Equilibrium Adsorption Layer Research Articles

Development of the equilibrium adsorption layer model for describing the dynamic adsorption of radioactive gases

Development of the equilibrium adsorption layer model for describing the dynamic adsorption of radioactive gases

Calculation of the Henry’s Constant and the Thickness of the Equilibrium Adsorption Layer of Radon in the Layer-by-Layer Measurement of the Sorbent Activity

The radioactive gas radon is ubiquitous in the environment and is a major contributor to the human inhalation dose. It is the second leading cause of lung cancer after smoking. Radon concentrations are particularly high in the air of radon-hazardous facilities—uranium mines and radioactive waste repositories containing radium. To reduce the dose load on the staff, air in these premises should be continuously or periodically purified of radon. Carbon adsorbers can be successfully used for this purpose. The design of sorption systems requires information on both equilibrium and kinetic parameters of radon dynamic adsorption. The traditional way of obtaining such characteristics of the sorbent is to analyze the breakthrough curves. The present paper proposes a simple alternative method for determining parameters of dynamic radon adsorption (Henry’s constant and equilibrium adsorption layer thickness) from the results of a layer-by-layer gamma-spectrometric measurement of the sorbent. The analytical equation for smooth distribution of radon activity in the sorbent layer is obtained based on equilibrium adsorption layer theory for elute chromatography (pulsed injection of radon into the column). Using the dynamic adsorption of 222Rn on AG-3 activated carbon as an example, both equilibrium (Henry’s constant) and kinetic (thickness of the equilibrium adsorption layer) parameters of the adsorption dynamics were calculated. It was shown that the exposure duration of the column bed in the air flow and superficial gas velocity do not affect the result of the Henry’s constant calculation. The dependence of the equilibrium adsorption layer thickness on the superficial gas velocity over a wide range of values (5–220 cm/min) is described by the van Deemter equation. It was shown that the optimum air flow velocity, which corresponds to the maximum effectiveness of the bed, is 15–30 cm/min. This corresponds to the minimum of the equilibrium adsorption layer thickness (about 0.6 cm). The developed mathematical model makes it easy to define both equilibrium and kinetic parameters of dynamic adsorption of radon based on discrete distribution of its activity over the sections of the adsorption column. These parameters can then be used to calculate and design gas delay systems. It can be useful for studying the sorption capacity of various materials relative to radon.

On the Informativity of Higher-Order Moments in Chromatography

Analytical solutions have been obtained for ordinary, normalized, and higher-order (third- and fourth-order) central moments using the model of an equilibrium adsorption layer. The solutions are represented by one-term fractions and comprise the length of an adsorbent layer, the velocity of a mobile phase, the effective kinetic constant, and the Henry constant. Expressions for the third- and fourth-order moments have been obtained and analyzed in the case of the rectangular input signal . It has been shown that, when solving the inverse problem of chromatography, the calculation of the higher-order moments provides no new information on the kinetic or any other properties of an adsorbent layer.

Correction to "Equilibrium Contact Angle and Adsorption Layer Properties with Surfactants".

The last line in eq 27 on page 7213 should read (Formula Presented) In the caption for Figure 2a on page 7213 it should read (a) In the macroscopic approach, the equilibrium contact angle is determined by the solid-liquid interfacial tension γsl and the liquid-gas and solid-gas interfacial tensions γ and γ sg that depend on the respective surfactant concentrations Gd and Ga on the droplet and the adsorption layer. (Formula Presented).

New Moment Equations in Chromatography

The exact solution obtained for the direct problem of chromatography within the model of an equilibrium adsorption layer using the integrand of the Euler γ-function has been analyzed. Analytical solutions have been presented for the first three temporal, two normalized, and two central moments as functions, which are represented by one-term fractions and comprise the length of an adsorbent layer, mobile phase velocity, effective kinetic constant, and Henry constant. The new moment equations substantially differ from those being used at present.

Equilibrium Contact Angle and Adsorption Layer Properties with Surfactants.

The three-phase contact line of a droplet on a smooth surface can be characterized by the Young equation. It relates the interfacial energies to the macroscopic contact angle θe. On the mesoscale, wettability is modeled by a film-height-dependent wetting energy f( h). Macro- and mesoscale descriptions are consistent if γ cos θe = γ + f( ha), where γ and ha are the liquid-gas interface energy and the thickness of the equilibrium liquid adsorption layer, respectively. Here, we derive a similar consistency condition for the case of a liquid covered by an insoluble surfactant. At equilibrium, the surfactant is spatially inhomogeneously distributed, implying a nontrivial dependence of θe on surfactant concentration. We derive macroscopic and mesoscopic descriptions of a contact line at equilibrium and show that they are consistent only if a particular dependence of the wetting energy on the surfactant concentration is imposed. This is illustrated by a simple example of dilute surfactants, for which we show excellent agreement between theory and time-dependent numerical simulations.

