Mass transfer coefficients spheres

In a quiescent fluid, the dimensionless mass-transfer coefficient, or the Nusselt number, djkj for a sphere is two. In fluidized beds the Nusselt... 

A study of mass transfer between a liquid and a particle forming part of an assemblage of particles was made by Mulun and Treleaven1116, who subjected a sphere of benzoic acid to the action of a stream of water. For a fixed sphere, or a sphere free to circulate in the liquid, the mass transfer coefficient was given, for 50 < Re c < 700, by ... 

Fig. 5.22 Mass transfer coefficients for a sphere in free rise (pp < p) or free fall (pp > p) in water at 20 C with Sc = 10. ...

The straight line for Ap = 0 represents diffusion in a stagnant medium [Eq. (3-44)]. In air spheres with diameters less than about 30 pm have transfer rates essentially equal to those in a stagnant medium, while in water the diameter for this to occur must be less than about 3 pm. In water the mass transfer coefficient is only weakly dependent on diameter, a prediction which has been verified experimentally (C2). For free fall in air, the transfer coefficient exhibits a larger decrease with diameter. The following expressions fit the predictions of Figs. 5.22 and 5.23 over the ranges indicated ... 

Many investigators base mass transfer coefficients upon the area of the volume-equivalent sphere, especially for oscillating drops ... 

The presence of container walls has a much smaller effect on Sherwood number than on drag since the mass transfer coefficient is only proportional to the one-third power of the surface vorticity. For a sphere with given settling on the axis of a cylindrical container, the Sherwood number decreases with 2, but it is still within 8% of the Sherwood number in an infinite fluid for 2 — 0.5. No data are available to test these predictions. 

Since the liquid is saturated with hydrogen, only the liquid-to-particle mass transfer coefficient and the intrinsic rate constant will be significant. In the case that the reaction is fast, the reaction rate will depend only on the liquid-sold mass transfer resistance. Since the particle are very small (10 micrometers), and the loading is moderate (0.8% mass), the Sherwood number will be that of lonely spheres, so Sh = 2. For this case we can take Sh = =4 [50], rather safely. 

The transfer coefficient can be correlated in the form of a dimensionless Sherwood number Sh(= h0dp/D). The particle diameter dp is often taken to be the diameter of the sphere having the same area as the (irregular shaped) pellet. Thaller and Thodos(38> correlated the mass transfer coefficient in terms of the gas velocity u and the Schmidt number Sc(= p/pD) ... 

Single Sphere Model II (Equations 4, 5, 8, 9 and 10 in reference 6) In this model allowance is made for the resistance to mass transfer offered by the surface film surrounding the herb particles. The mass transfer coefficient kf was obtained from correlations proposed by Catchpole et al (8, 9) for mass transfer and diffusion into near-critical fluids. An average of the binary diffusivities of the major essential oil components present was used in calculating kf (these diffusivities were all rather similar because of their similar structures). 

Specchia et al.32 measured gas liquid interfacial area and liquid-phase mass-transfer coefficients in an 8-cm-diameter packed column. Three types of packing, glass spheres, Berl saddles, and ceramic rings, all of 6 mm, were examined. Superficial velocities of 14 through 221 cm s 1 and 0.25 through 4.3 cm s 1 were used for the gas and liquid phase, respectively. The gas-liquid interfacial area was correlated to the pressure drop by an expression... 

Snider and Perona3 measured Ksas, the volumetric liquid-solid mass-transfer coefficient, for the case of hydrogenation of a-methyl styrene on 3-mm alumina spheres coated with palladium catalyst. The results were obtained in the bubble-flow regime. The measurements of Ks, the liquid-solid mass-transfer coefficient in a nonreacting system, were first reported by Mochizuki and Matsui.20 They... 

In the limiting case of mass transfer from a single sphere resting in an infinite stagnant liquid, a simple film-theory analysis122 indicates that the liquid-solid mass-transfer coefficient R s is equal to 2D/JV, where D is the molecular diffusivity of the solute in the liquid phase and d is the particle diameter. In dimensionless form, the Sherwood number... 

Figure 9-26 Calculated mass-transfer coefficient for a single sphere settling at its terminal velocity in a liquid.8...

K liquid solid mass-transfer coefficient for spheres settling at terminal... 

For a sphere, the mass transfer coefficient can be obtained from Ihe Colburn analogy for the Nusselt number ... 

The mass transfer coefficient,, for a sphere can be determined from the Sherwood number, Sh (= K JD g, where is the molecular diffusion coefficient of the solvent. A, in drying gas, B typical values are 10 -10 cm /sec) and the following engineering correlation [15]... 

In the preceding equations, Vg is the supei dal gas velocity, a is the total droplet area per unit volume (assumed to be a constant), and Kg is the mass transfer coefficient for a sphere, which can be determined from the Sherwood number, Sh (=, where is the molecu-... 

A close look at the available experimental data on heat and mass transfer coefficients Q),shows that in the low Reynolds numbers zone exists the peculiar fact that both,the heat and mass transfer coefficients fall well below the value predicted by Ranz ( )for a single sphere submerged in a fluid in laminar flow(Sh=2). In this zone,the numerical results from the different studies also show major disagreement. In general, this is not the case in the high Reynolds numbers zone. 

To obtain numerically the mass transfer coefficient, a porous medium is stochastically constructed in the form of a sphere pack. Specifically, the representation of the biphasic domains under consideration is achieved by the random deposition of spheres of radius Rina box of length L. The structure is digitized and the phase function (equal to zero for solid and unity for the pore space) is determined in order to obtain the porosity and to solve numerically the convection- diffusion problem. The next for this purpose is to obtain the detailed flow field in the porous domain through the solution of the Stokes equations ... 

Liquid toluene (C iHsCHj) was stored at6.4°C in an open top 20-cm-diameter cylindrical container. Tile vapor pressure of toluene at 6.4°C is 10 nun Hg. A gentle stream of fresh air at 6.4"C and 101.3 kPa was allowed to flow over the open end of the container. The rale of evaporation of toluene into air was measured to be 60 g/day. E.stimaie the concentration of toluene (in g/m ) at exactly 10 nun above the liquid surface. The diffusion coefficient of toluene at 2S° C is D.,a = 0.084 X 10-"inVs. 14-141 In an experiment, a sphere of crystalline sodium. chloride (NaCI) was suspended in a. stirred tank filled with water at 20°C. It-s initial mass was 100 g. In 10 minutes, the mass Of sphere was found to have decreased by 10 percent. The density of NaCl is 2160 kg/ra Its solubility in water at 20°C is 320 kg/m, Use these results to obalin an average value for the mass transfer coefficient. 

Clift et al. [IS] derived empirical relationships for the mass transfer coefficients from rigid spheres. Since the ends of Taylor bubbles can be roughly approximated as hemispheres and rigidity is also a quite reasonable assumption, these equations can be applied for the mass transfer from the ends of the Taylor bubbles. For 1 < Re s 400,... 

The ratio of the diffusivity to Ae film-thickness is the mass transfer coefficient, kc. The tildas in the terms kc and 6 denote that they are, respectively, the local transfer coefficient and the boimdary layer thickness at a particular point P on the sphere,... 

Because reaction is assumed to occur instantaneously on the external surface of the pellet, Caj = 0. Also, Ca , is given as 1 mol/dm, The mass transfer coefficient for single spheres is calculated from the Frossling correlation ... 

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