Interfacial convection

Mendes-Tatsis, M.A., Agble, D., Mass transfer with interfacial convection and added surfactants, Int. Solvent Extraction Conf (ISEC 96) Value adding through solvent extraction, Ed. Shallcross, D.C., Paimin, R. Prvcic, L.M., Melbourne, Australia, pp.267-272, 1996. 

The effects of surface-active agents on the motion of and transfer from bubbles and drops have been discussed in earlier chapters. The main effect is to reduce the mobility of all or part of the interface. In this section we consider briefly two other interfacial phenomena interfacial convection during mass transfer and interfacial barriers to mass transfer. 

The shape of a drop moving under the influence of gravity may be affected by interfacial motions the drop may also wobble and move sideways (S27, W3). In one system (S22) the terminal velocity was reduced yielding a drag coefficient nearly equal to that of a solid particle. Interfacial convection tends to increase the rate of mass transfer above that which would occur in the absence of interfacial motion. The interaction between mass transfer and interfacial convection has been treated by Sawistowski (S7) and Davies (D4, D5). 

Hence, the maximum increase in mass transfer due to interfacial convection is... 

Stemling and Scriven wrote the interfacial boundary conditions on nonsteady flows with free boundary and they analyzed the conditions for hydrodynamic instability when some surface-active solute transfer occurs across the interface. In particular, they predicted that oscillatory instability demands suitable conditions cmcially dependent on the ratio of viscous and other (heat or mass) transport coefficients at adjacent phases. This was the starting point of numerous theoretical and experimental studies on interfacial hydrodynamics (see Reference 4, and references therein). Instability of the interfacial motion is decided by the value of the Marangoni number, Ma, defined as the ratio of the interfacial convective mass flux and the total mass flux from the bulk phases evaluated at the interface. When diffusion is the limiting step to the solute interfacial transfer, it is given by... 

Here, the Biot number Bi = aa/U provides a measure of the relative importance of kinetic desorption relative to interfacial convection, cs and cs are the bulk-phase concentrations evaluated in the limit as we approach the surface of the drop, k = c,Xj/a is a measure of the ratio of adsorption to desorption to the exterior fluid and k = c.Xj /a is the same quantity for the drop. We recall that S and a are the adsorption and desorption rate constants defined following (2-150). 

In this case, the interfacial gradients of surfactant occur because of interfacial gradients in the bulk concentration driven by bulk convection rather than interfacial convection. Although generally requiring numerical analysis, an analytic approximation can be obtained in the limit k

interface concentration is small. Again, we shall consider this case shortly. 

Fig. 8.1. a. Surface concentration gradient created by interfacial convection... 

A schematic of an instability caused by temperature gradients between the two phases resulting in surface tension gradient along the interface is shown in Fig. 3C.2. A small initial disturbance like interfacial convection from R to S will be amplified by additional mass transport at higher temperature, because this leads to y < y j on condition dy / dT < 0. 

Schematic of instability caused by the temperature gradient of a sink, a) temperature gradients, b) sceme of initial interfacial convection...

In the two-medium treatment of the single-phase flow and heat transfer through porous media, no local thermal equilibrium is assumed between the fluid and solid phases, but it is assumed that each phase is continuous and represented with an appropriate effective total thermal conductivity. Then the thermal coupling between the phases is approached either by the examination of the microstructure (for simple geometries) or by empiricism. When empiricism is applied, simple two-equation (or two-medium) models that contain a modeling parameter hsf (called the interfacial convective heat transfer coefficient) are used. As is shown in the following sections, only those empirical treatments that contain not only As/but also the appropriate effective thermal conductivity tensors (for both phases) and the dispersion tensor (in the fluid-phase equation) are expected to give reasonably accurate predictions. 

After the formal derivations, the energy equation for each phase ((T)f and (T) ) can be written in a more compact form by defining the following coefficients. Note that both the hydrodynamic dispersion, that is, the influence of the presence of the matrix on the flow (noslip condition on the solid surface), as well as the interfacial heat transfer need to be included. The total thermal diffusivity tensors Dff, D , D/s, and Dv/ and the interfacial convective heat transfer coefficient hsf are introduced. The total thermal diffusivity tensors include both the effective thermal diffusivity tensor (stagnant) as well as the hydrodynamic dispersion tensor. A total convective velocity v is defined such that the two-medium energy equations become... 

The effective media properties D , Df, D , and Ds, which include both the molecular (i.e., conductive) and the hydrodynamic dispersion components, are also modeled. Due to the lack of any predictive correlations for the nonequilibrium transport, local thermal equilibrium conditions are used. For the interfacial convective transport, the local Nusselt and Sherwood numbers are prescribed. The effect of the solid particles geometry must also be addressed [160],... 

With that in mind the author and co-workers have been carrying out experiments with many hquid-liquid systems and in this paper the results obtained in recent years are summarised. Sections 2 and 3 include theory and the definition of interfacial convection, which give the background for the analysis of the experimental results shown later. Section 4 describes the experimental equipment and methods used to obtain the results presented in Section 5, for hquid-hquid partially miscible binary systems with and without surfactants Section 6, for the same systems under microgravity conditions and Section 7, for ternary systems with and without surfactants. Section 8 covers work previously done on stability criteria to predict Marangoni convection in hquid-hquid systems. In Section 9 some of the results presented in the previous sections are discussed. Relevant results obtained in the field of Biotechnology by the author and co-workers are mentioned in Section 10. Conclusions and future work follow in Section 11. 