Functions of moments in the elution dynamics of adsorption

An exact solution obtained for the direct problem concerning the elution dynamics of adsorption in terms of the model of an equilibrium adsorption layer using the gamma function is analyzed. Analytical expressions derived for the functions of moments comprise adsorbent layer lengths, mobile phase velocities, and adsorption constants. The functions are found to be interrelated via the slope coefficients of linear equations. The correctness of the results obtained is confirmed by good agreement between the theory and experimental data presented as tabulated values of the moments measured previously for the elution dynamics of Freon 13B1 adsorption on active carbon layers of different lengths.

On the interrelation between the Henry constant and retention parameters in chromatography

The relations between the Henry adsorption constant and the parameters of the output elution curve are analyzed based on an exact solution of the direct problem concerning the dynamics of adsorption. The solution is obtained in terms of the model of an equilibrium adsorption layer using the integral representation of the γ-function. Direct proportionality is shown to take place between the Henry constant and the time coordinate of the output curve center of gravity. A linear dependence is revealed between the time corresponding to the output curve center of gravity and the corrected retention time or the time corresponding to the maximum in the output curve determined via the relative length of an adsorbent layer. Recommendations are formulated for the measurement and calculation of the Henry constant in chromatography applying short adsorption layers.

Short time dynamic interfacial tension as studied by the growing drop capillary pressure technique

For the characterisation of interfaces between two immiscible liquids, capillary pressure tensiometry is the most versatile method. To measure short time interfacial tensions it has to be applied under very dynamic conditions for which the following protocols have been developed: 1—continuously growing drop (CGD); 2—pre-aged growing drop (PGD); 3—stopped growing drop (SGD). The CGD is a procedure analogous to the well-known maximum bubble pressure tensiometry for liquid–gas interfaces, however, the processes of drop detachment and formation of the subsequent drop require a rather complex data analysis. For the PGD protocol based on a growing drop with an initially pre-established equilibrium adsorption layer, the complexities are less, but for higher surfactant concentrations it is not optimum. The SGD protocol provides a drop with a fresh surface and the dynamic interfacial tension can be monitored in the absence of hydrodynamic effects. All three protocols complement each other and provide a good set of data for dynamic interfacial tensions at short adsorption times.

Measurement of adsorption isotherm of methanol on a humidified active carbon by the dynamic method

Elution dynamics of the adsorption of methanol vapors on humidified active carbon is studied. Elution curves are obtained for the various lengths of adsorbent layer. The isotherm of adsorption of methanol–water vapor mixtures on active carbon is calculated, using the model of the equilibrium adsorption layer.

Elution and frontal dynamics of adsorption of organic substances on activated carbon

The elution dynamics of adsorption on activated carbon was studied at various carrier-gas flow rates for a series of organic substances. With the help of the model of the equilibrium adsorption layer that uses the adsorption isotherm described by the theory of volume filling of micropores the outlet curves for the elution and frontal dynamics of adsorption can be adequately predicted. The effective kinetic coefficient and the parameters of the adsorption isotherm were found to be constant for the elution curves calculated both in the elution and frontal regimes of the adsorption dynamics over the whole range of concentrations studied. The effective kinetic coefficient in the mathematical model employed for the systems with microporous adsorbents is independent in fact of the nature of an adsorptive and is mainly determined by the parameters of porous structure of activated carbon and the experimental conditions of a dynamic run.

Linear dynamics of desorption on adsorbent layers of arbitrary length

Based on the concept of an equilibrium adsorption layer in the theory of plates, an analytical solution of the problem of the linear dynamics of desorption is obtained. The regularities of the formation and motion of the output curves of desorption on adsorbent layers of small length are analyzed. The calculated and experimental data are found to be in fine agreement. A program is worked out to predict and to model the dynamics of adsorption and desorption on adsorbent layers of arbitrary length.

Elution dynamics of adsorption of Chladon 113 and methyl bromide on active carbons

The elution dynamics of adsorption of Chladon 113 (at high contents of the adsorptive) and methyl bromide on active carbons with different lengths of the layer was studied. The adsorption isotherms were described by the equation of the theory of volume filling of micropores. The elution curves were calculated using the model of the equilibrium adsorption layer. The effective kinetic constant calculated in the framework of the model is 1.5 cm for Chladon 113 at a linear velocity of vapor-air flow of 1250 cm min−1 and 1.0 cm for methyl bromide at the velocity of 700 cm min−1.

