are presented for the general case of a density distribution over a boundary layer in subsonic flow. The results of computations on a digital computer are in good agreement with the proposed approximate formulas.

Mass exchange between spherical bodies and a fluid stream

A solution of the problem of determining the mass-exchange coefficient between the surface of a sphere and a liquid flowing over the sphere at low Reynolds number (second approximation) is presented.

Control of vertical transport of aerosols between 700 and 3000 meters by lapse rate and fine structure of temperature

The vertical-mass-exchange coefficient was determined from aerosol measurements by two independent methods over a considerable period of time. Well-substantiated relationships between the exchange coefficient and meteorological parameters were found to exist in the lower troposphere between 700 and 1800 meters. The first of the two methods consists of measuring RaB concentration in air at 700, 1800, and 3000 meters; the second is soundings of total air conductivity between 700 and 1800 meters. In the first method, mean exchange coefficients were computed from RaB concentration gradients. In the second, the air conductivity data were used to compute particle concentration profiles, from which incremental exchange coefficients can be computed for thin-layer increments. The mean exchange coefficient for the 700- to 1800- and the 1800- to 3000-meter layer is found to be a function of the average temperature lapse rate in the respective layer. The exchange coefficient of an inversion layer is a function of the greatest inverse lapse rate existing in any part of the inversion. Vertical aerosol transport through a layer of any thickness is primarily determined by the lowest incremental mass-exchange coefficient of any thinner layer contained therein.

Equations describing the kinetics of adsorption on porous adsorbents for the entire grain as a whole

1. The additivity of the coefficients of external and internal mass exchange within a broad range of variation of the Biot criterion was demonstrated on the basis of a theoretical analysis and calculations on a BESM-2 digital computer. 2. An empirical equation was obtained for determining the coefficient of internal mass exchange in the case of a linear adsorption isotherm. 3. The coefficients of internal diffusion and internal mass exchange were compared on the basis of experimental data on the kinetics of the adsorption of benzene on activated charcoals.

Effects of atmospheric fine structure characteristics on the vertical distribution of aerosols

The vertical component of the gradient of concentration of atmospheric aerosols is studied by measuring and/or recording the following: Ras radioactivity of aerosols in 700, 1800 and 3000 m, and the concentration of Aitken nuclei as a continuous function of height between 700 and 1800 m. These data, which are indicative of the vertical aerosol distribution at a given moment, are used to compute vertical-mass-exchange coefficients. The latter are, in turn, related to meteorological conditions as found from simultaneous measurements made at the same sites as the RaB counts and from observations of nearby weather stations. As a first result of this study, the relationship between the mass-exchange coefficient and the temperature lapse rate has been established. It has become clear that the resistance of an inversion to penetration by vertical air movements is directly related to the sharpness of the temperature variation inside the inversion layer, whereas no relation to the total amount of the temperature difference represented by the entire inversion is found to exist. However, a relationship between energy of stability and the vertical-mass-exchange coefficient can be stated for the lower tropospheric layers to which this study is confined.

A poblem of forced diffusion in a region with a moving boundary

A solution is found for a boundary problem of the equation of forced diffusion in a semi-infinite region with a moving boundary, with the dependence of the mass-exchange coefficient taken into account. The solution is obtained in the form of series of the Liebnitz type, which makes it convenient for numerical calculations.