Mass transfer solid-liquid interface

Interphase Mass Transfer. There are a number of interphase mass transfer steps that must occur in a trickle flow reactor. The mass transfer resistances can be considered as occurring at the more or less stagnant fluid layer interfaces, i.e., on the gas and/or the liquid side of the gas/llquld Interface and on the liquid side of the liquid/solid Interface. The mass transfer correlations (8) indicate that the gas/llquld Interface and the liquid/solid interface mass transfer resistances decrease with higher liquid velocity and smaller particle size. Thus, in the PDU, the use of small inert particles partially offsets the adverse effect of low velocity. These correlations indicate that for this system, external mass transfer limitations are more likely to occur in the PDU than in the commercial reactor because of the lower liquid velocity, but that probably there is no limitation in either. If a mass transfer limitation were present, it would limit conversion in a way similar to that shown for axial dispersion and incomplete catalyst wetting illustrated in Figure 1. Due to the uncertainty in the correlations and in the physical properties of these systems, particularly the molecular diffuslvities, it is of interest to examine if external mass transfer is influencing the PDU results. 

More directly related to turbulence and motion at the interface. Includes scale-up for rate of dissolving of solids or mass transfer between liquid phases. Using geometric similarity and equal power per volume results in same n value. 

The experimental and theoretical work reported in the literature will be reviewed for each of the five major types of ga s-liquid-particle operation under the headings Mass transfer across gas-liquid interface mass transfer across liquid-solid interface holdup and axial dispersion of gas phase holdup and axial dispersion of liquid phase heat transfer reaction kinetics. 

Mass Transfer across Liquid-Solid Interface... 

Mass transfer across the liquid-solid interface in mechanically agitated liquids containing suspended solid particles has been the subject of much research, and the data obtained for these systems are probably to some extent applicable to systems containing, in addition, a dispersed gas phase. Liquid-solid mass transfer in such systems has apparently not been studied separately. Recently published studies include papers by Calderbank and Jones (C3), Barker and Treybal (B5), Harriott (H4), and Marangozis and Johnson (M3, M4). Satterfield and Sherwood (S2) have reviewed this subject with specific reference to applications in slurry-reactor analysis and design. 

No work on mass transfer across the liquid-solid interface in gas-liquid fluidized beds has come to the author s attention. 

Date for mass transfer across the liquid-solid interface are virtually nonexistent for packed-bed gas-liquid-particle operations. The smaller particle size that may be employed in suspended-bed operations should be an advantage in this respect, but the packed-bed operations have, on the other hand, the advantage of having higher possible relative velocities between liquid and solid. 

On the other hand stable cavitation (bubbles that oscillate in a regular fashion for many acoustic cycles) induce microstreaming in the surrounding liquid which can also induce stress in any microbiological species present [5]. This type of cavitation may well be important in a range of applications of ultrasound to biotechnology [6]. An important consequence of the fluid micro-convection induced by bubble collapse is a sharp increase in the mass transfer at liquid-solid interfaces. In microbiology there are two zones where this ultrasonic enhancement of mass transfer will be important. The first is at the membrane and/or cellular wall and the second is in the cytosol i. e. the liquid present inside the cell. 

For a detailed description of the separation processes that may take place at the sensing microzone, the foundation of which is closely related to non-chromatographic continuous separation techniques based on mass transfer across a gas-liquid (gas diffusion), liquid-liquid (dialysis, ultrafiltration) or liquid-solid interface (sorption), interested readers are referred to specialized monographs e.g. [3]). 

In three-phase systems, two interfaces exist, i.e. the gas bubble-liquid interface and the liquid-solid interface and thus, four mass-transfer steps and the corresponding films are involved in the process (Figure 3.3)... 

Nonreacting liquid Under the assumption of complete mixing for the liquid phase and at steady-state conditions, mass transfer from gas to the liquid phase is equal to the mass transfer at the liquid-solid interface ... 

A key feature of catalytic slurry reactors is that the particles are small ( 0.1 mm), so it is relatively easy to promote suspension by the mechanical action of the impeller. Moreover, because of their small size they travel together with the liquid, and therefore a significant mass transfer resistance develops at the liquid/solid interface that cannot be removed completely with the standard impellers. Also, because of the liquids large Prandtl number, the catalyst and the liquid are at the same temperature, so hot spots do not occur in multiphase slurry reactors. 

Mass transfer coefficient at the liquid/solid interface... 

