Exact solution for diffusion to flow down an incline

Rotem, Zeev; Neilson, J. E.

doi:10.1002/cjce.5450470407

Cited by 40 publications

(7 citation statements)

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“…Subsequent solution of the diffusion equation in a coordinate system moving with the wave demonstrated enhancement of the mass transfer rate by a factor of 1.5-2.5 in comparison with the waveless film case. Rotem and Neilson (1969) considered the absorption of gas into a waveless falling film and determined the dependence of the Sherwood number Sh m on the Péclet number P e = ReSc. Knowledge of the film hydrodynamics allows the use of the relations derived by Howard and Lightfoot (1968) which characterise the rate of mass absorption at large Péclet numbers.…”

Section: Introductionmentioning

confidence: 99%

Absorption of gas into a wavy falling film

Sisoev¹,

Matar²,

Lawrence³

2005

Chemical Engineering Science

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Section: Introductionmentioning

confidence: 99%

Absorption of gas into a wavy falling film

Sisoev¹,

Matar²,

Lawrence³

2005

Chemical Engineering Science

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“…Following the method of Rotem and Neilson (1969), who solved the case of a parabolic profile, the eigenvalue solution to Eq. 23 which satisfies the far-field film saturation condition, Eq.…”

Section: Assuming a Linear Mean Velocity Profile U(y) -U(0)mentioning

confidence: 99%

Theoretical study of interfacial transport in gas‐liquid flows

Back¹,

McCready²

1988

AIChE Journal

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Mass transfer in sheared, concurrent gas-liquid flows is investigated theoretically using solutions to the unaveraged advection-diffusion equation. For sufficiently thick films, the resistance to mass transfer is shown to be confined completely within a thin region in the liquid near the interface and mass transfer coefficients are accurately predicted by an improved numerical technique that uses a velocity field derived from an Orr-Sommerfeld equation with the time-varying velocity computed directly from measurements of interfacial waves. The mass transfer coefficients are shown to depend on the magnitude and frequency content of the velocity fluctuations normal to the interface. As the film thickness decreases, transfer resistance extends throughout the film and turbulent mixing in the middle of the film controls the transfer rates. For this region, limiting values of transfer coefficients are predicted well by analytical solutions to the advection-diffusion equation, which assume a laminar flow. Introduction OverviewFor the absorption of slightly soluble gases or the condensation of a pure vapor onto a subcooled liquid, the primary resistance to transport lies in the liquid phase and as a consequence, transfer rates are controlled by the liquid velocity field in the near vicinity of the interface. At the interface a thin (as small as m for a sheared gas-liquid interface) concentration or thermal boundary layer will occur in which a balance exists between convective and diffusive modes of transport. If the flow is irregular in space and time, it is expected that the effectiveness of individual velocity fluctuations on mass (or heat) transfer will depend upon their size and duration as well as their magnitude. The resulting average transport rate and the temporal and spatial scales of the concentration fluctuations will be the result of the combined effects of forcing due to velocity fluctuations and smoothing caused by diffusion. Time-averaged advection-diffusion equations that use eddy diffusivities to account for scalar convection cannot accurately describe this balance because they neglect the inherent dynamical nature of the problem.Efforts to achieve an understanding of the diffusion-convection balance and exactly how the fluctuating flow field controls mass transfer have been limited by the small size of the region, which prevents direct measurements of either the velocity fields or the concentration fields. Until these experimental limitations are overcome, research to improve the understanding of the basic physics of interfacial mass transfer must rely on solutions, either analytical or numerical, of the governing mass balance equation using the best available representations for velocity fields.In the present paper, absorption of a slightly soluble component from a turbulent gas flow into a sheared liquid film where the surface is covered by nonbreaking waves is examined. These films exhibit mass transfer rates that are generally an order of magnitude larger than those for unsheared films. In order to ...

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“…We shall assume that at a certain moment t = 0, a concentration profile corresponding to the waveless flow takes place. This profile could be evaluated by the aid of the solution of the diffusion equation, proposed by Rotem & Neilson (1969):…”

Section: Gas Absorption Numerical Investigation 175mentioning

confidence: 99%