Film Penetration Model for Heat and Mass Transfer

Carnegie Institute of Technology, Pittsburgh, Pennsylvania
AIChE Journal (Impact Factor: 2.75). 03/1958; 4(1):97 - 101. DOI: 10.1002/aic.690040118
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    • "The original SR theory inspired a class of related models based on various heuristic depictions of the near-wall turbulent fluid flows. Some of the well-known variants of the SR theory include film-penetration models [Toor and Marchello, 1958; Brusset et al., 1973], periodic growth-breakdown models [Einstein and Li, 1958; Ruckenstein , 1958; Meek and Baer, 1970; Pinczewski and Sideman , 1974], random surface renewal models [Hanratty, 1956; Fortuin and Klijn, 1982; Fortuin et al., 1992], and surface rejuvenation models [Harriott, 1962; Bullin and Dukler, 1972; Thomas et al., 1975; Loughlin et al., 1985]. These eddy renewal models assume that the replacement of individual fluid elements near a surface may be represented as a stochastic process driven by a turbulent flow field away from the surface. "
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    ABSTRACT: [1] Evaporative fluxes from terrestrial porous surfaces are determined by interplay between internal capillary and diffusive transport, energy input, and mass exchange across the land-air interface. Turbulent airflows near the Earth's surface introduce complex boundary conditions that affect vapor, heat, and momentum exchange rates with the atmosphere. The impact of turbulent airflow on evaporation from porous surfaces was quantified using surface renewal theory coupled with a physically based pore scale model for vapor transfer from partially wet surfaces to individual eddies. The model considers diffusive vapor exchange with individual eddies interacting intermittently with a drying surface to quantify mean surface evaporative fluxes. The model captures nonlinearities between surface water content and evaporation flux during drying of porous surfaces, yielding close agreement with experimental results. This new diffusion-turbulence evaporation model provides a basic building block for improving estimation of field-scale evaporative fluxes from drying soil surfaces under natural airflows.
    Full-text · Article · Dec 2013
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    • "For the modeling of reactions between ozone and a dye in bubble columns it is necessary that the model takes into account a macroscopic model, describing the overall gas and liquid phases, and a microscopic model, describing the gas-liquid interface mass transfer in combination with the chemical reaction. The most frequently used models for gas absorption are: (i) the stagnant film model in which mass transfer is postulated to proceed via stationary molecular diffusion in a stagnant film of thickness d (Lewis and Whitman, 1924), (ii) the penetration model where the periodic replacement of fluid elements at the interface by liquid from the interior is assumed (Higbie, 1935), (iii) the surface renewal model where the probability of replacement of these fluid elements is introduced (Danckwerts, 1970) and (iv) the film-penetration model, a two-parameter model combining the stagnant film and the penetration model (Toor and Marchello, 1958). Recently, van Elk et al. (2000) have proposed a numerical solution for the Higbie Penetration Theory considering the existence of a liquid bulk that could be applied in the modeling of ozone gas-liquid reactors. "
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    ABSTRACT: In this study, the kinetic information reconstruction method is applied to measure the degradation of a dye in an ozonation gas-liquid reactor. The application of this method combined with the study of the ozone gas phase concentration has made possible a deeper study of the fast reaction between ozone and blue indigo trisulfonate. For this kinetic study different rigorous mathematical models based on Film Layer Theory, Surface Renewal Model and Penetration Theory have been used.
    Full-text · Article · Oct 2008 · Ozone Science and Engineering
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    • "To predict the mass transfer coefficient k l , many approaches have been developed to be more and more realistic toward capturing the interfacial mass transfer in last several decades (Kulkarni, 2007). Classical mass transfer models include the two-film model (Lewis and Whitman, 1924), penetration theory (Higbie, 1935), surface renewal model (Danckwerts, 1951), film penetration model (Toor and Marchello, 1958) and eddy cell model (Lamont and Scott, 1970). Some more complex models were also proposed in recent years, e.g., the surfacerenewal-stretch model (Jajuee et al., 2006), and model based on the vertical velocity gradient at the interface (Xu et al., 2006). "
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    ABSTRACT: Gas–liquid mass transfer in a bubble column in both the homogeneous and heterogeneous flow regimes was studied by numerical simulations with a CFD–PBM (computation fluid dynamics–population balance model) coupled model and a gas–liquid mass transfer model. In the CFD–PBM coupled model, the gas–liquid interfacial area a is calculated from the gas holdup and bubble size distribution. In this work, multiple mechanisms for bubble coalescence, including coalescence due to turbulent eddies, different bubble rise velocities and bubble wake entrainment, and for bubble breakup due to eddy collision and instability of large bubbles were considered. Previous studies show that these considerations are crucial for proper predictions of both the homogenous and the heterogeneous flow regimes. Many parameters may affect the mass transfer coefficient, including the bubble size distribution, bubble slip velocity, turbulent energy dissipation rate and bubble coalescence and breakup. These complex factors were quantitatively counted in the CFD–PBM coupled model. For the mass transfer coefficient klkl, two typical models were compared, namely the eddy cell model in which klkl depends on the turbulent energy dissipation rate, and the slip penetration model in which klkl depends on the bubble size and bubble slip velocity. Reasonable predictions of klakla were obtained with both models in a wide range of superficial gas velocity, with only a slight modification of the model constants. The simulation results show that CFD–PBM coupled model is an efficient method for predicting the hydrodynamics, bubble size distribution, interfacial area and gas–liquid mass transfer rate in a bubble column.
    Full-text · Article · Dec 2007 · Chemical Engineering Science
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