Backflow model

A simple extension of the backflow model is considered by Nishiwaki et al.,74 who assumed each stage to be backmixed but not perfectly mixed. The back-mixing in each stage was assumed to be expressed by the dispersion model. This model is, thus, named the dispersion/backflow model. A comparison of this model to the dispersion model is given hy Nishiwaki and Kato.73... 

In the more complicated backflow model, where the column is also divided into individual mixing cells, as in the cell model, additional longitudinal mixing between the cells in form of mixing flow is included. 

The die was divided into 2 sections a) Taper with a Backflow Model and b) Heated die with Expansion-Shrinkage Model. 

The earliest and simplest approach in this direction starts from Langevin equations with solutions comprising a spectrum of relaxation modes [1-4], Special features are the incorporation of entropic forces (Rouse model, [6]) which relax fluctuations of reduced entropy, and of hydrodynamic interactions (Zimm model, [7]) which couple segmental motions via long-range backflow fields in polymer solutions, and the inclusion of topological constraints or entanglements (reptation or tube model, [8-10]) which are mutually imposed within a dense ensemble of chains. 

For contactors in which discrete well-mixed compartments can be identified, for example sieve-plate columns, axial mixing effects are incorporated into the stagewise model by means of the backflow ratio a which is defined as the fraction of the net interstage flow of one phase which is considered to flow in the reverse direction. For a contactor in which there are many compartments, the axial dispersion coefficient and the backflow ratio, a, are interrelated as follows ... 

From now on, the permeation in (16) is neglected as it is several orders of magnitude smaller than the advection due to the radial component of the velocity vr (now playing the role of vz in the planar case). As far as the velocity perturbation is concerned, our aim is to describe its principal effect-the radial motion of smectic layers, i.e., instead of diffusion (permeation) we now have advective transport. In this spirit we make several simplifications to keep the model tractable. The backflow-flow generation due to director reorientation-is neglected, as well as the effect of anisotropic viscosity (third and fourth line of (19)). Thereby (19) is reduced to the Navier-Stokes equation for the velocity perturbation, which upon linearization takes the form... 

Index Entries Screw reactor computational fluid dynamics modeling backflow hydrolysis. 

Nishiwaki et al.74 Deckwer30 has applied the backflow cell model to correlate the temperature profiles in a nonisothermal liquid-phase reactor. 

Two main types of models are in common use for describing axial mixing in bubble columns. The most commonly used model is the Dispersion Model. Here, a diffusion-like process is superimposed on piston or plug flow. The stirred tanks-in-series model has also been used to describe flow of liquids in bubble columns. Levenspiel (1 ) presents a number of models incorporating various combinations of mixed tanks to model stagnant regions and backflow. 

Generalized Formalism A generalized membrane transport model, in the form of the black box models discussed earlier, can be considered in order to compare alternative mechanisms of water backflow in gradients of chemical potential, activity or concentration of water. Each of these gradients can be expressed by a gradient in w. The equation of net water flow is, thus,... 

As a (very simple) example, we consider the flowsheet in Fig. 4.2. The flowsheet has been designed in the process-integrated flowsheet editor that forms part of the PRIME environment (cf. Subsect. 3.1.3). The simulation model for the reactor device (CSTR - continuous stirred tank reactor) is already given. The developer s task is to find a suitable model to represent the separation. The designer can choose between several separation models, including complex combinations with recycle streams (backflows). 

The coefficient representing axial dispersion, E, is measured using a tracer by pulse, sinusoidal, or step-change residence time distribution tests, or by measuring backflow. Sometimes the phenomenon is represented by a cefl model, in which the number of well-mixed cells fits dispersion. The coefficient representing radial dispersion, is determined by measuring the radial spread of a tracer from the centerline toward the wall. 

Equilibrium titration of PdNOR showed the value of Fcb was 320 mV, that of heme was - -60 mV, and those of heme c and heme ft were +310 mV and +340 mV, respectively. The rates of intramolecular electron transfer between the redox centers of NOR have been investigated using the electron backflow technique. The photolysis of CO bound to the high-spin heme results in a decrease in of the heme to its basal value, causing a transient redistribution of electrons with the other redox centers before CO rebinding occurs. Time-resolved optical spectroscopy and electrometric changes in membrane potential induced by photolysis of the CO-bound mixed-valence state of PdNOR reconstituted into proteoliposomes indicate that the pathway of electron transfer is similar to that of the heme Cu oxidases, consistent with the modeling studies discussed above. Electrons are accepted from external donors by heme c, transferred to the low-spin heme... 

A closer similarity would be to modify the tanks-in-series model to include backflow streams. This model has mass balances... 

Marlow and Rowell (37) working with coal/water slurries and using the CVP technique have shown that, at the frequencies of their measurements (200 kHz), the effect of particle concentration can be adequately described by introducing a factor (1 — g ) into their equivalent of Eq. (1) where again, g was very close to unity. In their review article Marlow et al. (6) discuss the way the cell model of Levine and coworkers (38, 39) is introduced into the CVP theory and show that, for thin double layers, the result is that the hydrodynamic and electrostatic interactions essentially cancel one another and one is left with only the factor (1—d)) to take account of the backflow of liquid caused by the particle motion. 

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