Mass transfer models slip velocity

The rate parameters of importance in the multicomponent rate model are the mass transfer coefficients and surface diffusion coefficients for each solute species. For accurate description of the multicomponent rate kinetics, it is necessary that accurate values are used for these parameters. It was shown by Mathews and Weber (14), that a deviation of 20% in mass transfer coefficients can have significant effects on the predicted adsorption rate profiles. Several mass transfer correlation studies were examined for estimating the mass transfer coefficients (15, jL6,17,18,19). The correlation of Calderbank and Moo-Young (16) based on Kolmogaroff s theory of local isotropic turbulence has a standard deviation of 66%. The slip velocity method of Harriott (17) provides correlation with an average deviation of 39%. Brian and Hales (15) could not obtain super-imposable curves from heat and mass transfer studies, and the mass transfer data was not in agreement with that of Harriott for high Schmidt number values. 

Vasconcelos variant of the slip velocity model based on bubble contamination kinetics, Eqs. (4)-(8), was used by Alves et al. [9] to interpret kl data in a double Rush-ton turbine-stirred tank. The application of Vasconcelos model to the interpretation of unreliable mass transfer co-... 

The model based on terminal and slip velocity approach is rather tenuous. It breaks down as the density difference between liquid and solid approaches zero. Under highly turbulent conditions, an accurate estimation of slip velocity is rather difficult, and there is disagreement on whether or not the relative velocity between the solid and liquid alone is enough to obtain an accurate estimate of the mass-transfer coefficient. 

An understanding of the general hydraulics of a static contactor is necessary for estimating the diameter and height of the column, as this affects both capacity and mass-transfer efficiency. Accurate evaluations of characteristic drop diameter, dispersed-pnase holdup, slip velocity, and flooding velocities usually are necessary. Fortunately, the relative simplicity of these devices facilitates their analysis and the approaches taken to modeling performance. 

The just-suspended state is defined as the condition where no particle remains on the bottom of the vessel (or upper surface of the liquid) for longer than 1 to 2 s. At just-suspended conditions, all solids are in motion, but their concentration in the vessel is not uniform. There is no solid buildup in comers or behind baffles. This condition is ideal for many mass- and heat-transfer operations, including chemical reactions and dissolution of solids. At jnst-snspended conditions, the slip velocity is high, and this leads to good mass/heat-transfer rates. The precise definition of the just-suspended condition coupled with the ability to observe movement using glass or transparent tank bottoms has enabled consistent data to be collected. These data have helped with the development of reliable, semi-empirical models for predicting the just-suspended speed. Complete suspension refers to nearly complete nniformity. Power requirement for the just-suspended condition is mnch lower than for complete snspension. 

Current research falls into one of two schools of thought Calderbank s slip velocity model and Lamont and Scott s eddy turbulence model (Linek et al., 2004 Linek et al., 2005b). Even though both models are penetration-type models, they make very different assumptions. The slip velocity model assumes different behavior for small and large bubbles. It also assumes a significant difference between average velocities for the two phases. The slip velocity and the surface mobility control mass transfer and, in terms of penetration theory, surface renewal. 

The power dissipation influence on the liquid-phase mass transfer coefficient (/cl) is highly debated in STRs, especially at higher power densities. The slip velocity model and eddy turbulence model have been used to explain mass transfer, but they come to different conclusions with respect to power. The slip velocity model predicts a decrease in mass transfer with increasing power dissipation while the eddy turbulence model predicts an increase. Linek et al. (2004) postulate that the main reason for the confusion stems from the miscalculation of They investigated different measurement methods and models used by others and concluded that the slip velocity models were underestimating and, hence,... 

Mass transfer coefficients are the basis for models where the dissolved species are transported by a combination of diffusive and advective processes. The diffusive mass transfer coefficient ko, m/sec) is based on boundary layer theory. The basic premise of boundary layer theory is that, for laminar ffow, the ffuid velocity adjacent to a solid surface is zero (the no slip condition ) and the velocity increases as a parabolic function of distance away from the surface until it matches the velocity of the bulk fluid (Figure 7.5). This means that there is a thin layer of fluid with a thickness of 5d (m) adjacent to the surface that is effectively static. The rate of mass transport through this layer is limited by the diffusion rate of the dissolved species. The diffusional boundary layer is much thinner than the velocity boundary layer. For laminar flow past a flat surface, the thickness of the diffusional boundary layer is related to the thickness of the velocity boundary layer (Sy) by the Schmidt number, which compares the fluid viscosity to the diffusivity (Probstein, 1989). 

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