Interphase mass transfers diffusion between phases

The main problem is the representation of the competition between interphase mass transfer, diffusion within phases and chemical reaction. 

First, we must consider a gas-liquid system separated by an interface. When the thermodynamic equilibrium concentration is not reached for a transferable solute A in the gas phase, a concentration gradient is established between the two phases, and this will create a mass transfer flow of A from the gas phase to the liquid phase. This is described by the two-film model proposed by W. G. Whitman, where interphase mass transfer is ensured by diffusion of the solute through two stagnant layers of thickness <5G and <5L on both sides of the interface (Fig. 45.1) [1—4]. 

The interfacial diffusion model of Scott, Tung, and Drickamer is somewhat open to criticism in that it does not take into account the finite thickness of the interface. This objection led Auer and Murbach (A4) to consider a three-region model for the diffusion between two immiscible phases, the third region being an interface of finite thickness. These authors have solved the diffusion equations for their model for several special cases their solutions should be of interest in future analysis of interphase mass transfer experiments. 

If the adsorption equilibrium is not attained instantaneously, a different analysis is needed. Toei et al. (T18) studied the mechanism of heat and mass transfer between bubbles and emulsion phase under such circumstances. The dependence of diffusion rate on bulk flow across the bubble interface also becomes important when coarse particles are fluidized (H16). For two-dimensional bubbles Chavarie and Grace (C7a) compared various interphase mass-transfer models. 

The thickness of the fictitious film can neither be predicted nor measured experimentally. This limits the use of the film theory to directly calculate the mass transfer coefficients from the diffusivity. Nevertheless, the film theory is often applied in a two-resistance model to describe the interphase mass transfer between the two contacting phases (gas and liquid). This model assumes that the resistance to mass transfer only exists in gas and liquid films. The interfacial concentrations in gas and liquid are in equilibrium. The interphase mass transfer involves the transfer of mass from the bulk of one phase to the interfacial surface, the transfer across the interfacial surface into the second phase, and the transfer of mass from the interface to the bulk of the second phase. This process is described graphically in Fig. 1. 

Supercritical fluid can be defined as any substance that is above its critical temperature (Tc) and critical pressure (Pc) and exists as a single phase (Fig. 1). The physicochemical properties of a supercritical fluid are in between those of liquids and gases, and they can vary between those exhibited by gases to liquid-like values by small changes in pressure and temperature of supercritical fluid [2], For example, supercritical fluid exhibits larger diffusibility and lower viscosity compared to those of conventional liquids. Consequently, interphase mass transfer resistance is also lower relative to the liquid solvent. On the other hand, substrates and products that are sparingly soluble in the liquid phase can become significantly more soluble in supercritical fluids. Such unique and useful properties of the fluids make them viable solvent media for electrosynthesis. 

Regarding mass transfer, the slowest step is normally pore diffusion rather than external mass transfer, whilst for heat transfer the slowest step is the interphase heat transfer between the particle and the fluid phase rather than the internal heat transfer in the solid particle. 

Mass transport processes - diffusion, migration, and - convection are the three possible mass transport processes accompanying an - electrode reaction. Diffusion should always be considered because, as the reagent is consumed or the product is formed at the electrode, concentration gradients between the vicinity of the electrode and the bulk solution arise, which will induce diffusion processes. Reactant species move in the direction of the electrode surface and product molecules leave the interfacial region (- interface, -> interphase) [i-v]. The - Nernst-Planck equation provides a general description of the mass transport processes. Mass transport is frequently called mass transfer however, it is better to reserve that term for the case that mass is transferred from one phase to another phase. 

The purpose of the equipment used for mass-transfer operations is to provide intimate contact of the immiscible phases in order to permit interphase diffusion of the constituents. The rate of mass transfer is directly dependent upon the interfacial area exposed between the phases, and the nature and degree of dispersion of one phase into the other are therefore of prime importance. 

Dynamic analysis of a trickle bed reactor is carried out with a soluble tracer. The impulse response of the tracer is given at the inlet of the column to the gas phase and the tracer concentration distributions are obtained at the effluent both from the gas phase and the liquid phase simultaneously. The overall rate process consists the rates of mass transfer between the phases, the rate of diffusion through the catalyst pores and the rate of adsorption on the solid surface. The theoretical expressions of the zero reduced and first absolute moments which are obtained for plug flow model are compared with the expressions obtained for two different liquid phase hydrodynamic models such as cross flow model and axially dispersed plug flow model. The effect of liquid phase hydrodynamic model parameters on the estimation of intraparticle and interphase transport rates by moment analysis technique are discussed. 

A trickle bed reactor (TBR) consists of a fixed bed of catalyst particles, where liquid and gas phases flow cocurrently downward through the bed. Although its wide application in chemical and petrochemical industry it is one of the most complicated type of reactor in its design and scale-up. Essencially, the overall rate can be controlled by one or a combination of the following processes mass transfer between interphases, intraparticle diffusion, adsorption and surface reaction. The hydrodynamics, solid-liquid contacting efficiency and axial mixing can also affect the performance of TBR. 

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