When diffusional mass transfer is accompanied by interfacial convection the predictions given by the above equations are no longer correct. An understanding of the causes for interfacial convection is given in the next section. 

Lewis Pratt, in 1953, were the first to report that the observed Marangoni convection in their experimental ternary systems was beneficial to hquid-hquid extraction processes because it increased mass transfer rates. The effect of density gradients on interfacial convection was studied by several researchers including Berg Morig (1969), who investigated the interaction between buoyancy and interfacial tension driven effects in ternary systems. The combined interfacial convection was also seen to be beneficial to mass transfer processes. 

There are processes, however, which do not benefit from interfacial convection such as the formation of crystals. In this case interfacial convection causes the development of unwanted stria-tions in the crystals produced and hence has a detrimental effect on the process. 

It is, therefore, important to understand interfacial phenomena well to enable the development of means to manipulate the interfacial conditions in order to enhance or suppress interfacial convection. 

One type of substance that affects interfacial conditions is a surfactant. The presence of surfactants in liquid-liquid systems has traditionally been viewed as detrimental to mass transfer because it has been found they either damp interfacial convection or cause a barrier effect to mass transfer. On the other hand, mass transfer may also be increased because of the presence of surfactants, as it will be shown in the Sections 5 and 6. 

A comparison between the predicted and the various interferometric results obtained for the molar fluxes under different aqueous phase conditions is shown in Figure 4 for the case of the transfer of ethylacetate into water. The transfer into pure water is higher than theoretically predicted, as expected, since the interfacial convection seen in Figure 2 (case 2a), increases the mass transfer occurring across the interface. The addition of ATLAS G1300 shows that it hardly has any... 

In summary when a system shows reduced interfacial convection under microgravity, in comparison with the interfacial convection observed on Earth, the intensity of the convection can be re-instated to the system by the addition of an appropriate surfactant with the obvious increase in mass transfer rates. The presence of a surfactant in some mass transfer systems may therefore have significant implications on mass transfer processes occurring in space platforms. 

Previous work by many researchers on these systems has shown that when a ternary system has interfacial convection mass transfer rates are higher than theoretically predicted (e.g. Sherwood and Wei, 1957 and Bakker and co-workers, 1966,1967) and the presence of a surfactant reduces mass... 

It is also clear that if benefits are to be obtained from the understanding of those surfactant effects, it is important to be able to predict the occurrence of interfacial convection in the absence and presence of surfactants. The work done in this direction is mentioned in the next section. 

When a surfactant is present in a liquid -liquid system Stemling and Scriven suggested that it would have such an effect on surface viscosity as to preclude the occurrence of Marangoni convection. While this was confirmed by many researchers there have also been several experimental results (Nakache and Raharimalala, 1988, Aunins et al, 1993, Bennett et al., 1996, Agble and Mendes-Tatsis, 2000), which have shown that surfactants may also initiate interfacial convection. 

Unfortunately, despite the efforts by all the researchers mentioned above and others, interfacial convection in liquid-liquid systems cannot yet be accurately predicted. More work is in progress by the author and co-workers to achieve better predictions for the case of binary systems (Slavchev and Mendes, 2003) and binary systems with surfactants (Slavchev, Kalitzova-Kurteva and Mendes, 2003). 

The presence of surfactants in the mass transfer systems presented has been shown to affect the mass transfer process by inducing, reducing or suppressing interfacial convection. Since interfacial convection is caused by interfacial tension variations and the addition of a surfactant to a system alters interfacial tension, an examination of the effect surfactants have on the interfacial tension of the systems is of interest. 

Further work needs to be carried out to improve the simplified analysis presented by investigating, for example, the effect of dynamic interfacial tension on the interfacial convection. 

Increases in mass transfer rates have been obtained before (Lye and Stuckey, 2001) with similar systems but interfacial convection had not been observed and the explanation put forward was that the increase in rates was caused by an interaction/aggregation between the surfactant and the solute at the interface. 

The most important achievement of this research has been the finding that the addition of some surfactants to the binary liquid-liquid systems investigated can induce or increase interfacial convection that enhances greatly the initial mass transfer rates in comparison with values predicted by Pick s law. This shows that surfactants can be used as a means to manipulate the interfacial region to obtain variations in interfacial parameters, which induce interfacial convection and produce an... 

The effect surfactants have on ternary liquid-liquid systems unstable interfaces is of either reducing or suppressing completely any interfacial convection present. In turn, this causes the mass transfer rates to be reduced. 

Berg, J. C., and Morig, C. R. (1969). Density Effects in Interfacial Convection. Chemical Engineering Sciencey 24 937-945. 

Mendes-Tatsis, M. A., and Perez de Ortiz, E. S. (1992). Spontaneous Interfacial Convection in Liquid-Liquid Binary Systems Under Microgravity, Proceedings of the Royal Society London, A438, 389-396. 

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