Mass transfer resistance external film

A simpler version of the GRM model assumes that the mass transfer kinetics is controlled by mere pore diffusion and by the external film mass transfer resistance. The mass balances in the two fractions of the mobile phase are then written [52,62,101] ... 

There are at least two main sources of resistance to mass transfer (Figure 5.4 [96]) external film mass transfer resistance and intrapartide diffusion that is composed of pore and surface diffusion. The latter diffusion is insignificant in numerous adsorbents but plays an important role in most adsorbents used in RPLC. For particles having micropores, there is an additional mass transfer resistance, the resistance to diffusion through micropores which is often important. This explains why considerable attention is paid in the preparation of stationary phases for FIPLC to avoid the formation of micropores. This explains also why graphi-tized carbon black, which tends to be plagued by a profusion of micropores, has not been a successful stationary phase for HPLC. 

However, a solution in the Laplace domain has been derived by Kucera [30] and Kubin [31]. The solution cannot be transformed back into the time domain, but from that solution, these authors have derived the expressions for the first five statistical moments (see Section 6.4.1). For a linear isotherm, this model has been studied extensively in the literature. The solution of an extension of this model, using a macro-micropore diffusion model with external film mass transfer resistance, has also been discussed [32]. All these studies use the Laplace domain solution and moment analysis. 

For the separation of a binary mixture of species A and B, in the absence of external film mass-transfer resistances, the transport fluxes are given by equation (9-9) as... 

Dutta et al. [32] modified the pseudo-steady-state advancing reaction front model of Stroeve and Varanasi [30] by considering the polydispersity of the emulsion globules and the external phase mass transfer resistance. They also included the outer membrane film resistance in their model [5]. Their results were in good agreement with experimental data for phenol extraction. 

Consider separation of a binary mixture in a membrane module with the crossflow pattern shown in Figure 9.3. The feed passes across the upstream membrane surface in plug flow with no longitudinal mixing. The pressure ratio and the ideal separation factor are assumed to remain constant. Film mass-transfer resistances external to the membrane are assumed to be negligible. A total mass balance around the differential-volume element gives... 

Rgi external gas film mass transfer resistance Ry". internal pore diffusion resistance R reaction resistance... 

Figure 5.8 Variation of the external film mass transfer (1) and the transparticle mass transfer resistance (2) as a function of solid-core to core-shell ratio (p).

External Fluid Film Resistance. A particle immersed ia a fluid is always surrounded by a laminar fluid film or boundary layer through which an adsorbiag or desorbiag molecule must diffuse. The thickness of this layer, and therefore the mass transfer resistance, depends on the hydrodynamic conditions. Mass transfer ia packed beds and other common contacting devices has been widely studied. The rate data are normally expressed ia terms of a simple linear rate expression of the form... 

A final, obvious but important, caution about catalyst film preparation Its thickness and surface area Ac must be low enough, so that the catalytic reaction under study is not subject to external or internal mass transfer limitations within the desired operating temperature range. Direct impingement of the reactant stream on the catalyst surface1,19 is advisable in order to diminish the external mass transfer resistance. 

There are three distinct mass-transfer resistances (1) the external resistance of the fluid film surrounding the pellet, (2) the diffusional resistance of the macropores of the pellet, and (3) the diffusional resistance of the zeolite crystals. The external mass-transfer resistance may be estimated from well-established correlations (4, 5) and is generally negligible for molecular sieve adsorbers so that, under practical operating conditions, the rate of mass transfer is controlled by either macropore diffusion or zeolitic diffusion. In the present analysis we consider only systems in which one or other of these resistances is dominant. If both resistances are of comparable importance the analysis becomes more difficult. 

An enzyme is immobilized by copolymerization technique. The diameter of the spherical particle is 2 mm and the number density of the particles in a substrate solution is 10,000/L. Initial concentration of substrate is 0.1 mole/L. A substrate catalyzed by the enzyme can be adequately represented by the first-order reaction with k0 = 0.002 mol/Ls. It has been found that both external and internal mass-transfer resistance are significant for this immobilized enzyme. The mass-transfer coefficient at the stagnant film around the particle is about 0.02 cm/s and the diffusivity of the substrate in the particle is 5 x 10-6 cm2/s. 

