Advancing Front Model Research Articles

Mathematical Modeling of Chromium(Ш) Extraction by Emulsion Liquid Membrane

Advancing front model, carrier-facilitated transfer model and reversible reaction model were applied to simulate extracting chromium (Ш) from wastewater by emulsion liquid membrane using di-(2-ethylhexyl) phosphoric acid as carrier and Span-80 as surfactant. Parameters of the mathematic models were gained from the designed experiments, and the reversible reaction model can be used with a reasonably accuracy as estimates of chromium (Ш) permeation. The experimental results demonstrate that the role of reversibility of the chemical reaction between internal phase and membrane phase should be considered, and the diffusion resistance is the primary resistance of the mass transfer process.

Modeling Study of the Influence of Porosity on Membrane Absorption Process

A theoretical model based on the advancing front model was developed to analyze the influence of porosity on membrane absorption process. Perturbation solutions were obtained and a nonlinear transformation was applied to increase the accuracy of the solutions. The concentration profile of the solute in the liquid side near the membrane surface was simulated for different operation conditions. The influencing factors on the diffusing rate of the solute concentration profile were analyzed qualitatively. In the case of the rapid mass transfer system, the time of reaction front to reach the midpoint of two proximate pores is relatively long, which means that the concentration layer of solute overcasts the whole surface of membrane slowly, there is a “dead” area for mass transfer, so the influence of porosity should be taken into account. In the case of slow mass transfer system, the time can be ignored compared with the overall experiment time, and the influence of porosity is negligible. The absorption rates were calculated based on the developed model and the calculated results agreed well with the literature results.

Mathematical modeling of emulsion liquid membrane pertraction of gold (III) from aqueous solutions

Modeling of emulsion liquid membrane pertraction of gold (III) ions from aqueous solutions using MIBK as carrier and LK-80 as emulsifier has been performed. Three models were considered: Advancing front model, diffusion controlled mass transfer inside and outside of globule model and finally, reaction and diffusion controlled mass transfer model. Results showed that the model considered as reaction and diffusion controlled mass transfer model is more compatible with experimental results and the compatibility of the model and the experimental results is more than 90%. This modeling showed that the pH of external phase is the most important parameter for the extraction. The deviation for “Advancing front model”, “diffusion controlled mass transfer model” and “reaction and diffusion controlled mass transfer model” were 82.83, 65.69 and 9.38%, respectively.

Recovery of phenol from phenolic resin plant effluents by emulsion liquid membranes

In this work, the recovery of phenol from a phenolic resin plant effluent by emulsion liquid membranes has been investigated. The selected membrane phase allowed a selective recovery of phenol towards formaldehyde by this technology. The effect on phenol permeation of relevant variables such as volume phase ratio between the effluent and the internal phase (in the 10–42 range), stirring speed (in the 300–500 rpm range), temperature (in the 288–313 K range) and permeation time (in the 0–600 s range) was studied. The application of the advancing front model describes well the experimental results (deviations lower than 10% were obtained in the first minutes of permeation).

A comparison of models for 2-chlorophenol recovery from aqueous solutions by emulsion liquid membranes

Advancing front model and three reversible reaction models were applied to describe 2-chlorophenol permeation from aqueous solutions by emulsion liquid membranes. Similar results were obtained in most cases by using either of the reversible reaction models. Also differences between reversible reaction and the advancing front model were shown to be within experimental error in most cases (with the exception of low temperature permeation data) meaning that the role of reversibility of the chemical reaction between internal phase reagent and 2-chlorophenol can be considered negligible. Both advancing front and reversible reaction models can be used with a reasonably accuracy as estimates of 2-chlorophenol permeation for design purposes.

Recovery of 2-chlorophenol from aqueous solutions by emulsion liquid membranes: batch experimental studies and modelling

A study of 2-chlorophenol recovery by emulsion liquid membranes was undergone. The effect of several permeation variables such as membrane phase composition, internal reagent concentration, solute concentration, permeation stirring speed, temperature, permeation time and phase ratios between membrane phase and internal phase and also between external phase and internal phase on 2-chlorophenol permeation was studied. The most relevant of these parameters were permeation stirring speed, temperature and phase ratio between external phase and internal phase. Advancing front model was applied to these parameters and described the experimental results.