Dynamics of the adsorption of freons

The elution adsorption dynamics of some adsorption systems (freon-active carbon) has been studied at two temperatures. The peculiarities of the adsorption dynamics, which are determined by the properties of the adsorption system, have been established. A possibility to calculating elution curves based on the equilibrium adsorption layer model is shown. Preliminary results of the influence of the parameters of the adsorption system on the coefficient of the effective kinetic model are obtained.

A chromatographic theory based on the concept of a layer of equilibrium adsorption

The LEA model has been analyzed by comparing to other Chromatographic theoretical approaches. In the LEA model a layer of equilibrium adsorption, Le, serves as an effective kinetic constant. For the layer Le the concentration issuing from this layer is in equilibrium with the average value of adsorption on the whole layer at any moment of time. The value of Le is determined from all factors which broaden the Chromatographie zone. Such an approach permits us to combine the features of the mass balance (solute continuity in a Chromatographie column), of the mass transfer phenomenon, and of the adsorption isotherm into a single first order differential equation. Apart from other layer-by-layer models, the LEA model supposes that over the whole column a continuous (real) distribution of adsorption a (L, t) and concentration c (L, t) is observed. The usefulness of the LEA model in developing a Chromatographic theory has been discussed.

Elution Adsorption Dynamics of Organic Substances on Carbon Adsorbents

Breakthrough curves of CF3Cl on carbon black and of cyclo-hexane on active charcoal have been measured under elution adsorption dynamic conditions. For linear and non-linear adsorption dynamic modes, the experimental data and theoretical results calculated according to the layer of equilibrium adsorption (LEA) model closely coincide.

Theory of the Adsorption Dynamics of Vapours on Microporous Adsorbents. 1. Introduction into the Model of a Layer of Equilibrium Adsorption

The possibilities arising from the introduction of a layer of equilibrium adsorption into the model for a theory relating to the adsorption dynamics of vapours on microporous adsorbents have been studied. The initial first-order differential equation of the model combines the features of a material balance equation, the adsorption kinetics and an unsimplified isotherm. The results of computer simulation for the Dubinin-Radushkevich adsorption isotherm agree closely with the experimental data for ethyl chloride and carbon tetrachloride adsorption dynamics on activated carbons over a wide range of breakthrough concentrations.

Simulation of peak profiles in non-linear HPLC

The possibilities and domain of applicability of the ideal chromatography model for calculating peak profiles in non-linear chromatography are analyzed. For this purpose we used the main conclusion of the model of a layer of equilibrium adsorption (LEA model), which determines the difference between ideal and non-ideal chromatography in terms of the relative length of a chromatographic column. It is shown that the experimental data of non-linear high-performance liquid chromatography can be approximated in terms of the elementary analytical relations known in the theory of ideal chromatography.

New version of the layer-by-layer method in adsorption dynamics. Communication 3. Solution of the inverse problem for short adsorbent layers

1. An algorithm based on the equilibrium adsorption layer model has been devised for solving the inverse problem of adsorption dynamics (i.e., determining the adsorption isotherm and the effective kinetic constant) for experimental data obtained for short adsorbent layers. 2. From data on the adsorption dynamics of CCl4 on BPL activated charcoal, the adsorption isotherm and the effective kinetic constant were determined. 3. Using the equation for the shielding effect time in analyzing adsorption dynamics experimental data does not give constant values for the experimental coefficients.

A model of the equilibrium adsorption layer in chromatography. Communication 4. Characteristic properties of elution for the sorption isotherms a=kc1/n

1. Analytical and numerical solutions made within the framework of the equilibrium adsorption layer model have been used to discuss the elution characteristics of the sorption curve a=kc1/n (n > 1). 2. A systematic pattern previously established for a concave sorption curve has been confirmed: namely, that the fronts of the real developing curves approach those of ideal chromatography as the relative length of the chromatographic column increases. For l/Le > 150–250, the mass exchange processes in the column are described quite satisfactorily by the theory of ideal chromatography, and the fundamental equation of the equilibrium sorption layer model becomes that of the equation of ideal chromatography. 3. For l/Le > 10 a stable congruence is observed between the envelope of the maxima of the chromatographic peaks obtained for different size eluate samples and the isoplane of ideal chromatography. Practical recommendations are made for performing an experiment to determine the sorption isotherms in real chromatography using the Huber method.