Agitated jacketed vessel the main resistance to heat transfer is located at the wall, where there is practically no resistance to heat transfer inside the reaction mass. Due to agitation, there is no temperature gradient in the reactor contents. Only the film near the wall presents a resistance. The same happens outside the reactor in its jacket, where the external film presents a resistance. The wall itself also presents a resistance. In summary, the resistance against heat transfer is located at the wall. 

The influence of heat effects and of external mass transfer resistances (film resistance) may be significantly reduced by the application of flow methods. In the usual chromatographic experiment, a steady flow of an inert (nonadsorbing) carrier is passed through a... 

The average dimensionless solid phase concentration Y can be given409 the numerical value of 0.5, and if the effect of the film mass transfer is negligible, i.e., if K f - 00, then adsorption with the nonporous HPLC sorbent in a well-packed bed is controlled by second-order kinetics.169,399 When the external film resistance Kf controls the adsorption, equilibrium is assumed to exist between the polypeptide or protein and the polypeptide- or protein-ligate complex at each point on the particle surface. 

The elimination or estimation of the axial dispersion contribution presents a more difficult problem. Established correlations for the axial dispersion coefficient are notoriously unreliable for small particles at low Reynolds number(17,18) and it has recently been shown that dispersion in a column packed with porous particles may be much greater than for inert non-porous particles under similar hydrodynamic conditions(19>20). one method which has proved useful is to make measurements over a range of velocities and plot (cj2/2y ) (L/v) vs l/v2. It follows from eqn. 6 that in the low Reynolds number region where Dj. is essentially constant, such a plot should be linear with slope Dj, and intercept equal to the mass transfer resistance term. Representative data for several systems are shown plotted in this way in figure 2(21). CF4 and iC io molecules are too large to penetrate the 4A zeolite and the intercepts correspond only to the external film and macropore diffusion resistance which varies little with temperature. 

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... 

According to the assumptions in Section 6.2.1, the liquid phase concentration changes only in axial direction and is constant in a cross section. Therefore, mass transfer between liquid and solid phase is not defined by a local concentration gradient around the particles. Instead, a general mass transfer resistance is postulated. A common method describes the (external) mass transfer mmt i as a linear function of the concentration difference between the concentration in the bulk phase and on the adsorbent surface, which are separated by a film of stagnant liquid (boundary layer). This so-called linear driving force model (LDF model) has proven to be sufficient in... 

The transport dispersive model (TDM) is an extension of the transport model and summarizes the internal and external mass transfer resistance in one lumped film (= effective) transfer coefficient, keii (compare Eq. 6.30) ... 

If mass transfer in the film and diffusion inside the pores are taken into account the effective mass transfer coefficient is given as a series connection of the internal (1/kpore) and external (l/kf,im) mass transfer resistance (Eq. 6.138) ... 

A very important practical application of the above film model is to determine the external mass transfer resistance to catalyst particles (Example 8.2.2). 

Two simple extensions of SCM can be used to describe CIS behavior. The external shell is treated as a separate phase surrounding the pellet (Figure CS6.4) that offers one more step of pure mass transfer resistance with no reaction in addition to the fluid film. Akiti. (2001) used such a model to obtain an approximate fit of the data. 

Three main types of mass transfer resistances are recognized film diffusion (which occnrs at the external surface of the adsorbent), intraparticle diffusion (which occnrs within the pores or amorphous structure of the adsorbent), and adsorption/desorption kinetics (which occnrs at the internal surface of the adsorbent). 

Such characteristic horizontal bands, as shown in Figure 5.43, might be termed adsorption multiplicity since they arise primarily from the interactions of external film heat and mass transfer resistances with the adsorption resistance. For smaller adsorption resistance, the horizontal bands disappear giving way to the more familiar multiplicity regions, arising from the interactions of physical transport and surface reaction resistances. 

When mass-transfer resistances external to the membrane are not negligible, concentration gradients exist in the films adjacent to the membrane surfaces, as illustrated in Figure 9.1. In that case, the total mass-transfer resistance is the sum of three individual resistances, and the transmembrane flux of solute i is given by... 

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