Mass transfer fluid-particle system

Nelson, P.A. and Galloway, T.R. (1975), Particle to fluid heat and mass transfer in dense systems of fine particles, Chem. Eng. Sci., 30, 1-6. 

Microscale fluid turbulence is, by deflnition, present only when the continuous fluid phase is present. The coefficients Bpv describe the interaction of the particle phase with the continuous phase. In contrast, Bpvf models rapid fluctuations in the fluid velocity seen by the particle that are not included in the mesoscale drag term Ap. In the mesoscale particle momentum balance, the term that generates Bpv will depend on the fluid-phase mass density and, hence, will be null when the fluid material density (pf) is null. In any case, Bpv models momentum transfer to/from the particle phase in fluid-particle systems for which the total momentum is conserved (see discussion leading to Eq. (5.17)). 

Each stage of particle formation is controlled variously by the type of reactor, i.e. gas-liquid contacting apparatus. Gas-liquid mass transfer phenomena determine the level of solute supersaturation and its spatial distribution in the liquid phase the counterpart role in liquid-liquid reaction systems may be played by micromixing phenomena. The agglomeration and subsequent ageing processes are likely to be affected by the flow dynamics such as motion of the suspension of solids and the fluid shear stress distribution. Thus, the choice of reactor is of substantial importance for the tailoring of product quality as well as for production efficiency. 

Several reported chemical systems of gas-liquid precipitation are first reviewed from the viewpoints of both experimental study and industrial application. The characteristic feature of gas-liquid mass transfer in terms of its effects on the crystallization process is then discussed theoretically together with a summary of experimental results. The secondary processes of particle agglomeration and disruption are then modelled and discussed in respect of the effect of reactor fluid dynamics. Finally, different types of gas-liquid contacting reactor and their respective design considerations are overviewed for application to controlled precipitate particle formation. 

Steps 1 and 7 are highly dependent on the fluid flow characteristics of the system. The mass velocity of the fluid stream, the particle size, and the diffusional characteristics of the various molecular species are the pertinent parameters on which the rates of these steps depend. These steps limit the observed rate only when the catalytic reaction is very rapid and the mass transfer is slow. Anything that tends to increase mass transfer coefficients will enhance the rates of these processes. Since the rates of these steps are only slightly influenced by temperature, the influence of these processes... 

In Volume 1, the behaviour of fluids, both liquids and gases is considered, with particular reference to their flow properties and their heat and mass transfer characteristics. Once the composition, temperature and pressure of a fluid have been specified, then its relevant physical properties, such as density, viscosity, thermal conductivity and molecular diffu-sivity, are defined. In the early chapters of this volume consideration is given to the properties and behaviour of systems containing solid particles. Such systems are generally more complicated, not only because of the complex geometrical arrangements which are possible, but also because of the basic problem of defining completely the physical state of the material. 

SZEKELY, J. Third Congress of the European Federation of Chemical Engineering (1962). The Interaction between Fluids and Particles 197. Mass transfer between the dense phase and lean phase in a gas-solid fluidised system. 

A fluidized bed is made up of a mass of particles buoyed up out of permanent contact with each other by a flowing fluid. Turbulent activity in such a bed promotes high rates of heat and mass transfer and uniformity of temperature and composition throughout. The basic system includes a solids feeding device, the fluidizing chamber with a perforated distributing plate for the gas, an overflow duct for removal of the dry product, a cyclone and other equipment for... 

It should be understood that this rate expression may in fact represent a set of diffusion and mass transfer equations with their associated boundary conditions, rather than a simple explicit expression. In addition one may write a differential heat balance for a column element, which has the same general form as Eq. (17), and a heat balance for heat transfer between particle and fluid. In a nonisothermal system the heat and mass balance equations are therefore coupled through the temperature dependence of the rate of adsorption and the adsorption equilibrium, as expressed in Eq. (18). 

For a system with n components (including nonad-sorbable inert species) there are n — 1 differential mass balance equations of type (17) and n — 1 rate equations [Eq. (18)]. The solution to this set of equations is a set of n — 1 concentration fronts or mass transfer zones separated by plateau regions and with each mass transfer zone propagating through the column at its characteristic velocity as determined by the equilibrium relationship. In addition, if the system is nonisothermal, there will be the differential column heat balance and the particle heat balance equations, which are coupled to the adsorption rate equation through the temperature dependence of the rate and equilibrium constants. The solution for a nonisothermal system will therefore contain an additional mass transfer zone traveling with the characteristic velocity of the temperature front, which is determined by the heat capacities of adsorbent and fluid and the heat of adsorption. A nonisothermal or adiabatic system with n components will therefore have n transitions or mass transfer zones and as such can be considered formally similar to an (n + 1)-component isothermal system. 

Another classification involves the number of phases in the reaction system. This classification influences the number and importance of mass and energy transfer processes in the design. Consider a stirred mixture of two liquid reactants A and B, and a catalyst consisting of small particles of a solid added to increase the reaction rate. A mass transfer resistance occurs between the bulk liquid and the surface of the catalyst particles. This is because the small particles tend to move with the liquid. Consequently, there is a layer of stagnant fluid that surrounds each particle. This results in reactants A and B transferring through this layer by diffusion in order to reach the catalyst surface. The diffusion resistance gives a difference in concentration between... 

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