Mass transfer models turbulence

Dreybrodt W, Buhmann D. A mass transfer model for dissolution and precipitation of calcite from solutions in turbulent motion. Chem Geol 1991 107-122. 

In fight of this analogy, we anticipate that the effect of turbulence may be dealt with in a similar manner like the random motion of molecules for which die gradient-flux law of diffusion (Eq. 18-6) has been developed. In addition, the mass transfer model (Eq. 18-4) may provide an alternative tool for describing the effect of turbulence on transport... 

In Chapter 7 we define mass transfer coefficients for binary and multicomponent systems. In subsequent chapters we develop mass transfer models to determine these coefficients. Many different models have been proposed over the years. The oldest and simplest model is the film model this is the most useful model for describing multicomponent mass transfer (Chapter 8). Empirical methods are also considered. Following our discussions of film theory, we describe the so-called surface renewal or penetration models of mass transfer (Chapter 9) and go on to develop turbulent eddy diffusivity based models (Chapter 10). Simultaneous mass and energy transport is considered in Chapter 11. 

This chapter describes models of mass transfer in turbulent conditions. Beginning with a brief survey of turbulent eddy diffusivity models we develop solutions to the binary mass transport equations at length before presenting the corresponding multicomponent results. 

A number of investigators used the wetted-wall column data of Modine to test multicomponent mass transfer models (Krishna, 1979, 1981 Furno et al., 1986 Bandrowski and Kubaczka, 1991). Krishna (1979b, 1981a) tested the Krishna-Standart (1976) multicomponent film model and also the linearized theory of Toor (1964) and Stewart and Prober (1964). Furno et al. (1986) used the same data to evaluate the turbulent eddy diffusion model of Chapter 10 (see Example 11.5.3) as well as the explicit methods of Section 8.5. Bandrowski and Kubaczka (1991) evaluated a more complicated method based on the development in Section 8.3.5. The results shown here are from Furno et al. (1986). 

Note that the sign and magnitude of the flux of acetone is sensitive to the value of the Re number (why ) and to the choice of the turbulent mass transfer model (again, why ). Rationalize your results in terms of the results portrayed in Figure 10.8. 

Von Behren et al. (1972) analyzed multicomponent mass transfer in turbulent flow in a pipe. Show that their model is fundamentally incorrect. You may also refer to the paper by Stewart (1973). 

Derevich, I. V. 2000. Statistical modeling of mass transfer in turbulent two-phase dispersed flows — 1. Model development. Int. J. Heat Mass Transfer 43 3709. 

Mass Transfer and Turbulence Models. Pure water at a velocity of 0,11 m/s is flowing at 26.1°C past a flat plate of solid benzoic acid where L = 0.40 m. Do as follows. 

Computational Fluid Dynamic (CFD) and mechanistic models of gas-liquid flow and mass transfer at turbulent conditions are useful for studying local inhomogeneities and operation conditions of gas-liquid stirred tanks. They are applicable also as scale-up and design tools of gas-liquid stirred tank reactors and other gas-liquid contacting devices with greater confidence compared to purely heuristic design methods. Experiments are needed for the development and the verification of these models. 

A dynamic mathematical model of the three-phase reactor system with catalyst particles in static elements was derived, which consists of the following ingredients simultaneous reaction and diffusion in porous catalyst particles plug flow and axial dispersion in the bulk gas and liquid phases effective mass transport and turbulence at the boundary domain of the metal network and a mass transfer model for the gas-liquid interface. 

One of the specialists who used electrochemical methods on a wide basis was Professor Mark Khaimovich Kishinevskiy (Fig. 5.7.4). His research was focused on the fundamental laws of mass transfer under turbulent flow conditions at interfaces, especially at the solid-liquid interface. Electrochemical methods have been used to model these processes based on measuring limiting currents. 

Abstract In this chapter, the two CMT models, i.e., c — Eci model and Reynolds mass flux model (in standard, hybrid, and algebraic forms) are used for simulating the chemical absorption of CO2 in packed column by using MEA, AMP, and NaOH separately and their simulated results are closely checked with the experimental data. It is noted that the radial distribution of Di is similar to a, but quite different from fit. It means that the conventional assumption on the analogy between the momentum transfer and the mass transfer in turbulent fluids is unjustifled, and thus, the use of CMT method for simulation is necessary. In the analysis of the simulation results, some transport phenomena are interpreted in terms of the co-action or counteraction of the turbulent mass flux diffusion. 

Film Theory. Many theories have been put forth to explain and correlate experimentally measured mass transfer coefficients. The classical model has been the film theory (13,26) that proposes to approximate the real situation at the interface by hypothetical "effective" gas and Hquid films. The fluid is assumed to be essentially stagnant within these effective films making a sharp change to totally turbulent flow where the film is in contact with the bulk of the fluid. As a result, mass is transferred through the effective films only by steady-state molecular diffusion and it is possible to compute the concentration profile through the films by integrating Fick s law ... 

Another concept sometimes used as a basis for comparison and correlation of mass transfer data in columns is the Clulton-Colbum analogy (35). This semi-empirical relationship was developed for correlating mass- and heat-transfer data in pipes and is based on the turbulent boundary layer model... 

Kishinev ski/23 has developed a model for mass transfer across an interface in which molecular diffusion is assumed to play no part. In this, fresh material is continuously brought to the interface as a result of turbulence within the fluid and, after exposure to the second phase, the fluid element attains equilibrium with it and then becomes mixed again with the bulk of the phase. The model thus presupposes surface renewal without penetration by diffusion and therefore the effect of diffusivity should not be important. No reliable experimental results are available to test the theory adequately. 

When two or more phases are present, it is rarely possible to design a reactor on a strictly first-principles basis. Rather than starting with the mass, energy, and momentum transport equations, as was done for the laminar flow systems in Chapter 8, we tend to use simplified flow models with empirical correlations for mass transfer coefficients and interfacial areas. The approach is conceptually similar to that used for friction factors and heat transfer coefficients in turbulent flow systems. It usually provides an adequate basis for design and scaleup, although extra care must be taken that the correlations are appropriate. 

When electrically insulated strip or spot electrodes are embedded in a large electrode, and turbulent flow is fully developed, the steady mass-transfer rate gives information about the eddy diffusivity in the viscous sublayer very close to the electrode (see Section VI,C below). The fluctuating rate does not give information about velocity variations, and is markedly affected by the size of the electrode. The longitudinal, circumferential, and time scales of the mass-transfer fluctuations led Hanratty (H2) to postulate a surface renewal model with fixed time intervals based on the median energy frequency. 

In a system with both heat and mass transfer, an extra turbulent factor, kx, is included which is derived from an adapted energy equation, as were e and k. The turbulent heat transfer is dictated by turbulent viscosity, pt, and the turbulent Prandtl number, Prt. Other effects that can be included in the turbulent model are buoyancy and compressibility. 

---