SESSION 4

MODELLING OF TRANSPORT PHENOMENA IN LIQUID-LIQUID SYSTEMS

MODELLING OF LIQUID-LIQUID NON-DISPERSIVE CONCENTRATION PROCESSES IN HOLLOW FIBER MODULES

H. Escalante*, A.I. Alonso, I. Ortíz and A. Irabien.
Departamento de Química, Universidad de Cantabria. Avda de Los Castros s/n. 39005 Santander. Spain.
*Universidad Industrial de Santander. A.A. 678 Bucaramanga. Colombia.

Separation/concentration of differents solutes, such as metals, amino acids, etc has been studied using Non-Dispersive Extraction in hollow fiber modules (NDX). This technology combines some properties of solvent extraction processes with classical membrane processes, which allows a better control of the separation step.

In this type of process the solutes are separated and concentrated using two hollow fiber modules: Module-1 used for the extraction process and Module-2 for the backextraction step, and three stirred tanks for the aqueous phases and the organic phase. The aqueous feed phase (F) flows through the extraction module, and the stripping solution (S) flows through the backextraction module, while the organic phase (O) remains flowing in a closed cycle through both modules.

A typical concentration evolution of the three phases in the stirred tanks when the system is running in a batch mode is shown in figure l.

Figure 1. Kinetic behaviour of the concentration of L-Phenylalanine.

For a process working in a non-steady state, it is necessary to describe the change of the solute concentration with time, requiring important efforts in the solution of the system of differential equations.

In this work five differents approaches to the mathematical modelling of the system are presented:

• As a first attempt, the system is easily modelled by means of the macroscopic mass balances in the aqueous phases using an apparent mass transfer coefficient, which includes different parameters of the hollow fibres and batch mode operation. Therefore the system is described by two total differential equations easily integrated.
• If the main resistence to the solute transfer in the extraction and backextraction steps is considered to be the membrane mass transfer coefficient, the process can be described using the differential mass balances for the two modules along the lenght and for the three tanks. In this case the system is described by two diferential equations in the axial direction, and two algebraic equations for the modules and two total differentïal equations with time and one algebraic equation for the balances in the tanks.
• If the change with time of the solute concentration in both modules can not be neglected compared to the concentration change in the tanks, the time differential term should be included in the mass balance equations for the modules. In this case the system is described by four partial differential equations for the modules and three total differential equations for the tanks.
• If the solute diffusion in the aqueous phases need to be considered as an important resistence in the mass transfer process, the radial diffusion term second order differential equations should be included in the mass balance of the modules.
• Due to laminar flow through the modules and depending on the Peclet number the axial dispersion in the module for each phase should be considered by including the axial dispersion (second order differential equations) term in the mass balance equations for the modules.

The selection of the appropriate method for the modelling of NDX process in hollow fiber modules depends mainly of some dimensionless numbers which will be shown in this paper.

BIBLIOGRAPHY

1. H. Escalante, I. Ortíz, A.Irabien. Concentration of L-Phenylalanine by non-dispersive extraction in hollow fibre modules. Value Adding through Solvent Extraction, vol. 2.1493-1498, Proceeding of the ISEC'96. Melbourne 1996.
2. M. I. Ortíz, B. Galán, A. Irabien. Kinetic analysis of the simultaneous non-dispersive extraction and backextraction of Cr(VI). Ind. & Eng. Chem. Res., 35,1369-1377,199ó.
3. M. I. Ortíz. B. Galán, A. Irabien., Membrane mass transport coefficient for the recovery of Cr(VI) in hollow fiber extraction and backextraction modules. J. of Mem. Sci.,118, 213-221,1996.
4. A. I. Alonso and C.C. Pantelides. Modelling and Simulation of the Integrated Membrane Processes for recovery of Cr(VI) with ALIQUAT 336. J. Memb. Sci. 110, 151-167,1996.

MARANGONI AND BUOYANCY DRIVEN FLOWS OF NON-NEWTONIAN FLUIDS IN LAYERED FLUID SYSTEMS

Dennis A. Siginer, Li Yunling & Thomas E. Jacks
Department of Mechanical Engineering
Auburn University
Auburn, AL 36849-5341, USA

ABSTRACT

It is well known that a number of earth-bound manufacturing processes may suffer from undesirable buoyancy-driven effects. For instance, in crystal growth natural convection may cause striations which act as a dopant and reduce the quality and size of the crystal product. If the manufacturing process could take place in earth-orbit in a reduced gravity field many problems plaguing these processes may be overcome to a large extent as gravity induced convection would be minimized. However, thermocapillary convection, which is often negligible in one g as it is drowned out by natural convection, becomes a major flow driving mechanism in such an environment. Grashof numbers for typical manufacturing processes in one g are of the order of 10⁶ for gases, 10⁷ for liquids, and 10⁹ for liquid metals. Typically, gravity for near-earth orbits is reduced by a factor of 10^-3~10^-4. Therefore, the effect of microgravity generated buoyancy driven convection should not be neglected in space manufacturing processes, though most analyses do.

