Rate-governed processes

In recent years a new approach to the modeling of distillation and absorption processes has become available the nonequilibrium or rate-based models. These models treat these classical separation processes as the mass-transfer rate governed processes that they really are, and avoid entirely the (a priori) use of concepts such as efficiency and HETP [Krishnamurthy and Taylor, AZChE/., 31, 449-465 (1985) Taylor, Kooijman, and Hung, Comput. Chem. Engng., 18, 205-217 (1994)]. 

These categories do not denote the rate-governing process for the fouling. Almost any pair of the above fouling modes are mutually reinforcing. This is particularly true of corrosion fouling in conjunction with each of the other modes. One exception is scaling accompanied by particle deposition, which tends to weaken an otherwise tenacious scale. 

The oxidation process in a stabilised polymer therefore includes several chemical processes operating in parallel. Each process will proceed at a rate governed either by chemical rate kinetics or by the rate of migration of oxygen or one of the radicals involved into previously unaffected regions. Each will depend on temperature in a different way. 

In polymeric membrane and matrix-based micropumps, the membrane or the matrix makes the essential component of the delivery device that controls the rate of release. In matrix controlled delivery, the rate of the hydrolytic breakdown of the matrix is the governing process. In polymeric membrane-controlled release, the rate of hydration of the membrane and the subsequent diffusion of drug are the rate-controlling steps. 

Either the rate of diffusion to the surface or the speed of the surface reaction governs the rate of removal of the gas from the air stream, depending on which is the slower process. If k is dependent on flow rate, then diffusion is the rate-governing step. From Table XII it is evident that k is proportional to L. Therefore, one can assume that mass transfer is the rate-controlling step and the surface reaction is much faster than the diffusion process. 

They neglected the reverse rate governed by b (assuming an exothermic initial step) and assumed rapid nonradiative relaxation of nascent D BA (governed by rate constant e). The steady-state result once again identifies the charge injection process as the rate-determining step (i.e., k -t = a) under the conditions d e. 

The entropy flux difference and the integral over a can be calculated independently, and they must give the same answer. The entropy production rate governs the transport processes that take place in the system. We have... 

The transfer of mass within a fluid mixture or across a phase boundary is a process that plays a major role in various engineering and physiological applications. Typical operations where mass transfer is the dominant step are falling film evaporation and reaction, total and partial condensation, distillation and absorption in packed columns, liquid-liquid extraction, multiphase reactors, membrane separation, etc. The various mass transfer processes are classified according to equilibrium separation processes and rate-governed separation processes. Fig. 1 lists some of the prominent mass transfer operations showing the physical or chemical principle upon which the processes are based. 

During the cross polarization process magnetization is transferred from protons to carbons according to the strength of the C-H dipole interaction, at a rate governed by a second time constant... 

Analysis of separation processes can be placed into two fundamental categories equilibrium-based and rate-based processes. These separation categories are designated using thermodynamic equilibrium relationships between phases and the rate of transfer of a species from one phase into another, respectively. The choice of which analysis to apply is governed by which is the limiting step. If mass transfer is rapid, such that equilibrium is quickly approached, then the separation is equilibrium limited. On the other hand, if mass transfer is slow, such that equilibrium is not quickly approached, the separation is mass transfer limited. In some separations, the choice of analysis depends upon the type of process equipment used. 

---