Numerical simulation of mass transfer in circulating drops

Ubal, Sebastian; Harrison, C.H.; Grassia, Paul; Korchinsky, W.J.

doi:10.1016/j.ces.2010.01.021

Cited by 28 publications

(72 citation statements)

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“…Since the time scale for diffusive processes is sensitive to distance (as can be established on dimensional grounds), convective-diffusive liquid-liquid extraction should proceed over a substantially shorter time scale than a comparable process without any convection. This has been verified by Ubal et al (2010) using full numerical simulations of the convectivediffusive mass transfer process.…”

Section: Introductionmentioning

confidence: 67%

“…Convection is beneficial to the extraction process (Ubal et al, 2010;Uribe-Ramirez and Korchinsky, 2000b) and the more complex the flow pattern is, the more beneficial convection tends to be (Edelmann et al, 2017). In the case, for instance, of transfer of a solute from the outside of a drop to the inside, the fluid flow past the drop (see Figure 1(a)) ensures that the drop surface is continually exposed to a new source of solute (rather than the solute concentration immediately outside the drop starting to become depleted, as would happen in the absence of any fluid flow).…”

Section: Introductionmentioning

confidence: 99%

“…A way to understand liquid-liquid extraction in circulating drops has been considered by Ubal et al (2010) based on ideas originally proposed by Kronig and Brink (1950) and by Abramzon and Borde (1980); Brignell (1975); Oliver et al (1985); Prakash and Sirignano (1978). Convection is, by definition, along streamlines, so that (at least in a system with steady and laminar fluid flow) the only way to transport material across streamlines is via diffusion, no matter how fast the flow.…”

Section: Introductionmentioning

confidence: 99%

“…Convection is, by definition, along streamlines, so that (at least in a system with steady and laminar fluid flow) the only way to transport material across streamlines is via diffusion, no matter how fast the flow. Since in high Peclet number flows, convection along streamlines is much faster than diffusion across them, it is expected (Ubal et al, 2010) that the solute concentration field should very rapidly become uniform along streamlines, but with diffusion-driven concentration variations from streamline to streamline (see Figure 1(c)). This then constitutes a streamline-averaged formulation of liquid-liquid extraction.…”

Section: Introductionmentioning

confidence: 99%

“…It is expected that a streamline-averaged theory will be much more amenable computationally, as it does not need to resolve the (very short) timescale associated with individual streamline circulations, but instead can focus exclusively on the longer diffusive time-scale over which mass transfer actually occurs. The necessary equations were in fact formulated by Ubal et al (2010) but the solution was not implemented in that work, albeit there are previous implementations in literature for very a specific streamline layout (Brignell, 1975;Kronig and Brink, 1950;Prakash and Sirignano, 1978). Our purpose here is to revisit the implementation of the streamline-averaged theory, and to analyse the predictions it makes.…”

Section: Introductionmentioning

confidence: 99%

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Streamline-averaged mass transfer in a circulating drop

Grassia

Ubal

2018

Chemical Engineering Science

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Solute mass transfer is considered from the outside to the inside of a circulating drop in the context of liquid-liquid extraction. Specifically an internal problem is treated with resistance to mass transfer dominated by the liquid inside the drop. The Peclet number of the circulation is large, on the order of tens of thousands. A model is proposed by which the mass transfer into the drop begins in a boundary layer regime, but subsequently switches into a so called streamline-averaged regime. Solutions are developed for each regime, and also for the switch between them. These solutions are far easier to obtain than those of the full advection-diffusion equations governing this high Peclet number system, which are very stiff. During the boundary layer regime, the rate at which solute mass within the drop grows with time depends on Peclet number, with increases in Peclet number implying faster growth. However larger Peclet numbers also imply that the switch to the streamline-averaged regime happens sooner in time, and with less solute mass having been transferred to date. In the streamline-averaged regime, solute concentration varies across streamlines but not along them. In spite of the very large Peclet number, the rate of mass transfer is controlled diffusively, specifically by the rate of diffusion from streamline-to-streamline: sensitivity to the Peclet number is thereby lost. The model predictions capture, at least qualitatively, findings reported in literature for the evolution of the solute concentration in the drop obtained via full numerical simulation.

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Section: Introductionmentioning

confidence: 67%