Mass-transfer rate-limiting step

Hence, with porous particles, surface interaction will predominantly occur when the polypeptide and protein adsorbates reach the internal surface of the particles, thus enabling the mass balance, rate-limiting steps, and the mass transfer coefficients to be quantitatively and independently described. If it is assumed that the pores of the porous HPLC particles are initially filled with buffer liquid before the adsorption process starts, then the overall mass balance for a polypeptide or protein in a finite bath is given by... 

If the interaction were instantaneous and without mass-transfer rate limitations, then we would have a simple transmission of whatever input of adsorbate that was admitted to the bed, with the input function at the exit of the bed at a time equal to the residence time in the bed. A step-function input is shown in Curve A. More commonly, we have breakthrough curves such as B in Figure 9.1, there the mass transport and/or adsorption processes are not infinitely rapid, or C in the figure, where rates are slow and even some reversible reaction may occur. 

Tubular reactors often offer the greatest potential for inventory reduction. They are usually simple, have no moving parts, and a minimum number of joints and connections that can leak. Mass transfer is often the rate-limiting step in gas-liquid reactions. Novel reactor designs that increase mass transfer can reduce reactor size and may also improve process yields. 

Analogously to external mass transfer, internal mass transfer can be the rate-limiting step. In that case, it appears that the observed activation energy is related to the true activation energy as follows ... 

Principles and Characteristics Supercritical fluid extraction uses the principles of traditional LSE. Recently SFE has become a much studied means of analytical sample preparation, particularly for the removal of analytes of interest from solid matrices prior to chromatography. SFE has also been evaluated for its potential for extraction of in-polymer additives. In SFE three interrelated factors, solubility, diffusion and matrix, influence recovery. For successful extraction, the solute must be sufficiently soluble in the SCF. The timescale for diffusion/transport depends on the shape and dimensions of the matrix particles. Mass transfer from the polymer surface to the SCF extractant is very fast because of the high diffusivity in SCFs and the layer of stagnant SCF around the solid particles is very thin. Therefore, the rate-limiting step in SFE is either... 

In addition to the effects of formulation factors on freeze-drying behavior, it is important for the pharmaceutical scientist to understand basic principles of heat and mass transfer in freeze-drying [29,30]. Because of the high heat input required for sublimation (670 cal/g), transfer of heat from the heated shelf to the sublimation front is often the rate-limiting step in the coupled heat... 

The reader is referred to basic studies of mass transfer in freeze-drying by Pikal and coworkers for in-depth treatment of the theoretical and practical aspects of mass transfer [29,32], Briefly, the rate-limiting step in mass transfer is transfer of water vapor through the partially dried matrix of solids. Resistance of the dried layer increases in a more or less continuous fashion as the depth of the dried layer increases, and the resistance also increases with the concentration of solids in the dried layer. Other factors can also affect the resistance of the dried layer, such as the method of freezing faster freezing tends to create a higher resistance in the dried layer. 

The dimensionless limiting current density N represents the ratio of ohmic potential drop to the concentration overpotential at the electrode. A large value of N implies that the ohmic resistance tends to be the controlling factor for the current distribution. For small values of N, the concentration overpotential is large and the mass transfer tends to be the rate-limiting step of the overall process. The dimensionless exchange current density J represents the ratio of the ohmic potential drop to the activation overpotential. When both N and J approach infinity, one obtains the geometrically dependent primary current distribution. 

The three remaining steps (chemisorption of reactants, reaction on the surface, and desorption of adsorbed products) are all chemical in nature. It is convenient to employ the concept of a rate limiting step in the treatment of these processes so that the reaction rate becomes equal to that of the slowest step. The other steps are presumed to be sufficiently rapid that quasiequilibrium relations may be used. The overall rate of conversion will then be determined by the interaction of the rate of the process that is rate limiting from a chemical point of view with the rates of the physical mass transfer processes discussed above. 

The membrane is the regulating barrier for exchange of chemical species between the environmental medium and cell interior. It may be practically impermeable to one type of species and highly permeable to another. In the chain of transport steps from the bulk of the medium to the cell interior, the membrane transfer step may thus vary from fully rate-limiting to apparently fast with respect to transport in the medium. The overall rate of this biouptake process is determined by mass transport either in the medium or through the membrane the actual rate-limiting step will depend on a large variety of factors. Membrane... 

As the temperature is varied in a reactor, we should expect to see the rate-controlling step vary. At sufficiently low temperature the reaction rate coefficient is small and the overall rate is reaction limited. As the temperature increases, pore diffusion next becomes controlling (Da is nearly independent of temperature), and at sufficiency high temperature external mass transfer might limit the overall process. Thus a plot of log rate versus 1 / T might look as shown in Figure 7-15. 

Rate of protein transfer to or from a reverse micellar phase and factors affecting the rate are important for the practical applications of RME for the extraction and purification of proteins/enzymes and for scale-up. The mechanism of protein exchange between two immiscible phases (Fig. 2) can be divided into three steps [36] the diffusion of protein from bulk aqueous solution to the interface, the formation of a protein-containing micelle at the interface, and the diffusion of a protein-containing micelle in to the organic phase. The reverse steps are applicable for back transfer with the coalescence of protein-filled RM with the interface to release the protein. The overall mass transfer rate during an extraction processes will depend on which of these steps is rate limiting. 

Why adsorption, ion exchange and heterogeneous catalysis in one book The basic similarity between these phenomena is that they all are heterogeneous fluid-solid operations. Second, they are all driven by diffusion in the solid phase. Thus, mass transfer and solid-phase diffusion, rate-limiting steps, and other related phenomena are common. Third, the many aspects of the operations design of some reactors are essentially the same or at least similar, for example, the hydraulic analysis and scale-up. Furthermore, they all have important environmental applications, and more specifically they are all applied in gas and/or water treatment. 

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