Mechanism of Mass Transfer

Several different mechanisms have been proposed to provide a basis for a theory of interphase mass transfer. The three best known are the two-film theory, the penetration theory, and the surface renewal theory. 

The two-film theory supposes that the entire resistance to transfer is contained in two fictitious films on either side of the interface, in which transfer occurs by molecular diffusion. This model leads to the conclusion that the mass-transfer coefficient kL is proportional to the diffusivity DAB and inversely proportional to the film thickness Zy as 

Penetration theory (Higbie, 1935)assumes that turbulent eddies travel from the bulk of the phase to the interface where they remain for a constant exposure time te. The solute is assumed to penetrate into a given eddy during its stay at the interface by a process of unsteady-state molecular diffusion. This model predicts that the mass-transfer coefficient is directly proportional to the square root of molecular diffusivity 

Surface renewal theory (Danckwerts, 1951) proposes that there is an infinite range of ages for elements of the surface and the surface age distribution function j (t) can be expressed as 

All these theories require knowledge of one unknown parameter, the effective film thickness zf the exposure time 4, or the fractional rate of surface renewal s. Little is known about these properties, so as theories, all three are incomplete. However, these theories help us to 

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For electrolytic solutions, migration of charged species in an electric field constitutes an additional mechanism of mass transfer. Thus the flux of an ionic species Nj in (g mol)/(cm s) in dilute solutions can be expressed as... 

In the previous chapters, the stresses arising from relative motion within a fluid, the transfer of heat by conduction and convection, and the mechanism of mass transfer are all discussed. These three major processes of momentum, heat, and mass transfer have, however, been regarded as independent problems. 

Since the absolute thickness of the effective hydrodynamic boundary layer is very small, below a particular size range minimum, no hydrodynamic effects are perceived experimentally with varying agitation. This, however, does not mean, that there are no such influences Further, the mechanisms of mass transfer and dissolution may change for very small particles depending on a number of factors, such as the fluid viscosity, the Sherwood number (the ratio of mass diffusivity to molecular diffusivity), and the power input per unit mass of fluid. 

There have been many recent studies of the mechanism of mass transfer in a gas absorption system. Many of these have been directed towards investigating whether there is a significant resistance to mass transfer at the interface itself. In order to obtain results which can readily be interpreted, it is essential to operate with a system of simple geometry. For that reason a laminar jet has been used by a number of workers. 

The mechanism of mass transfer to the external flow is essentially the same as for spheres in Chapter 5. Figure 6.8 shows numerically computed streamlines and concentration contours with Sc = 0.7 for axisymmetric flow past an oblate spheroid (E = 0.2) and a prolate spheroid (E = 5) at Re = 100. Local Sherwood numbers are shown for these conditions in Figs. 6.9 and 6.10. Figure 6.9 shows that the minimum transfer rate occurs aft of separation as for a sphere. Transfer rates are highest at the edge of the oblate ellipsoid and at the front stagnation point of the prolate ellipsoid. 

In fluidized beds, mass transfer involves two different mechanisms. The first one is the ordinary mass transport between the fluid and the solid. The treatment of this type of transport is quite similar to fluid-solid mass transfer found in other types of operations such as fixed beds and agitated tank reactors. This mechanism of mass transfer is not always significant in fluidized beds and can be totally neglected in some cases. 

Mechanism of mass transfer from bubbles in dispersions Part II Mass transfer coefficients in stirred gas-liquid reactor and bubble column... 

The various theories for the mechanism of mass transfer across a phase boundary are discussed in Section 10.5. 

Miniemulsion copolymerization of a 50 50 styrene/methyl methacrylate monomer mixture, using hexadecane as hydrophobe, was carried out by Rodriguez et al. [78]. The mechanism of mass transfer between miniemulsion droplets and polymer particles in the miniemulsion copolymerization of styrene-methyl methacrylate (AIBN as initiator, hexadecane as hydrophobe) was studied, analyzing the mass transfer of highly water-insoluble compounds from miniemulsion droplets to polymer particles by both molecular diffusion and collisions between droplets and particles [79,80]. 

The rate of extraction is due, firstly, to the solubility of the analyte in the supercritical fluid and, secondly, to the transfer of the mass of the solute outside of the matrix. As indicated in Figure 5, we can therefore conveniently consider four mechanisms of mass transfer ... 

Figure 7.5 Mechanisms of mass transfer for catalytic pellets. (Source Ref. 18 with permission).

Understand Ihe concenralion gradient and the physical mechanism of mass transfer, B Recognize the analogy between heat and mass transfer,... 

E.U. Schlunder, On the mechanism of mass transfer in heterogeneous systems—in particular in fixed beds, fluidized beds and on bubble trays, Chem. Eng. ScL 32 845 (1977). 

The gas flow velocity through the emulsion phase is close to the minimum fluidization velocity When the particles are spherical and have diameters of several tens of microns, this flow condition gives a quite small particle Peclet number, dpUmf/Dc. For example, the Peclet number is estimated as 0.1-0.01 when 122-/Lim-diam. cracking catalyst is fluidized by gas, with Umt = 0.73 cm/sec and Dq = 0.09 cmVsec and it is estimated as 0.001-0.01 for 58-/u.m-diam. particles, with Umt = 0.16 cm/sec. The mechanism of mass transfer between fluid and particles in packed beds is controlled by molecular diffusion under such low Peclet numbers, and the particle Sherwood number kfdp/Dc, is well over 10 (M24). Consequently with intraparticle diffusion shown to be negligible (M21), instantaneous equilibrium is established to be a good approximation [see Eq. (6-24)]. 

External Mass Transfer In a reactor, the solid catalyst is deposited on the surface of narrow tubes (such as monolith or foams), is packed as particles in a tube, or is suspended in slurry or in a fluidized bed as fine particles. For these systems, the bulk concentration of the gas phase approaches that on the catalyst surface if the mass-transfer rate from bulk to surface is substantially larger than the reaction rates on the surface. This, however, is often not the case. The mechanism of mass transfer and reaction on the external catalyst surface includes the following consecutive steps ... 

Several models have been proposed to represent the mechanics of mass transfer across the phases. In the two-film theory, the resistance to mass transfer is assumed to take place in a liquid film and a vapor film at the phase boundary interface, as shown schematically in Figure 15.3b. The coordinates X and Y in Figure 15.3a represent the mole fractions of a given component in the liquid and vapor, respectively. For simplicity, component subscripts are dropped and the discussions refer to one... 

Plucinski, P. and Nitsch, W., Mechanism of mass transfer between aqueous phase and water in oil microemulsion, Langmuir, 10, 371, 1994... 

Examples of mass transfer under high vacuum are distillation of thermally unstable organic compounds, high-vacuum freeze drying, vacuum concentration of fruit juices, vacuum drying of coffee concentrate, vacuum purification of molten metals, etc. The mechanism of mass transfer in the concentration of fruit juices can be adequately described by the Gilliland-Sherwood equations (Gl), since the mean free path is negligible relative to the dimensions of the vessel at the pressures used. These equations show that the mass transfer coefficient is inversely proportional to the pressure. By extrapolation to very low pressures, it should be possible... 

The LSW theory dealing with Ostwald ripening [50,51] is, strictly speaking, valid for the case of immobile oil droplets when the molecular diffusion is the only mechanism of mass transfer. Under these circumstances, the contributions of molecular and convective diffusion are related by the Peclet number (Npe) ... 

Internal transport of moisture within the solid may occur by any one or more of the following mechanisms of mass transfer ... 

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