Application of surface-renewal-stretch model for interface mass transfer

Jajuee, Babak; Margaritis, Argyrios; Karamanev, Dimitre; Bergougnou, M.A.

doi:10.1016/j.ces.2006.01.026

Cited by 49 publications

(32 citation statements)

References 24 publications

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“…This assumption can greatly simplify the problem, but may be not true (some investigators also made similar suggestions 4,5,8,10 ). In a sense, the liquid film has an analogy to the boundary layer in turbulent flows and is very thin.…”

Section: Determination Of Depth Of Liquid Film Dmentioning

confidence: 90%

“…For example, the eddy concept models assumed a two-dimensional steady-state mass transfer mechanism containing convection and diffusion, [9][10][11] and the recent more complex surface renewal-stretch model from the penetration theory further considered a one-dimensional unsteady-state mechanism of convection and diffusion normal to the surface. 8 The main difference between the eddy concept models and the classical penetration (or surface renewal) models is that the former assumes the eddy velocity close to the surface can be accurately predicted by using a function based on the turbulence theory, and the mass transfer is steady-state and mainly controlled by certain scales of eddies, for example, large-scale containing-energy eddies (viz. large-eddy model 9 ) or smallscale viscosity eddies (viz.…”

Section: Introductionmentioning

confidence: 99%

“…Since the two-film theory 1 was proposed in 1924, the theoretical and experimental research for mass transfer has been developed at the same time. Many theories and models, such as penetration theory, 2 surface renewal theory, 3 and their improved models, [4][5][6][7][8] eddy concept model, [9][10][11][12] and statistics theory, 13 have been proposed. A large number of experiential correlations with regard to several key parameters, for example, per unit volume power and superficial gas velocity, have been presented.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A multi‐scale theoretical model for gas–Liquid interface mass transfer based on the wide spectrum eddy contact concept

et al. 2011

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On the basis of the wide spectrum eddy contact concept and the isotropic turbulence theory, a multi-scale theoretical model for the prediction of liquid-side mass transfer coefficient in gas-liquid system was developed. The model was derived from an unsteady-state convection and diffusion equation and considered the contributions of eddies with different sizes to the overall mass transfer coefficient. The proper contact time distribution at the surface is need to be determined to obtain satisfactory results with this model. Moreover, a simplified model was also proposed based on the assumption of steady-state mass transfer mechanism for single eddy. The results predicted by this model showed a very good agreement with the available experimental data in a comparatively wide range of turbulence intensities. V

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Section: Determination Of Depth Of Liquid Film Dmentioning

confidence: 90%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A multi‐scale theoretical model for gas–Liquid interface mass transfer based on the wide spectrum eddy contact concept

et al. 2011

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“…But when the scale of turbulence is high, Jajuee et al (2006) found that the integrand in Eq. (47) had the value of 2.…”

Section: Methodsmentioning

confidence: 99%

“…Inspired by this point, Angelo et al (1966) developed the penetration concept in the absence of bulk motion and turbulence and proposed a promising theory called "surfacestretch theory". Jajuee et al (2006) further developed the model by incorporating Dankwerts (1951) surface-renewal model with the penetration theory for surface stretch proposed by Angelo et al (1966) and extended the model to liquid-liquid systems.…”

Section: Introductionmentioning

confidence: 99%

Mass transfer of SO2 absorption with an instantaneous chemical reaction in a bubble column

Zhu

et al. 2013

Braz. J. Chem. Eng.

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-Gas absorption accompanied by an instantaneous irreversible chemical reaction in bubble columns has been analyzed theoretically. A mass transfer model based on the Dankwerts surface-renewal model as well as the penetration theory for surface stretch proposed by Angelo et al. was developed, in which the effects of bulk motion and turbulence on mass transfer were taken into account. The analytical expressions for the time-average mass transfer coefficient and the enhancement factor have been obtained. The fast reactive absorption of SO 2 from gas mixtures into aqueous NH 4 HCO 3 solution was investigated experimentally in a bubble column reactor to validate the mass transfer model, and the results calculated by the present model agree well with the experimental results.

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A theoretical unsteady‐state model for k_L of bubbles based on the framework of wide energy spectrum

Han

et al. 2015

AIChE Journal

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An unsteady-state model for predicting mass-transfer coefficient k L of bubbles with mobile surface was developed for turbulent gas-liquid dispersions. This model was derived from an unsteady-state convection and diffusion equation through a characteristics method. Unlike the previous work, this model considered the contributions of the amount of fluid structures of different scales (i.e., eddies) existing in the turbulent flows, the frequency of eddies arriving at the surface, the deformation and oscillation of bubbles to mass transfer. This model was based on the framework of wide energy spectrum and can account for the role of eddies of different sizes in mass transfer. Thus the assumption adopted by the previous models that mass transfer was controlled by eddies of certain sizes is no more needed. The overall k L predicted by the proposed model showed a better agreement with the reported experimental data. Derivation of liquid-side mass-transfer coefficientAccording to the points of (1) and (3) mentioned above, the convection-diffusion equation for the solute concentration in the thin concentration layer close to surface can take the form of Ã c is the dimensionless distance. It can be seen from Figure 5a that this distance increases with the increasing s. Nevertheless, our calculations indicate that y c will not be changed obviously when s > 1.0 under the action of the convections of eddies, which are responsible to sweep the surface and remove the solute-enriched liquid to the bulk fluid. As shown in Figure 5b, the turbulent dissipation rate e, the diffusion coefficient D and the size of eddy k affect the solute concentration distribution Figure 4. The variation of R L with f min .

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Application of surface-renewal-stretch model for interface mass transfer

Cited by 49 publications

References 24 publications

A multi‐scale theoretical model for gas–Liquid interface mass transfer based on the wide spectrum eddy contact concept

A multi‐scale theoretical model for gas–Liquid interface mass transfer based on the wide spectrum eddy contact concept

Mass transfer of SO2 absorption with an instantaneous chemical reaction in a bubble column

A theoretical unsteady‐state model for k_L of bubbles based on the framework of wide energy spectrum

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Application of surface-renewal-stretch model for interface mass transfer

Cited by 49 publications

References 24 publications

A multi‐scale theoretical model for gas–Liquid interface mass transfer based on the wide spectrum eddy contact concept

A multi‐scale theoretical model for gas–Liquid interface mass transfer based on the wide spectrum eddy contact concept

Mass transfer of SO2 absorption with an instantaneous chemical reaction in a bubble column

A theoretical unsteady‐state model for kL of bubbles based on the framework of wide energy spectrum

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Product

Resources

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A theoretical unsteady‐state model for k_L of bubbles based on the framework of wide energy spectrum