Mass transfer by convection

The mass transfer by convection and diffusion within the channel is precisely calculable. Numerical methods are used to fit measured concentrations at the detector electrode to the fluid flow in the cell, and to the reaction kinetics at the surface and in solution [24]. The technique was extensively developed during a study of the dissolution of calcite in dilute aqueous acid [25], and has latterly been applied to a number of organic reactions. 

The plug-flow model indicates that the fluid velocity profile is plug shaped, that is, is uniform at all radial positions, fact which normally involves turbulent flow conditions, such that the fluid constituents are well-mixed [99], Additionally, it is considered that the fixed-bed adsorption reactor is packed randomly with adsorbent particles that are fresh or have just been regenerated [103], Moreover, in this adsorption separation process, a rate process and a thermodynamic equilibrium take place, where individual parts of the system react so fast that for practical purposes local equilibrium can be assumed [99], Clearly, the adsorption process is supposed to be very fast relative to the convection and diffusion effects consequently, local equilibrium will exist close to the adsorbent beads [2,103], Further assumptions are that no chemical reactions takes place in the column and that only mass transfer by convection is important. 

Another difficulty is related to the mass transfer by convection, as, by definition, the films are stagnant and hence, there should be no mass transport mechanism, except for molecular diffusion in the direction normal to the interface (Kenig, 2000). Nevertheless, convection in films is directly accounted for in correlations. Moreover, in case of reactive systems, the film thickness should depend on the reaction rate, which is beyond the two-film theory consideration. 

Therefore, the mixture is stationary on a molar basis and thus mass transfer is by diffusion only (there is no mass transfer by convection) so (hat... 

Since the gas side resistance to mass transfer is negligible in microporous membrane BOs, only the liquid side film is considered. Mass transfer by convection within the film is negligible. Further there is no mass accumulation at any point within the film. Consequently, steady-state mass balances in the liquid film on [O2], [Hb], and [Hb(02) ] lead to Equations 23.32 through 23.34 [36,52] ... 

The effect of temperature and panicle size on melting time (until the solid phase has disappeared) has been dealt with in many laboratory studies. Figure 68 demonstrates the marked effect of temperature bringing about an increase in diffusion coefficient and that of Si02 solubility in the melt, as well as a decrease of viscosity which in turn permits better mass transfer by convection. The dependence of batchffreetimeon glass composition and temperature is shown in Fig. 69. 

There is no flow past the bubble. Hence, mass transfer by convection in the polar coordinate direction 6 is absent. 

Peclet (mass) Pe u 1 D mass transfer by convection mass transfer by diffusion... 

Stanton (mass) St, i u total mass transfer mass transfer by convection... 

Dissolution rate data obtained under forced convection conditions can be correlated by means of equation 6.64 or 6.65. As described in section 6.2.2, equation 6.64 is the preferred relationship on theoretical grounds, since Sh = 2 for mass transfer by convection in stagnant solution (Re = 0), whereas equation 6.65 incorrectly predicts a zero mass transfer rate (Sh = 0) for this condition. However, at reasonably high values of Sh (>100) the use of the simpler equation 6.65 is quite justified. The exponent of the Schmidt number b is usually taken to be and for mass transfer from spheres the exponent of the Reynolds number a =... 

For mass transfer by convection, the mass flow is given by ... 

In the packed bed reactor, there is also the influence of heat conduction from particle. As we know, the temperature affects substantially the rate constant and therefore the reaction rate. In parallel, there are the effects of mass transfer by convection and diffusion in the pores of the particles. Therefore, these effects change the kinetics considerably and hence the chemical reaction rate. 

Ratio of mass transfer by convection and that by molecular diffusion... 

Moreover, mass transfer by convection is a well documented topic in the literature in which a hydrodynamic viscous convective layer develqts due to fluid flow. This convective layer is known as Prandtl boundary layer, which depends on the fluid velocity. According to Erdey-Gruz [66] and Probstein [671 among other excellent authors, the convective layer is defined as... 

Mass species transport describes the motion of species in a mixture as well as in base fluids and solids. There are two basic modes of mass transfer mass transfer by diffusion owing to the presence of species concentration gradient and mass transfer by convection or advection owing to the bulk fluid motion. Figure 6.11 shows different modes of mass transport across the fuel cell. 

In this book a combination of the principles of separation processes, process modelling, process control and numerical methods is used to describe the dynamic behaviour of separation processes. The text is largely mathematical and analytical in nature. Adsorption processes are commonly operated in a cyclic manner involving complex sequences of individual steps which are dynamic in nature and three chapters in this book specifically address this separation process. Chapter 11 covers the fundamentals of adsorption processes and includes physical adsorption of pure gases and mixtures, mass transfer by convective transport and the roles of pore and surface diffusion in the adsorption process. Chapter 12 addresses the separation of multicomponent mixtures by the use of adsorption columns and includes the Gleuckauf, film resistance and diffusion models and adiabatic operation of a fixed bed adsorption column together with periodic operation. Chapter 14 addresses the thermodynamics of the physical adsorption of pure gases and multicomponent gas mixtures. 

Schmidt number A dimensionless number. Sc, characterizing mass transfer by convection that relates viscosity and dlfusion of a gas through itself It is the ratio of the kinematic viscosity to the molecular dilluslvity ... 

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