Mass transfer single particles

Fig. 40. Comparison of transfer factors for different particle-fluid systems. Heavy solid lines L/S heat light solid lines L/S mass heavy dashed lines G/S heat light dashed lines G/S mass. S, single particles F, fluidized bed X, fixed bed. [After Kwauk and Tai, 1964.]...

The mass transfer between particles and stagnant fluid is a well established problem when a single particle and the infinite surrounding fluid are involved. Asa matter of fact, when mass transfer takes place from a single spherical particle to an infinite body of fluid, the basic differential equation to describe diffusion around the particle is ... 

Other reactors and uses of tracers. Tracers are used extensively in all other two-phase (gas-liquid, gas-solid, liquid-solid) and three-phase reactor types (gas-liquid-solid, liquid-liquid-solid). Tracers confined to a single phase are used to determine the RTD of that phase and evaluate its flow pattern. Tracers that can be transported from one phase to another are frequently used for evaluation of various rate parameters and transport coefficients such as mass transfer coefficients, particle effective diffusivity, adsorption rate constants, kinetic rate constants, etc. The interpretation of tracer studies in evaluation of the above parameters is always dependent on the selected model for the system. We do not attempt to review this vast literature but will just cite a few examples as good starting points for the interested reader. 

If a linear mbber is used as a feedstock for the mass process (85), the mbber becomes insoluble in the mixture of monomers and SAN polymer which is formed in the reactors, and discrete mbber particles are formed. This is referred to as phase inversion since the continuous phase shifts from mbber to SAN. Grafting of some of the SAN onto the mbber particles occurs as in the emulsion process. Typically, the mass-produced mbber particles are larger (0.5 to 5 llm) than those of emulsion-based ABS (0.1 to 1 llm) and contain much larger internal occlusions of SAN polymer. The reaction recipe can include polymerization initiators, chain-transfer agents, and other additives. Diluents are sometimes used to reduce the viscosity of the monomer and polymer mixture to faciUtate processing at high conversion. The product from the reactor system is devolatilized to remove the unreacted monomers and is then pelletized. Equipment used for devolatilization includes single- and twin-screw extmders, and flash and thin film evaporators. Unreacted monomers are recovered for recycle to the reactors to improve the process yield. 

Convection occurs in a moving fluid, generally from the fluid to a solid surface or vice versa. Although heat transfer between single particles is by conduction, it is the energy transfer with the matter that governs the heat transfer. The basic laws of heat and mass transfer have to be considered in order to describe convection mathematically. 

Parameters a and b are related to the diffusion coefficient of solutes in the mobile phase, bed porosity, and mass transfer coefficients. They can be determined from the knowledge of two chromatograms obtained at different velocities. If H is unknown, b can be estimated as 3 to 5 times of the mean particle size, where a is highly dependent on the packing and solutes. Then, the parameters can be derived from a single analytical chromatogram. 

A considerable amount of information has been reported regarding mass transfer between a single fluid phase and solid particles (such as those of spherical and cylindrical shape) forming a fixed bed. A recent review has been presented by Norman (N2). The applicability of such data to calculations regarding trickle-flow processes is, however, questionable, due to the fundamental difference between the liquid flow pattern of a fixed bed with trickle flow and that of a fixed bed in which the entire void volume is occupied by one fluid. 

Most theoretical studies of heat or mass transfer in dispersions have been limited to studies of a single spherical bubble moving steadily under the influence of gravity in a clean system. It is clear, however, that swarms of suspended bubbles, usually entrained by turbulent eddies, have local relative velocities with respect to the continuous phase different from that derived for the case of a steady rise of a single bubble. This is mainly due to the fact that in an ensemble of bubbles the distributions of velocities, temperatures, and concentrations in the vicinity of one bubble are influenced by its neighbors. It is therefore logical to assume that in the case of dispersions the relative velocities and transfer rates depend on quantities characterizing an ensemble of bubbles. For the case of uniformly distributed bubbles, the dispersed-phase volume fraction O, particle-size distribution, and residence-time distribution are such quantities. 

