Confined fluids, mass transfers

Chapter 11 treats reactors where mass and component balances are needed for at least two phases and where there is interphase mass transfer. Most examples have two fluid phases, typically gas-liquid. Reaction is usually confined to one phase, although the general formulation allows reaction in any phase. A third phase, when present, is usually solid and usually catalytic. The solid phase may be either mobile or stationary. Some example systems are shown in Table 11.1. 

In the film theory the complete resistance to mass transfer from the interface to the bulk of the liquid is confined to a fictitious film along the interface. The bulk of the fluid is considered to be perfectly mixed in the direction perpendicular to the interface, i.e. the concentration of A is uniform beyond the film. Figure 7.13 shows the concentration profile of A according to the film theory. 

A theory which incorporates some of the principles of both the two-film theory and the penetration theory has been proposed by TOOR and Marchello The whole of the resistance to transfer is regarded as lying within a laminar film at the interface, as in the two-film theory, but the mass transfer is regarded as an unsteady state process. It is assumed that fresh surface is formed at intervals from fluid which is brought from the bulk of the fluid to the interface by the action of the eddy currents. Mass transfer then takes place as in the penetration theory, except that the resistance is confined to the finite film, and material which traverses the film is immediately completely mixed with the bulk of the fluid. For short times of exposure, when none of the diffusing material has reached the far side of the layer, the process is identical to that postulated in the penetration theory. For prolonged periods of exposure when a steady concentration gradient has developed, conditions are similar to those considered in the two-film theory. 

The external mass transfer process can be described by the so-called film model as shown in Figure 2.19. According to the film model, a stagnant fluid layer of thickness 5 surrounds the external surface, where the total resistance to mass transfer is located. Accordingly, the concentration profile is confined to this layer. The molar flux of reactant A is proportional to the difference in concentration (the driving... 

This chapter provides an overview of the mass transfer characteristics of multiphase microreactors. Basic concepts are explained and related to mass transfer in sequented (drop/bubble) flow, annular flow, and to multiphase flow through packed microchannels. In multiphase microreactors, a chemical reaction can either involve two immiscible fluid phases (e.g. for gas-liquid reactions) or two fluid phases in the presence of a solid catalyst or the reaction is exclusively confined to one of the fluid phases that are present in the system. 

We now move from the differential balance equation for a given species [Equations (11.1) and (11.2)] to an integral equation. One of the phases of a multiphase fluid system is considered. If the phase is confined to a volume V with an rnterfadal area A that is available for exchange with a second phase, a balance of reaction and mass transfer gives... 

Carslaw HS, Jaeger JC (1946) Conduction of heat in solids. Clarendon, Oxford Cerclier CV, Ndao M, Busselez R, Lefort R, Grelet E, Huber P, Kityk AV, Noirez L, Schonhals A, Morineau D (2012) Stmcture and phase behavior of a discotic columnar liquid crystal confined in nanochannels. J Phys Chem C 116(35) 18990-18998 Cussler EL (2009) Diffusion mass transfer in fluid systems, 3rd edn. Cambridge University Press, Cambridge... 

The hydrodynamic diameters of microchannels usually range from 10 to 1000 rm. In such confined flowing spaces, the multiphase flow patterns of Newtonian fluids are more variable compared with the common bubbly or droplet flows in larger vessels and columns. The confined flowing channel first affects the shape of droplets therefore, the flow patterns of liquid/hquid dispersed systems are usually categorized as plug flow and droplet flow, as shown in Fig. 1A and B. Usually, the droplet flow has larger specific surface area, which is fit for the mass transfer enhancement process (Mary et al,... 

Items 2 and 3 of Table 1.2 concern what we term convective mass and heat transfer. Let us illustrate these terms by making use of Figure 1.4a. This figure depicts turbulent flow of either a gas or liquid past a liquid or solid boxmdary shown crosshatched on the left. That boundary can be the confining wall of a duct, or the interface separating two phases. Mass transfer is assumed to occur from a concentration Q2 of the boimdary to a lower concentration in the bulk of the flowing fluid. This can come about if the boxmdary consists of a soluble substance or if a volatile liquid evaporates into a floxving gas stream. 

In the case of tubular mass transfer coefficients, we distinguish between mass transfer in the so-called entry or Leveque region, in which concentration changes are confined to a thin bmmdary layer 8(x) adjacent to the wall, and the so-called fully developed region, in which the concentration changes have penetrated into the fluid core. The situation is depicted in Figure 5.1, and represents a tubular wall coated with a soluble material of solubility dissolving into pure solvent. 

The resistance to transfer of mass between a gas and a hquid is assumed confined to that of fluid films between the phases. Let... 

There have been many studies of the effect of boundary films on mass and heat transfer to single pellets and in packed beds, including the work of Ranz and Marshall 27 and Dwivedi and Upadhey(28). Other theories of mass and heat transfer are discussed in Volume 1, Chapter 10, although only the steady-state film-theory is considered here. It is assumed that the difference in concentration and temperature between the bulk fluid and the external surface of a pellet is confined to a narrow laminar boundary-layer in which the possibility of accumulation of adsorbate or of heat is neglected. 

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