The rate-based models usually use the two-film theory and comprise the material and energy balances of a differential element of the two-phase volume in the packing (148). The classical two-film model shown in Figure 13 is extended here to consider the catalyst phase (Figure 33). A pseudo-homogeneous approach is chosen for the catalyzed reaction (see also Section 2.1), and the corresponding overall reaction kinetics is determined by fixed-bed experiments (34). This macroscopic kinetics includes the influence of the liquid distribution and mass transfer resistances at the liquid-solid interface as well as dififusional transport phenomena inside the porous catalyst. 

The Mass Transfer Coefficient at the Liquid-Solid Interface ks... 

Normally, KSa and Ksc are assumed to be equal. Once again, conditions kG - oo, k,.oo, and KSA, Ksc - co imply that the gas-film resistance, the liquid-film resistance for the mass transfer at the gas-liquid interface, and the liquid-film resistance for the mass transfer at the liquid-solid interface are negligible. When all the mass-transfer resistances are important, the typical concentration distributions of A and C are as shown in Fig. 2-6. 

When (a) there are no external mass-transfer resistances (such as gas-liquid, liquid solid, etc.), (b) catalysts are all effectively wetted, (< ) there is no radial or axial dispersion in the liquid phase, (d) a gaseous reactant takes part in the reaction and its concentration in the liquid film is uniform and in excess, (e) reaction occurs only at the liquid-solid interface, (/) no condensation or vaporization of the reactant occurs, and (g) the heat effects are negligible, i.e., there is an isothermal operation, then a differential balance on such an ideal plug-flow trickle-bed reactor would give... 

Figure 6-17 The mass-transfer film coefficient Ks at the liquid-solid interface in a trickle-flow column...

When the reaction is controlled by mass transfer at the liquid-solid interface, a similar differential mass balance on the liquid phase would give... 

In the past, there have been two major approaches to analyze the problem of heat and mass transfer across the liquid-solid interface. The first approach can be broadly classified as "Analogies." This method essentially consists of (von Karman ( ) and Wasan and Wilke ( )) (i) development of velocity profile near the interface, (ii) suitable assumption for the variation of eddy diffusivity with respect to the distance from the interface, and... 

A heterogeneous catalytic reaction occurs at or very near the fluid-solid interface. The principles that govern heterogeneous catalytic reactions can be applied to both catalytic and noncatalytic fluid-solid reactions. These two other types of heterogeneous reactions involve gas-liquid and gas-Hquid-solid systems. Reactions between gases and liquids are usually mass-transfer limited. 

We now consider the case where the total particle is being completely consumed. We choose as an example the case where species A must diffuse to the smface to react with solid B at the liquid-solid interface. Reactions of this type are typically zero-order in B and first-order in A. The rate of mass transfer to the surface is equal to the rate of surface reaction. 

The ways in which reaction parameters affect a two phase batch reaction are similar to those considered above for the three phase systems. Since there is no gas phase, agitation only serves to keep the catalyst suspended making it more accessible to the dissolved reactants so it only has a secondary effect on mass transfer processes. Substrate concentration and catalyst quantity are the two most important reaction variables in such reactions since both have an influence on the rate of migration of the reactants through the liquid/solid interface. Also of significant importance are the factors involved in minimizing pore diffusion factors the size of the catalyst particles and their pore structure. 

The sources of band broadening of kinetic origin include molecular diffusion, eddy diffusion, mass transfer resistances, and the finite rate of the kinetics of ad-sorption/desorption. In turn, the mass transfer resistances can be sorted out into several different contributions. First, the film mass transfer resistance takes place at the interface separating the stream of mobile phase percolating through the column bed and the mobile phase stagnant inside the pores of the particles. Second, the internal mass transfer resistance controls the rate of mass transfer between this interface and the adsorbent surface. It is composed of two contributions, the pore diffusion, which is molecular diffusion taking place in the tortuous, constricted network of pores, and surface diffusion, which takes place in the electric field at the liquid-solid interface [60]. All these mass transfer resistances, except the kinetics of adsorption-desorption, depend on the molecular diffusivity. Thus, it is important to study diffusion in bulk liquids and in porous media. 

Mass transfer coefficients for the lower surface of a laminar film are strongly influenced by the shear at the liquid-solid interface. A solution for liquid-solid mass transfer coefficients for a diffusive process in a laminar film was provided by Bird et al. as the follow-... 

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