Linear sink

A linear sink will create a two-dimensional airflow. The radial velocity (m/s) at a distance r (m) from the sink is calculated as a volume rate of (mVs) per meter of linear sink length divided by the surface area of an imaginary cylinder of radius r ... 

The effect of restricting surfaces on the flow created by the linear sink will be similar to that described for the point source. The equations for the inflow velocity (t,.) and the corresponding capture distance (rj for some typical situations are listed in Table 7.24. 

To describe an airflow in rhe vicinity of some realistic, finite-dimensional luxids, theoretical considerations that are valid for hypothetical point or linear sinks can be applied. 

TABLE 7.24 Inflow Velocity and Capture Distance for Some Common Locations of a Linear Sink... 

The linear stability analysis of eqns (2.30) shows that the domain of instability of the unique steady state is larger than in the case of a linear sink of product. The main effect of the Michaelian sink of product is, however, to allow the occurrence of sustained oscillations in the absence of enzyme cooperativity - but not of autocatalytic regulation (Goldbeter Dupont, 1990). 

This nullcline retains an S-shape for n > 1. In the case of an enzyme comprising a single subunit, for which the phenomenon of cooperativity is necessarily absent, the nullcline y=X., obtained for a linear sink, did not possess any region of negative slope. This is no more the case for eqn (2.31), which can admit up to two distinct values of y for a given value of a (fig. 2.28). 

For the special case of a uniform wind, where and are constants, an isolated source located at (0,0,H) continuously emits a mass per unit time of species i at a constant rate Q, and the removal rate from internal sinks is governed by linear processes, C, = -C /tj. with t. being a characteristic decay time. 

Efforts to apply Equations (6) and (7) to distributions of Th isotopes in the oceans showed that the situation was more complex. For example. Bacon and Anderson (1982) measured vertical distributions of Th in the deep sea and found that both the particulate and dissolved fractions increased linearly with depth. While the former observation is predictable from Equation (7) if sinking particles continue to scavenge Th during their descent, the latter is inconsistent with Equation (6). Bacon and Anderson (1982) suggested that the data could best be explained by a reversible scavenging equilibrium maintained between dissolved and particulate Th. Thus Equation (6) must be modified to ... 

If a small polydisperse sample of powder is dissolved under sink conditions, then the dimensions, b, of the particle will decrease linearly with respect to time [33-37] ... 

Strictly speaking, sink conditions are when the amount dissolved plotted versus time yields a line which, within experimental error, is linear. When the surface area, A, is constant, then this corresponds to 15% dissolved. When the surface area changes (e.g., during particulate dissolution), then this number may be smaller. 

In PAMPA measurements each well is usually a one-point-in-time (single-timepoint) sample. By contrast, in the conventional multitimepoint Caco-2 assay, the acceptor solution is frequently replaced with fresh buffer solution so that the solution in contact with the membrane contains no more than a few percent of the total sample concentration at any time. This condition can be called a physically maintained sink. Under pseudo-steady state (when a practically linear solute concentration gradient is established in the membrane phase see Chapter 2), lipophilic molecules will distribute into the cell monolayer in accordance with the effective membrane-buffer partition coefficient, even when the acceptor solution contains nearly zero sample concentration (due to the physical sink). If the physical sink is maintained indefinitely, then eventually, all of the sample will be depleted from both the donor and membrane compartments, as the flux approaches zero (Chapter 2). In conventional Caco-2 data analysis, a very simple equation [Eq. (7.10) or (7.11)] is used to calculate the permeability coefficient. But when combinatorial (i.e., lipophilic) compounds are screened, this equation is often invalid, since a considerable portion of the molecules partitions into the membrane phase during the multitimepoint measurements. 

Passive transport flux is therefore linearly dependent on mucosal solute concentration, provided the transported solute is readily removed by the villus blood supply (sink conditions). 

Figure 18 Linear fluxes of hydrocortisone across Caco-2 cell monolayers in the Transwell system into a receiver sink as a function of stirring (rotary platform shaker) rate at 25 °C.

The flux of 3H-labeled PNU-78,517 across MDCK cell monolayers shows the characteristic disparity between the kinetics of disappearance from the donor solution and appearance in the receiver sink (Fig. 32). Drug uptake is rapid and exponential with time and approaches a quasi-equilibrium state in contrast, the concomitant efflux of drug into the receiver is slow and linear. While maintaining a 3% bovine serum albumin (BSA) concentration in the donor and varying the BSA concentration between 0.5 and 5% in the receiver, the results show that the... 

The light fluxes are now linear functions of the depth coordinate z as it is predicted also by Fick s first law for steady-state diffusion without sink. For weak absorption, the equations for Td and Ro of the Kubelka-Munk formalism are also directly equivalent to the results of the diffusion approximation. Comparing Eqs. (8.22) and (8.23) with Eqs. (8.11), (8.12), and (8.14) under diffuse irradiation or under //o = 2/3, the Kubelka-Munk coefficients can be expressed by<31 34)... 

---