Interest extends from transfer to single particles to systems in which the particles are in the form of fixed or fluidised beds. The only case for which there is a rigorous analytical solution is that for heat by conduction and mass transfer by diffusion to a sphere. 

Figure 8. Image and diffraction pattern from an (100) epitaxial. specimen of gold prepared in an unbaked UHV evaporator by depo.sition onto KOI and then transfer onto amorphous carbon. Here water vapour was the dominant residual gas (determined by mass spectrometry). The particles are square pyramidal single crystals.

Thus, just as for incompressible single-phase flow, the pressure p constrains the velocity fields to ensure (in the case of multiphase flows) that the sum of the phase volume fractions equals unity. In the presence of mass transfer, the right-hand side of Eq. (148) is nonzero nevertheless, the role of the pressure is still the same. Finally, we should note that in gas-solid flows the maximum volume fraction of the solid phase is less than unity due to physical constraints (i.e., when particles are close packed there is still room for the gas phase so that 0solid-pressure term ps that becomes extremely large when ag approaches its minimum value (e.g., oc — 0.4). 

Dispersion in packed tubes with wall effects was part of the CFD study by Magnico (2003), for N — 5.96 and N — 7.8, so the author was able to focus on mass transfer mechanisms near the tube wall. After establishing a steady-state flow, a Lagrangian approach was used in which particles were followed along the trajectories, with molecular diffusion suppressed, to single out the connection between flow and radial mass transport. The results showed the ratio of longitudinal to transverse dispersion coefficients to be smaller than in the literature, which may have been connected to the wall effects. The flow structure near the wall was probed by the tracer technique, and it was observed that there was a boundary layer near the wall of width about Jp/4 (at Ret — 7) in which there was no radial velocity component, so that mass transfer across the layer... 

As shown in Example 22-3, for solid particles of the same size in BMF, the form of the reactor model resulting from equation 22.2-13 depends on the kinetics model used for a single particle. For the SCM, this, in turn, depends on particle shape and the relative magnitudes of gas-film mass transfer resistance, ash-layer diffusion resistance and surface reaction rate. In some cases, as illustrated for cylindrical particles in Example 22-3(a) and (b), the reactor model can be expressed in explicit analytical form additional results are given for spherical particles by Levenspiel(1972, pp. 384-5). In other f l cases, it is convenient or even necessary, as in Example 22-3(c), to use a numerical pro-... 

For heat and mass transfer through a stationary or streamline fluid to a single spherical particle, it has been shown in Volume 1, Chapter 9, that the heat and mass transfer coefficients reach limiting low values given by ... 

There are four main processes (i.e., bulk transport chemical reaction film and particle diffusion) which can affect the rate of solid phase chemical reactions and can broadly be classified as transport and chemical reaction processes [10, 31,103 -107]. The slowest of these will limit the rate of a particular reaction. Bulk transport process of a certain pollutant(s), which occurs in the aqueous phase, is very rapid and is normally not rate-limiting. In the laboratory, it can be eliminated by rapid mixing. The actual chemical reaction at the surface of a solid phase (e.g., adsorption) is also rapid and usually not rate limiting. The two remaining transport or mass transfer processes (i.e.,film and particle diffusion processes), either singly or in combination, are normally rate-limiting. Film diffusion invol-... 

The literature offers numerous calculation models for mass transfer in single liquid particles. However, they provide only a rough approximation to reality in industrial columns, since the processes in droplet swarms are much more complicated, especially when pulsing and rotating motion are superimposed. For estimation, the following relationships are sufficient ... 

The development of the electrodynamic balance and other particle traps has made it possible to perform precise measurements of the properties of small particles by focusing on the single particle. The variety of processes and phenomena that can be investigated with particle traps is quite extensive and includes gas/liquid and gas/solid chemical reactions, chemical spectroscopies, heat and mass transfer processes, interfacial phenomena, thermodynamic properties, phoretic forces, and other topics of interest to chemical engineers. 

Table 2.2 gives examples of mass transfer coefficients determined from both the single particle and fixed bed models for the evaporation of water from particles of the same diameter and density as in Table 2.1, assuming the diffusivity of water in air to be 3 x 10 m s h Once... 

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