A mathematical model for the analysis of extraction data of weak acids/bases in liquid surfactant membranes

An attempt has been made in this paper to overcome the shortcomings of the advancing front model while simplifying the mathematical treatment of mass transfer and reaction occurring in the emulsion globule during extraction by liquid surfactant membranes. This model combines the mathematical simplification achieved in assuming a reaction front in the emulsion globule along with the realistic assumption of reaction equilibrium existing in the internal and external continuous phases. The proposed model predicts satisfactorily the experimental results of the extraction of weak acids and weak bases in a batch separation system as presented in various literatures.

Modeling of liquid emulsion membranes facilitated by two carriers

A mathematical model was proposed to describe the behavior of liquid emulsion membranes for the extraction of penicillin G in a continuous countercurrent mixing column. A polyamine-type surfactant acts not only as a carrier but also as a surface-stabilizing agent; thus the influence of surfactant on extraction should be considered in mathematical modeling when its effect is significant. The proposed model takes into account the influence of surfactant on mass transfer. The advancing front model was employed for deriving the overall mass transfer coefficient in the emulsion globule, and the axial dispersion model was applied to the external feed phase. The experimental data were compared with the proposed model, the calculations without considering the contribution of the surfactant to extraction, and the calculations without considering diffusion in the emulsion phase.

Modeling of liquid emulsion membranes facilitated by two carriers

A mathematical model was proposed to describe the behaviour of liquid emulsion membranes for the extraction of penicillin G in a continuous countercurrent mixing column. A polyamine-type surfactant acts non only as carrier but also as surface-stabilizing agent; thus the influence of surfactant on extraction should be considered in mathematical modeling when its effect is significant. The proposed model takes into account the influence of surfactant on mass transfer. The advancing front model was employed for deriving the overall mass transfer coefficient in the emulsion globule, and the axial dispersion model was applied to the external feed phase. The experimental data were compared with the proposed model, the calculations without considering the contribution of the surfactant to extraction, and the calculations without considering diffusion in the emulsion phase.

Modeling of liquid membrane separation processes

With the separation of ammonia from dilute aqueous solutions as an example, relationships for the design of a liquid membrane process based on the principle of double emulsions will be given in this paper for the case of a stirred countercurrent flow column. The advancing front model in its pseudo steady-state form has been employed for the calculation of mass transport in the emulsion drops. Backmixing in the column has been taken into account by employing a simple two layer dispersion model. Experiments have been carried out with a stirred countercurrent flow column of 67 mm inner diameter and an active length of 1.8 m. The experimental results confirm that the calculations are sufficient for design pruposes.

A MODEL FOR LIQUID MEMBRANE EXTRACTION WITH INSTANTANEOUS REACTION IN CASCADED MIXERS

The Advancing Front Model for the description of extraction processes using liquid surfactant membranes has been invoked in the analysis and comparison of cascaded mixer systems with and without interstage settling. It is demonstrated that the extraction efficiency can be enhanced significantly if interstage settling is permitted.

Analysis of staged liquid surfactant membrane operations

AbstractGraphical and numerical procedures are presented for the design and analysis of cocurrent and countercurrent multistaged mixer‐settler units for liquid membrane extraction operations—these are based on the recently developed Advancing Front Model of Ho et al. (1982) and Hatton et al. (1983). The numerical results indicate that the extraction efficiency in a countercurrent cascade is only slightly improved over that for cocurrent operation. However, for any given stage, marked improvements in extraction efficiency are indicated if an external emulsion recycle over the mixer settler unit is used to ensure adequate holdup ratios in the mixer. Premixing of the emulsion feed and recycle streams will impair the extraction performance, however,

A generalized advancing front model describing the oxygen transfer in flowing blood.

It is well known from literature that under certain conditions the steady state transport of oxygen in flowing blood can be described relatively simple when a sharp boundary (advancing front) is assumed between oxygenated and unoxygenated blood (4). Advancing Front (A F) theories have been used to predict oxygen transfer rates in membrane oxygenators (e.g. 2,5). Advancing Front models presented in literature (2,3,4,5,6) have been derived for specific geometries of the flow channel and well defined velocity profiles. A general A F theory would be useful to predict oxygen transport performance for the variety of flow geometries and flow conditions encountered in experimental studies with membrane oxygenators and to analyse the data of existing oxygenators. In this work a general A F theory is presented.