Film Penetration Model for Heat and Mass Transfer

Carnegie Institute of Technology, Pittsburgh, Pennsylvania
AIChE Journal (Impact Factor: 2.58). 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.
    12/2013; 49(12). DOI:10.1002/2012WR013324
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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.
    Chemical Engineering Science 12/2007; 62(24):7107–7118. DOI:10.1016/j.ces.2007.08.033 · 2.61 Impact Factor
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    • "In the past, various concepts of mass transfer between the gas and liquid phases were proposed. They are the two-film concept [1] [2] [3], the penetration concept [4] [5] [6], the film-penetration concept [7] [8], and unsteady two-film concept [9] [10]. In all of the above, the penetration concept was widely applied in practice to describe the mass transfer systems between the gas and liquid phases, but all the models developed in the past only concern the mass transfer rate at the interface and can not ascertain the concentration profiles in the main body of the fluids and the reactant conversion. "
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    ABSTRACT: An axial dispersion reactor model for gas–liquid reaction systems is proposed in this paper based on the penetration theory. The mass transfer mechanism accompanied by a chemical irreversible first-order reaction is mathematically treated in a new way in order to use its results to develop the model conveniently. Analytical solutions can be obtained for the equation system involving linear differential equations by using of the eigenvalues of the equation system. In addition, an iteration procedure is given to solve the nonlinear differential equation system numerically. The influences of the important model parameters on the concentration profile, the mass transfer and the reactant conversion are also studied.
    Chemical Engineering and Processing 07/1997; 36(4-36):291-299. DOI:10.1016/S0255-2701(97)00005-6 · 1.96 Impact Factor
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