Numerical simulation of multi-component mass transfer in rigid or circulating drops: Multi-component effects even in the presence of weak coupling

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

doi:10.1016/j.colsurfa.2010.11.058

Cited by 7 publications

(5 citation statements)

References 38 publications

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“…This outcome is mainly due to the intensive internal circulation of the microbubble which helps to homogenize it both thermally and chemically at sufficiently early residence times in the liquid. 22,38,39 Figures 3, 4, and 5 show respectively the time profiles for the average bubble temperature, the average bubble concentration and the average mole fraction obtained from the numerical simulations.…”

Section: Simulation Results and Discussionmentioning

confidence: 99%

“…Clearly, the temperature profile is nearly isothermal at 294 K and the concentration profile of ethanol is nearly constant throughout the bubble at around 1.64 mol/m 3 . This outcome is mainly due to the intensive internal circulation of the microbubble which helps to homogenize it both thermally and chemically at sufficiently early residence times in the liquid. ,, …”

Section: Simulation Results and Discussionmentioning

confidence: 99%

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Purification of Bioethanol Using Microbubbles Generated by Fluidic Oscillation: A Dynamical Evaporation Model

Abdulrazzaq

Al-Sabbagh

Rees

et al. 2016

Ind. Eng. Chem. Res.

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A computational model of a single gas microbubble immersed in a liquid of ethanol–water mixture is developed and solved numerically. This complements earlier binary distillation experiments in which the ethanol–water mixture is stripped by hot air microbubbles achieving around 98% vol. ethanol from the azeotropic mixture. The proposed model has been developed using Galerkin finite element methods to predict the temperature and vapor content of the gas microbubble as a function of its residence time in the liquid phase. This model incorporates a novel rate law that evolves on a time scale related to the internal mixing of microbubbles of 10–3s. The model predictions of a single bubble were shown to be in very good agreement with the existing experimental data, demonstrating that the ratio of ethanol to water in the microbubble regime are higher than the expected ratios that would be consistent with equilibrium theory for all initial bubble temperatures and all liquid ethanol mole fractions considered and within the very short contact times appropriate for thin liquid layers. Our previous experiments showed a decrease in the liquid temperature with decreasing liquid depth in the bubble tank, an increase in the outlet gas temperature with decreasing liquid depth, and an improvement in the stripping efficiency of ethanol upon decreasing the depth of the liquid mixture and increasing the temperature of the air microbubbles, all of which are consistent with the predictions of the computational model.

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Section: Simulation Results and Discussionmentioning

confidence: 99%

Section: Simulation Results and Discussionmentioning

confidence: 99%

Purification of Bioethanol Using Microbubbles Generated by Fluidic Oscillation: A Dynamical Evaporation Model

Abdulrazzaq

Al-Sabbagh

Rees

et al. 2016

Ind. Eng. Chem. Res.

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“…Mass transfer to and/or from individual drops has been a widely studied topic in chemical engineering (Brodkorb et al, 2003;Handlos and Baron, 1957;Johns and Beckmann, 1966;Korchinsky et al, 2009;Kumar and Hartland, 1999;Piarah et al, 2001;Ubal et al, 2011;Waheed et al, 2002), and the field becomes wider still if one accounts for analogous systems including heat transfer to/from drops (see e.g. Prakash and Sirignano (1978); Sadhal et al (1997); Sirignano (2010)) as well as mass transfer to/from bubbles (see e.g.…”

Section: Introductionmentioning

confidence: 99%

“…This means that fluid must circulate around the drop many times before the extraction process is complete. Numerical simulations of the process, whilst possible (Edelmann et al, 2017;Ubal et al, 2011), are computationally very expensive owing to the need to resolve each individual circulation: convective-diffusive problems at high Peclet number are, in numerical terms, exceedingly stiff (Press et al, 1992).…”

Section: Introductionmentioning

confidence: 99%

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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“…From the numerical simulations made in order to compute the spatial convergence rate, a selection is presented in Tables 1 and 2. The discrete Euclidean norm (p = 2) was used in relation (26). The time step used to compute the results presented in Tables 1 and 2 was constant and equal to ∆ τ = 10 -4 .…”

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confidence: 99%

Splitting Algorithm for Numerical Solving of Parabolic Nonlinear Multi - Component Convection – Diffusion Mass Transfer Equations

Juncu¹,

Popa²,

Sarbu³

2023

Preprint

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The splitting method developed in a previous study for linear, multi – component, convection-diffusion mass transfer equations is extended to non-linear, multi-component, convection-diffusion mass transfer equations. The diffusion term is non-linear (the diffusion coefficients depend on chemical species concentrations). Theoretical results about the splitting error are presented, as well as numerical simulations for mixtures with n ≤ 5. The numerical experiments show second-order accuracy and stability for the present splitting algorithm.

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Numerical simulation of multi-component mass transfer in rigid or circulating drops: Multi-component effects even in the presence of weak coupling

Cited by 7 publications

References 38 publications

Purification of Bioethanol Using Microbubbles Generated by Fluidic Oscillation: A Dynamical Evaporation Model

Purification of Bioethanol Using Microbubbles Generated by Fluidic Oscillation: A Dynamical Evaporation Model

Streamline-averaged mass transfer in a circulating drop

Splitting Algorithm for Numerical Solving of Parabolic Nonlinear Multi - Component Convection – Diffusion Mass Transfer Equations

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