Bulk liquid phase, diffusion

If the bulk-liquid phase is well mixed and no diffusion occurs in the solid phase, a simple expression relating the solid-phase composition to the frac tion frozen can be obtained for the case in which the distribution coefficient is independent of composition and fraction frozen... 

The gaseous components must be transferred from the bulk gaseous phase to the bulk liquid phase. The components are transferred to the gas-liquid interface by convection and diffusion in the gas and from the interface by diffusion and convection in the liquid. 

The absorbed components must be transferred from the bulk liquid phase to the exterior surface of the catalyst by convection and diffusion. 

The products of the catalytic reaction are transferred by convection and diffusion to the bulk liquid phase. 

The charge or zeta ( ) potential of the filler particle (i.e. the charge at the plane of shear between the particle s diffuse double layer and the bulk liquid phase) can be obtained by measuring its mobility in an applied electric field of known magnitude. The mobility is a function of the field gradient and is therefore expressed as a speed per unit potential gradient (/im/s/V/cm). Mobility and therefore zeta potential are both a function of pH (Figure 6.4). 

Treatment of systems in which gas-phase diffusion, mass accommodation, liquid phase diffusion, and reaction both in the bulk and at the interface must be taken into account is discussed in Section E.l. 

FIGURE 5.16 Schematic of resistance model for diffusion, uptake, and reaction of gases with liquids. Tg represents the transport of gases to the surface of the particle, a the mass accommodation coefficient for transfer across the interface, rso, the solubilization and diffusion in the liquid phase, riM the bulk liquid-phase reaction, and rinlcrl.ll c the reaction of the gas at the interface. 

Three fundamental processes can limit overall reaction rates in heterogeneous catalysis mass transfer of the reactants from the bulk liquid phase(s) to the surface of the solid catalyst, diffusion of the reactants from the catalyst surface to the active site, and the intrinsic reaction at the active site 61,62). Each of these processes depends on one or more experimental parameters, as shown in Fig. 1. 

Hashimoto et al. (1977) studied the removal of DBS from an aqueous solution in a carbon fixed-bed adsorber at 30 °C. The dimensions of the bed were D = 20 mm and Z = 25.1 cm. Carbon particles of 0.0322-cm radius were used, with 0.82 g/cm3 particle density, and 0.39 g/cm3 bulk density. The concentration of the influent stream was 99.2 rng/L and the superficial velocity was 0.0239 cm/s. The fixed bed was operated under upflow condition. Furthermore, the isotherm of the DBS-carbon system at 30 °C was found to be of Freundlich type with Fr = 0.113 and = 178 (mg/g)(L/mg)0113. Finally, the average solid-phase diffusion coefficient was found to be 2.1 X 10 10 cm2/s. The approximate value of 10 9 m2/s could be used for DBS liquid-phase diffusion coefficient. 

Since the electrochemical reduction or oxidation of a molecule occurs at the electrode-solution interface, molecules dissolved in solution in an electrochemical cell must be transported to the electrode for this process to occur. Consequently, the transport of molecules from the bulk liquid phase of the cell to the electrode surface is a key aspect of electrochemical techniques. This movement of material in an electrochemical cell is called mass transport. Three modes of mass transport are important in electrochemical techniques hydrodynamics, migration, and diffusion. 

It seems that the cavities enclose a vapor of the solute because of the high vapor pressure of these compounds. The primary reaction pathway for these compounds appears to be the thermal dissociation in the cavities. The activation energy required to cleave the bond is provided by the high temperature and pressure in the cavitation bubbles. This leads to the generation of radicals such as hydroxyl radical, peroxide radical, and hydrogen radical. These radicals then diffuse to the bulk liquid phase, where they initiate secondary oxidation reactions. The solute molecule then breaks down as a result of free-radical attack. The oxidation of target molecules by free radicals in the bulk liquid phase under normal operating pressures and temperatures can be presented by a second-order rate equation ... 

Concentration polarization Convective transport and retention of solutes by the membrane results in an accumulation of species at wall. Local concentrations, C , are higher than in the bulk, Cb, and a back-diffusion from near the wall into the bulk liquid phase takes place. This is the so-called "concentration polarization" phenomenon (Fig. 12.1). A simple mass balance leads to the classical equation ... 

The diffusivity of a liquid adsorbate through the meso-macropores is much slower than that for a gas. For example, the diffusivity of bulk liquid phase water from ethanol into an alumina sample was... 

Transport of reactants to catalyst. To supply the catalyst with fresh reactant, several mass transfer steps are involved. The hydrogen must first transfer through the gas-liquid interface before it is in the bulk liquid phase. Then, dissolved hydrogen and oil reactant (sulfur, nitrogen, aromatics) in the bulk phase transfer through the liquid film around the catalyst to its outer surface. Finally, the reactants diffuse into the catalyst pores. 

Mass transfer from the bubble interface to the bulk-liquid phase Mixing and diffusion in the bulk liquid Mass transfer to the external surface of the catalyst particles Reaction at the catalyst surface ... 

In regime 2, the reaction is fast enongh to keep the bulk liquid phase concentration of the gaseous reactant essentially zero but not fast enough to occur substantially in the liquid film. There is no enhancement of mass transfer due to reaction. Diffusion and reaction take place in series fashion. 

The presence of two phases, namely gas and liquid, is characteristic for non-catalytic or homogeneously catalysed reaction systems. Components in the gas phase diffuse to the gas-liquid interphase, dissolve in the liquid phase and react with components in the bulk liquid phase. The liquid phase may also contain a homogeneous catalyst. Some of the product molecules desorb from the liquid phase to the gas phase and some product molecules remain in the liquid. The processes taking place in a gas-liquid reactor are displayed in Figure 9.5. 

The type of diffusion in the pore, bulk or Knudsen, depends on whether the diffusing species collide more often with each other or with the pore wall surface. Liquid-phase diffusion is described by liquid-liquid... 

The first phase, called catalyst design, studies the kinetic problem, namely the rate-limiting step and measures to enhance it. For example, in the case of a solid catalyst the design variables are the particle size, its shape, porous structure and distribution of active material. For gas-liquid systems the decisions concern the choice between gas-dispersed or liquid-dispersed systems, and provisions of an appropriate ratio between liquid-phase bulk flow and liquid-phase diffusion layer. 

If we return to the Hatta picture of reaction and diffusion, recall that reaction and diffusion occur only in the film. Reaction also occurs in the bulk liquid phase, of course, but there the concentration of reactants as a function of position is determined by the nature of mixing in that phase. Let us reformulate the problem so that the fraction of liquid phase occupied by the film, a, is defined explieitly. If L is film thickness and interfacial area, then... 

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