Flux of compound

Figure 75. The biochemical model for indole alkaloid formation in Catharanthus roseus. The arrows represent the direction of the formation and the flux of compounds in skeleton construction. On the diagram, enzymes are shown by a circle.

There will also be a temporal mean concentration. If there is a source or sink in the flow, or transport across the boundaries as in Figure 5.1, then the temporal mean concentration profile will eventually reach a value such as that given in Figure 5.1. This flux of compound seems to be from the bottom toward the top of the flow. Superimposed on this temporal mean concentration profile will be short-term variations in concentration caused by turbulent transport. The concentration profile is flatter in the middle of the flow because the large turbulent eddies that transport mass quickly are not as constrained by the flow boundaries in this region. Now, if we put a concentration-velocity probe into the flow at one location, the two traces of velocity and concentration versus time would look something like that shown in Figure 5.2. 

The equation for mass flux of compound A, and mass of A per unit volume will be written by analogy to equation (8.77) ... 

If equations (8.77) and (8.81) are combined to eliminate shear velocity, an equation can be developed for the flux of compound A ... 

Figure 19.3 schematically describes in more detail the transport phenomena occurring during pervaporation. First, solutes partition into the membrane material according to the thermodynamic equilibrium at the liquid-membrane interface (Fig. 19.3a), followed by diffusion across the membrane material owing to the concentration gradient (Fig. 19.3b). A vacuum or carrier gas stream promotes then continuous desorption of the molecules reaching the permeate side of the membrane (Fig. 19.3c), maintaining in this way a concentration gradient across the membrane and hence a continuous transmembrane flux of compounds.

Using the numbers given in Table 3.5 we can now inspect Table 3.4 in order to get some feeling of the temperature dependency of partition constants. Except for the hexadecane/water partitioning of hexane and benzene, there is a significant effect of temperature on the partition constants, particularly if one of the phases is the gas phase. For example, the air/water partition constant of diethylether is about 4 times larger at 25°C as compared to 5°C (An// = 46.8 kJ-mol 1). As we will see later in various other chapters, in cases in which equilibrium is not established, temperature may have an important effect on the direction of fluxes of compounds between environmental compartments. 

L flux of compound i relative to mass average velocity... 

Permeation in PAMPA experiments is also expressed as a flux rate Papp with the unit [cm/sec] under the assumption that transport equilibrium is not reached and back-transport can be neglected in course of the experiment. Papp values represent kinetic information and describe the flux of compounds over the membrane. 

The model is composed of 10 compartments. These 10 compartments are connected by 17 linear transfer coefficients using 21 parameters. The whole system describes the flux of compounds between a central compartment (the blood) and outer compartments which connect with the central compartment only. The 10 compartments are labeled blood, bone 1, bone 2, liver 1, liver 2, kidney 1, kidney 2, residual 1, residual 2, and excretion. The organs are divided into two compartments one compartment represents the short term and one represents the long term. For example, the short-term compartment for the bone is the bone surface and bone marrow, and the long-term compartment is the deep bone. In the liver, the short-term compartment is assumed to be the lysosomes, and the long-term compartment is assumed to be the telolysosomes. Separation of these organs into two components helps to account for the reabsorption and rapid excretion. Using the symbols BP=blood, EC=excretion, Bl=bone 1, Ll=liver 1, Kl=kidney 1, Rl=residual 1, B2=bone 2, L2=liver 2, K2=kidney, and R2=residual 2, the calculated transfer coefficients for this model are shown in Table 2-7. 

At different time points, each insert is transferred in another well containing RH buffer (to minimize an eventual flux of compounds from the abluminal to the luminal compartment) (Fig. 3). 

This phenomenon is denoted feed-side concentration polarization and, in practice, affects mainly the fluxes of compounds of high sorption coefficient, even under turbulent hydrodynamic conditions over the membrane, as their permeability (and hence flux across the membrane) is high. It should at this point be emphasized that contrary to the non-ideal transport phenomena discussed earlier, feed-side concentration polarization is not a membrane-intrinsic phenomenon, but stems from poor design of the upstream flow conditions in practice it may in fact not be overcome owing to module design limitations (Baker et ah, 1997). 

Secondly, if compound-2 has a low but non-zero solubility in the continuous phase (with Co,i >> Co,2) an equilibrium condition according to the case where Q.2 = 0 can be applied. There exists a critical drop size (Dd,c) in the DSD for which the flux of compound-2 out of the drops is zero. Note that for > D c and for the flux is positive and negative,... 

How well the process has been running can thus be distinguished by the use of methods characterizing the membrane itself. Another way to monitor the process is to use markers and sensors to measure (besides fouling) the permeate flux of compounds of interest. 

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