A temperature gradient is required for crystal manufacturing processes such as the Czochralski method. A major concern in the use of these methods with some important semiconductor materials stems from some volatile components distilling off of the melt as is the case with gallium arsenide when arsenic tends to evaporate from the melt. Encapsulation of the melt one way or another is required to prevent this undesirable phenomenon from happening. In the Liquid-Encapsulated Czochralski (LEC) method, the melt is encapsulated by an immiscible liquid to prevent dissociation. The rise in interest in the LEC method has lead to the need to study convective flows in two layer systems.

In this paper, we investigate the flow physics of two layered, two dimensional systems of equal height heated from the side and driven by buoyancy and Marangoni effects of comparable magnitude using a numerical approach based on the finite volume discretization. The top layer is a high Prandtl number nonlinear shear-thinning fluid and the bottom layer is both a very low Prandtl number Newtonian fluid and a very high Prandtl number shear-thinning fluid. Pure thermocapillary flows are studied in zero gravity for two layers of fluids with and without a free surface on top. We also investigate the interaction of the buoyancy driven flow with Marangoni flows in reduced gravity when the gravitational acceleration is of the order of 10^-3 times earth gravity. At this level of gravity the Grashof number in most processes suitable for space manufacturing assumes appreciable values, and sets off a buoyancy driven flow of comparable magnitude to the thermocapillary flow for the same values of the temperature gradient. Both Carreau and power-law models are used to characterize shear-rate-dependent viscosity fluids. Results are reported for both high and low values of the interfacial Marangoni number representing relatively high and low surface tension gradients. We also look for the first time at the case of a viscoelastic liquid in the top layer encapsulating a Newtonian liquid in the bottom layer when the layers are of both equal and unequal heights and report preliminary results. Viscoelastic fluids are modelled by the corotational constitutive structure. A switching algorithm capable of handling both elliptic and hyperbolic field equations is employed to account for the possible change of type of the field equations in parts of the flow field depending on the shear wave speed as determined by the constitutive structure and the velocity at the given point. Interfaces are assumed to remain almost flat in the range of the Marangoni and Grashof numbers used in the low aspect ratio (height of one layer over the length of the box) configuration adopted in this study. Since the work of Scriven and Sterling who showed that the deformability of the free surface in single layer flow configurations enhances the surface tension gradient driven flow in thin films, but not significantly in other situations, it has been customary to assume flat interfaces in investigations of this kind. The results of Scriven and Sterling were obtained for single layers heated from the bottom. But, their conclusions were largely extended to the case of a layer heated from the side by Sen and Davis. Following these authors, we assume that interface deformations do not significantly enhance and otherwise alter the flow. But the point should be made that no study exists as to the effect of the interface deformability on the flow in multiple layer configurations. Therefore, the question remains open. In a forthcoming study, we will address this point.

EXPERIMENTAL STUDY ON THE TRANSIENT NATURAL CONVECTIVE MOTION OF TWO STRATIFIED LIQUIDS INSIDE A CAVITY

R. Tovar*, F.E. Avila**, J. A. Rojas**, and B. Vargas**
*Posgrado en Energía Solar, del CCH. de la UACPyP., UNAM, at Laboratorio de Energía Solar
**Centro de Investigación en Energía, UNAM, A.P. No. 34, Temixco, Mor., 62580, México

ABSTRACT. A two dimensional experimental study on the transient natural convective motion of two stratified miscible liquids was undertaken. The propose of it was to gain in-depth knowledge of the phenomena that take place in the liquids as one wall of their container is suddenly heated up to a fixed temperature. The angle of the hot wall could be changed as desired so that its influence on the dynamics of the process could be studied. Also, several densities for the more dense liquid were tested and the global effect of this investigated. Presumably, the understanding of the interactions between strata will eventually be helpful in the design of some useful devices such as Solar Ponds.

Pure water and brine of several concentrations were used to form the strata; though it is physically impossible to make a neat interface (of zero thickness) between these fluids, we managed to achieved interfaces as thin as eight millimeters in thickness. To further improve on this mark, the possibilities of getting even thinner interfaces by means of selective withdrawal at low Froude number were explored. In the search for a good technique to produce this thin diffuse interfaces, we came across the design and construction of a special container whose bottom part serves like both a (stand by) brine deposit while forming the layer of water, and a brine diffuser while forming the layer of brine; once the layer of water was ready, the brine was carefully introduced into the container, through the base-deposit-diffuser, so that it pushed the water layer up, becoming itself the lower layer. With the strata at rest and in thermal equilibrium, its concentration profile was measured by means of a conductivity probe. This information indicated how well the liquid layers were made and, in time, it also gave us a good feeling about the more convenient positions where to place the temperature sensors used to monitor the temperature signals.

Apart from giving information about the temperature evolution in the fluids, the temperature sensors (copper-constantan type T thermocouples, gauge 36) were also used as monitoring devices to track down the average velocity at which the temperature intrusions moved toward the opposite wall, their thicknesses, and even their fluctuations. The thermocouples, twelve in total, were hooked to a data acquisition system and their signals recorded and processed. Several interesting occurrences were observed and discussed in the light of theoretical studies whenever possible.

Besides the many interesting particular features about the behavior of the transport properties in these liquid-liquid experiments which are discussed here in detail, there are also several general observations about the flow patterns. Most interesting is the greater average velocity with which the thermal intrusion in the upper layer moves toward the opposite wall (as compared with that of thermal intrusion in the bottom layer). This was always the case regardless the value given to the angle of inclination of the wall and the concentration used for the liquid in the bottom layer.