Taylor mass transfer

R. Krishna and R. Taylor iu N. P. Chemetisiuoff, ed.. Handbook for Heat and Mass Transfer Operations, Vol. 2, Gulf Publishing Corporation, Houston, Tex., 1986. 

R. Krishna and R. Taylor, Multicomponent Mass Transfer,John Wiley Sons, Inc., New York, 1991. 

Taylor and Krishna, Multicomponent Mass Transfer, Wiley, 1993. Toumie, Laguerie, and Couderc, Chem. Engr. Sd., 34, 1247 (1979). Treybal, Mass Transfer Operations, 3d ed., McGraw-Hill, 1980. 

Equihbrium concentrations which tend to develop at solid-liquid, gas-liquid, or hquid-liquid interfaces are displaced or changed by molecular and turbulent diffusion between biilk fluid and fluid adjacent to the interface. Bulk motion (Taylor diffusion) aids in this mass-transfer mechanism also. 

Naturally, there are two more Peclet numbers defined for the transverse direction dispersions. In these ranges of Reynolds number, the Peclet number for transverse mass transfer is 11, but the Peclet number for transverse heat transfer is not well agreed upon (121, 122). None of these dispersions numbers is known in the metal screen bed. A special problem is created in the monolith where transverse dispersion of mass must be zero, and the parallel dispersion of mass can be estimated by the Taylor axial dispersion theory (123). The dispersion of heat would depend principally on the properties of the monolith substrate. Often, these Peclet numbers for individual pellets are replaced by the Bodenstein numbers for the entire bed... 

Multicomponent mass transfer is discussed in more detail by Taylor and KRISHNA031, Cusslhr04 and Zielinski and Hanley 151... 

Taylor, R., and Krishna, R. Multicomponent Mass Transfer (Wiley, New York, 1993). 

Taylor-Prandtl modification of Reynolds analogy for heat transfer and mass transfer... 

Obtain the Taylor-Prandtl modification of the Reynolds Analogy for momentum and heat transfer, and give the corresponding relation for mass transfer (no bulk flow). 

Obtain the Taylor-Prandtl modification of the Reynolds analogy between momentum and heat transfer and write down the corresponding analogy for mass transfer. For a particular system, a mass transfer coefficient of 8,71 x 10 8 m/s and a heat transfer coefficient of 2730 W/m2 K were measured for similar flow conditions. Calculate the ratio of the velocity in the fluid where the laminar sub layer terminates, to the stream velocity. 

Obtain the Taylor-Prandtl modification of the Reynolds Analogy between momentum transfer and mass transfer (equimolecular counterdiffusion) for the turbulent flow of a fluid over a surface. Write down the corresponding analogy for heat transfer. State clearly the assumptions which are made. For turbulent flow over a surface, the film heat transfer coefficient for the fluid is found to be 4 kW/m2 K. What would the corresponding value of the mass transfer coefficient be. given the following physical properties ... 

In the design of optimal catalytic gas-Hquid reactors, hydrodynamics deserves special attention. Different flow regimes have been observed in co- and countercurrent operation. Segmented flow (often referred to as Taylor flow) with the gas bubbles having a diameter close to the tube diameter appeared to be the most advantageous as far as mass transfer and residence time distribution (RTD) is concerned. Many reviews on three-phase monolithic processes have been pubhshed [37-40]. 

As mentioned earlier, in curved channels a secondary flow pattern of two counter-rotating vortices is formed. Similarly to the situation depicted in Figrue 2.43, these vortices redistribute fluid volumes in a plane perpendicular to the main flow direction. Such a transversal mass transfer reduces the dispersion, a fact reflected in the dependence in Eq. (108) at large Dean numbers. For small Dean numbers, the secondary flow is negligible, and the dispersion in curved ducts equals the Taylor-Aris dispersion of straight ducts. 

Reactors which generate vortex flows (VFs) are common in both planktonic cellular and biofilm reactor applications due to the mixing provided by the VF. The generation of Taylor vortices in Couette cells has been studied by MRM to characterize the dynamics of hydrodynamic instabilities [56], The presence of the coherent flow structures renders the mass transfer coefficient approaches of limited utility, as in the biofilm capillary reactor, due to the inability to incorporate microscale details of the advection field into the mass transfer coefficient model. 

