Mass-transfer coefficients flow past solids

In principle, the mass transfer coefficient for a single liquid spherical droplet in an immiscible liquid flowing with velocity z/ll past the spherical droplet can be calculated from a Froessling-type equation, which was originally derived for a solid particle (see Atiemo-Obeng, Penney, and ArmenanteJ ) ... 

Maximum stable drop diameter, m Impeller diameter, m Diffusivity of dissolved component or reactant in liquid, m /s Gravitational acceleration, m/s Height of liquid in vessel, m Mass transfer coefficient, m/s Mass transfer coefficient for a single spherical droplet immersed in a liquid flowing at constant velocity past the droplet, m/s Mass of liquid, kg Rate of mass transfer of solute or reactant, kg/s Impeller speed, rotations/s Minimum speed to just suspend solid particles in vessel, rotations/s Minimum impeller speed to completely incorporate dispersed phase into continuous phase in liquid-liquid systems, rotations/s Power dissipation, W Time, s... 

The mass transfer coefficient to a single solid spherical particle immersed in a liquid flowing with velocity rsL past the particle can be calculated from ... 

As an incompressible fluid of infinite extent approaches and flows past either a spherical solid pellet or a gas bubble, a mobile component undergoes inteiphase mass transfer via convection and diffusion from the sphere to the fluid phase. The overall objective is to calculate the mass transfer coefficient and the Sherwood number at any point along the interface (i.e., the local transfer coefficients), as well as surface-averaged transfer coefficients. The results are applicable in the laminar flow regime (1) when the sphere is stationary and the fluid moves,... 

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). 

Boundary-layer theory. The boundary-layer theory has been discussed in detail in Section 7.9 and is useful in predicting and correlating data for fluids flowing past solid surfaces. For laminar flow and turbulent flow the mass-transfer coefficient fc oc D g. This has been experimentally verified for many cases. 

This is the oldest and most obvious picture of the meaning of the mass-transfer coefficient, borrowed from a similar concept used for convective heat transfer. When a fluid flows turbulently past a solid surface, with mass transfer occurring from the surface rn the fluid, the concentration-distance relation is as shown by the full curve of Fig. 3.6, the. shape of which is controlled by the... 

Experimental data are usually obtained by blowing gases over various shapes wet with evaporating liquids or causing liquids to flow past solids which dissolve. Average, rather than local, mass-transfer coefficients are usually obtained. In most cases, the data are reported in terms of K, and the like,... 

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