Mass transfer through stationary

Mass transfer through a stationary second component... 

For heat and mass transfer through a stationary or streamline fluid to a single spherical particle, it has been shown in Volume 1, Chapter 9, that the heat and mass transfer coefficients reach limiting low values given by ... 

The pore structure and size is critical for efficient chromatography and this is borne out by the fact that many supports of identical particle size, and nominally of similar pore size, often display different characteristics. As discussed in Chapter 2, van Deemter s theory suggests that the most critical attribute of a stationary phase is the ease of mass transfer through the pores of the particle. 

FIGURE 16 Schematic representation of the origins of zone-broadening behavior and mass transfer effects of a polypeptide or protein due to Brownian motion, eddy diffusion, mobile phase mass transfer, stagnant fluid mass transfer, and stationary-phase interaction transfer as the polypeptide or protein migrated through a column packed with porous particles of an interactive HPLC sorbent. 

Equation (41) is subjected to the following boundary conditions given by Eqs. (43) and (44), where is the radius of the secondary particle, fej is the mass-transfer coefficient in the external film surrounding the secondary particle, and Mj, is the monomer concentration in the bulk phase. Equations (43) and (44) are the classic boundary conditions for heterogeneously catalyzed chemical reactions, namely symmetry at the center of the particle and stationary convective mass transfer through the mass-transfer boundary layer surrounding the particle, respectively. Finally, the initial condition is given by Eq. (45). 

When a damp cloth is laid in an air flow, it settles after a certain time ic an equilibrium temperature, the so-called wet bulb temperature (0 ), which is determined through heat and mass transfer. Negotiating the heat flow obtained by radiation and conduction, the heat balance of the wet cloth in a stationary situation can be expressed as... 

A slightly different approach was taken by Gill (G15), who considered the case of a bubble moving through a stationary liquid with mass transfer accompanied by simultaneous first-order chemical reaction. His assumptions were as follows ... 

The penetration and film-penetration theories have been developed for conditions of equimolecular counterdiffusion only the equations are too complex to solve explicitly for transfer through a stationary carrier gas. For gas absorption, therefore, they apply only when the concentration of the material under going mass transfer is low. On the other hand, in the two-fihn theory the additional contribution to the mass transfer which is caused by bulk flow is easily calculated and hp (Section 10.23) is equal to (D/L)(Cr/Cum) instead of D/L. 

Ctl is the mass transfer term and arises because of the finite time taken for solute molecules to move between the two phases. Consequently, a true equilibrium situation is never established as the solute moves through the system, and spreading of the concentration profiles results. The effect is minimal for small particle size and thin coatings of stationary phase but increases with flow rate and length of column or surface. 

The most important feature of monolithic media is that the mobile phase flows exclusively through the separation unit. In contrast, there is no flow inside the conventional porous chromatographic particles and only a partial flow through the perfusion beads. Just as with the membrane adsorbers, monolith stationary phases may be operated with a minimum in mass transfer resistance with the concomitant advantages in terms of speed and throughput. 

---