A moving boundary problem and orthogonal collocation in solving a dynamic liquid surfactant membrane model including osmosis and breakage

Abstract

A dynamic kinetic-diffusive model for the extraction of metallic ions from aqueous liquors using liquid surfactant membranes is proposed. The model incorporates undesirable intrinsic phenomena such as swelling and breakage of the emulsion globules that have to be controlled during process operation. These phenomena change the spatial location of the chemical reaction during the course of extraction, resulting in a transient moving boundary problem. The orthogonal collocation method was used to transform the partial differential equations into an ordinary differential equation set that was solved by an implicit numerical routine. The model was found to be numerically stable and reliable in predicting the behaviour of zinc extraction with acidic extractant for long residence times

Reactive Extraction Using Moving Liquid Membranes - Mathematical Model Calibration Through Experiments

“…The high partition coefficient under thermodynamic equilibrium is responsible for the sequestration of a large quantity of acid inside the MLRM, in the case of passive discontinuous extraction/back-extraction in/to water. It is worth mentioning that, for equal volumes of water ( a V ) in the extraction/back-extraction zones (the volume of organic phase, o V being the same), the final concentration of transported acid in the latter zone, starting from , A in ex C in the former, is: (21) In the case of passive extraction followed by reactive back-extraction in alkaline solution of NaOH, the process efficiency increases but the best results are obtained using a reactive carrier in the MLRM.…”

“…The MLSM extraction is generally modeled using one of the following approaches: ordinary permeation, facilitated transport and molecular pumping. Recent works take into account undesirable intrinsic phenomena such as swelling and breakage of the drops, whose distribution have to be controlled during the RE process [21]. Few works present a complete mathematical model including all the processes implied by a reactive MLSM: the RE, the chemical processes within the moving liquid membrane (MLM) and the reactive back extraction.…”

A modified orthogonal collocation method for reaction diffusion problems

“…It was then subsequently studied and applied to many chemical engineering problems by several authors (Finalyson, 1972;Villadsen and Michelsen, 1978;Finalyson, 1980;Torres et al, 2000;Biscaia Junior et al, 2001).…”

Inclusion separation of alkali metals in emulsion liquid membranes by nanobaskets of calix[4]crown-3

“…The emulsion liquid membrane (ELM) was invented by Li (1968) and is known as one of the most promising separation methods for trace extraction of metal contaminants (Kumbasar and Sahin, 2008;Chakraborty et al, 2003;Ortiz et al, 2003;Biscaia Junior et al, 2001;Ferraz et al, 2007) and hydrocarbons (Correia and de Carvalho, 2003;Park et al, 2006) owing to the high mass transfer rate, high selectively, low solvent inventory and low equipment cost. Frankenfeld et al (1981) reported that the ELM could be up to 40% cheaper than other solvent extraction methods.…”