There is no restriction against applying polythermal models in open systems. In this case, the modeler defines mass transfer as well as the heating or cooling rate in terms of . Realistic models of this type can be hard to construct (e.g., Bowers and Taylor, 1985), however, because the heating or cooling rates need to be balanced somehow with the rates of mass transfer. 

Since interaction phenomena due to simultaneous diffusion of several components play an important role, the Maxwell-Stefan theory has been selected to describe the mass transfer processes. The general form of the flux expressions can be represented by (Taylor and Krishna, 1993)... 

Turbulent mass transfer near a wall can be represented by various physical models. In one such model the turbulent flow is assumed to be composed of a succession of short, steady, laminar motions along a plate. The length scale of the laminar path is denoted by x0 and the velocity of the liquid element just arrived at the wall by u0. Along each path of length x0, the motion is approximated by the quasi-steady laminar flow of a semiinfinite fluid along a plate. This implies that the hydrodynamic and diffusion boundary layers which develop in each of the paths are assumed to be smaller than the thickness of the fluid elements brought to the wall by turbulent fluctuations. Since the diffusion coefficient is small in liquids, the depth of penetration by diffusion in the liquid element is also small. Therefore one can use the first terms in the Taylor expansion of the Blasius expressions for the velocity components. The rate of mass transfer in the laminar microstructure can be obtained by solving the equation... 

Atkinson and Taylor (A7), 1963 Study of the effect of discontinuities on mass transfer to a liquid film. It is concluded that the mixing effect at discontinuities is a result of ripple action. 

As the concentration of EtOH increased from 0 to 10%, the effective steady-state mass transfer coefficient declined from 0.17 1/hr to 0.11 1/hr, which was due in part to the change in Darcy velocity. Using correlations developed for Ke,ss as a function of Darcy velocity and alcohol concentration (Taylor, 1999), the effect of EtOH concentration can be evaluated at a single, representative Darcy velocity. For example, using a Darcy velocity of 4.0 cm/hr, the value of Ke,ss would be 0.14, 0.13, and 0.13 for 4% Tween 80, 4% Tween 80 + 5% EtOH and 4% Tween 80 + 10% EtOH, respectively. Thus, the addition of EtOH to 4% Tween 80 had no discemable influence on the effective steady-state mass transfer coefficient. It should be recognized, however, that although the mass transfer coefficient remained essentially unchanged, the steady-state concentration of PCE in the column effluent (C") and the cumulative PCE mass recovery increased substantially as a result of EtOH addition (Table 2). This behavior can be explained by the fact that the equilibrium solubility of PCE (C" sat) increased by more than 50%, from 26,900 mg/L to 42,300 mg/L, with the addition of 10% EtOH. 

Figure 16 Relative increase of friction and mass transfer due to gas-liquid Taylor flow, compared to developed laminar flow in small tubes. represents the dimensionless length of a liquid slug. Re the Reynolds number based on the liquid.

In fast reactions, mass transfer or intraparticle diffusion becomes controlling. Thinner catalyst coatings, Taylor flow, etc. can be applied to optimize these... 

Irandoust S, Andersson B. Simulation of flow and mass transfer in Taylor flow through a capillary. Computers Chem Eng 1989 13 519-526. 

Higler AP, Krishna R, Ellenberger J, Taylor R. Countercurrent operation of a structured catalytically packed-bed reactor liquid-phase mixing and mass transfer. Chem Eng Sci 1999 54 5145-5152. 

It is interesting that, in the experiments by Taylor et al. [90] after the repetition of the same standard experimental run (increase and then decrease of temperature), the hysteresis peculiarities of kinetic curves were preserved but not reproduced quantitatively. Apparently, this is also associated with the fact that the time to achieve a steady state was insufficient. It could also be due to the slow mass transfer processes between surface and bulk. 

These two conditions (Eqs. (4.97) and (4.98)) are usually sufficient for assuming the medium as quiescent in dilute systems in which both cua.s and cda,oo are small. However, in nondilute or concentrated systems the mass transfer process can give rise to a convection normal to the surface, which is known as the Stefan flow [Taylor and Krishna, 1993]. Consider a chemical species A which is transferred from the solid surface to the bulk with a mass concentration cua.oo- When the surface concentration coa,s is high, and the carrier gas B does not penetrate the surface, then there must be a diffusion-induced Stefan convective outflux, which counterbalances the Fickian influx of species B. In such situations the additional condition for neglecting convection in mass transport systems is [Rosner, 1986]... 

---