Mass transfer molecular movement

Equation 10.4, which describes the mass transfer rate arising solely from the random movement of molecules, is applicable to a stationary medium or a fluid in streamline flow. If circulating currents or eddies are present, then the molecular mechanism will be reinforced and the total mass transfer rate may be written as ... 

The basic biofilm model149,150 idealizes a biofilm as a homogeneous matrix of bacteria and the extracellular polymers that bind the bacteria together and to the surface. A Monod equation describes substrate use molecular diffusion within the biofilm is described by Fick s second law and mass transfer from the solution to the biofilm surface is modeled with a solute-diffusion layer. Six kinetic parameters (several of which can be estimated from theoretical considerations and others of which must be derived empirically) and the biofilm thickness must be known to calculate the movement of substrate into the biofilm. 

Transport Processes. The velocity of electrode reactions is controlled by the charge-transfer rate of the electrode process, or by the velocity of the approach of the reactants, to the reaction site. The movement or trausport of reactants to and from the reaction site at the electrode interface is a common feature of all electrode reactions. Transport of reactants and products occurs by diffusion, by migration under a potential field, and by convection. The complete description of transport requires a solution to the transport equations. A full account is given in texts and discussions on hydrodynamic flow. Molecular diffusion in electrolytes is relatively slow. Although the process can be accelerated by stirring, enhanced mass transfer... 

In addition to the rates of olefin reactions, mass transfer also plays an important role in determining the extent of propylene conversion and the product distribution from SAPO molecular sieves. Restrictions on molecular movement may be severe in the SAPO catalysts, due to pore diameters (4.3 A for SAPO-34) and structure (one-dimensional pores in SAPO-5 and SAPO-11). The deactivation of SAPO-5 and SAPO-11 catalysts may be more directly related to mass transfer than the coking of SAPO-34. Synthesis of large or highly-branched products, having low diffusivities, inside the pores of SAPO-5 or SAPO-11 essentially block internal acid... 

Effective rates of sorption, especially in subsurface systems, are frequently controlled by rates of solute transport rather than by intrinsic sorption reactions perse. In general, mass transport and transfer processes operative in subsurface environments may be categorized as either macroscopic or microscopic. Macroscopic transport refers to movement of solute controlled by movement of bulk solvent, either by advection or hydrodynamic (mechanical) dispersion. For distinction, microscopic mass transfer refers to movement of solute under the influence of its own molecular or mass distribution (Weber et al., 1991). 

When the conposiksn of a fluid mixture varies from one point to another, each component has a tendency to flow in the direction that witl reduce the local differences in concentration. If the bulk fluid is either stationary or in laminar flow in a direction normal to the concentration gradient, the mass transfer reducing the concentration difference occurs by a process of molecular diffusion. This mechanism is characterized by random movement of individual molecules. 

Mass transfer can be definnd simply as the movement of any identifiable species from one spatial location to another. Tha mechanism of movement can be macroscopic as in the flow of a fluid in a pipe (convection) or in the mechanical transport of solids by a conveyor belt. In addition, the transport of a panicolar species may be the result of madom molecular motion (molecular diffusion) or randum microscopic fluid motion (eddy or turbulent diffusion) in the presence of a composition gradient within a phase. This chapter is concerned primarily with mass transfer owing to molecular or microscopic processes. 

Diffusion is the mass transfer caused by molecular movement, while convection is the mass transfer caused by bulk movement of mass. Large diffusion rates often cause convection. Because mass transfer can become intricate, at least five different analysis techniques have been developed to analyze it. Since they all look at the same phenomena, their ultimate predictions of the mass-transfer rates and the concentration profiles should be similar. However, each of the five has its place they are useful in different situations and for different purposes. We start in Section 15.1 with a nonmathematical molecular picture of mass transfer (the first model) that is useful to understand the basic concepts, and a more detailed model based on the kinetic theory of gases is presented in Section 15.7.1. For robust correlation of mass-transfer rates with different materials, we need a parameter, the diffusivity that is a fundamental measure of the ability of solutes to transfer in different fluids or solids. To define and measure this parameter, we need a model for mass transfer. In Section 15.2. we discuss the second model, the Fickian model, which is the most common diffusion model. This is the diffusivity model usually discussed in chemical engineering courses. Typical values and correlations for the Fickian diffusivity are discussed in Section 15.3. Fickian diffusivity is convenient for binary mass transfer but has limitations for nonideal systems and for multicomponent mass transfer. 

Heat transfer is directly related to the concept of mass transfer. Q is used to heat products of the reaction, which, on a molecular level, means tiiat the greater Q is, the more kinetic energy is transferred to the product molecules. This Hnetic energy can be transferred to other molecules via coUision. However, for that transfer to occur to key molecules such as those found in the vaporized candle wax, the energy has to be delivered, via fast-moving molecules, to the right place. That movement of mass is called mnss transfer. 

The two phases are separated from each other under severe mixing during the extraction process. There is an interface between them. Relatively slow movement exists between liquids on either side of the interface. It can be called the retention or interface layer. In this area, mass transfers through molecular diffusion. Mass transfer occurs through the interface it is not only a longer path but also being more complex in this way. Far from the interface, due to the effect of stirring,... 

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