Probability circulation time

Most of the indices of the mixing capacity in the left-hand side column in Table 2.1 are related to the mixing rate—residence time for the flow system (e.g., ratio of the standard deviation of the probability density distribution of the residence time to the average residence time residence time is the stay time of the inner substance in an equipment), circulation time for a batch system (e.g., ratio of the standard deviation of the probability density distribution of the circulation time to the average circulation time circulation time is the time required for one circulation of the inner substance in an equipment), mixing time (e.g., the time required for the concentration of the inner substances at a specific position in the equipment to reach a final constant value within some permissible deviation), and so on. 

Cell models. In order to predict chemical conversion in stirred tanks, Patterson and coworkers ( 3, 39 > 40) divided the tank volume into 30 mixing segments connected by specified flowrates Q-jj Nd2. The turbulence level in each segment is characterized by Ls ( dT) and e( d2) (HDM model). Mann and coworkers (148,149) also studied a model where cells (or segments) are connected according to the average flow pattern. Commutation according to a specified probability at each cell s outlet allows a stochastic path to be simulated, for instance for a flow follower. They thus obtained circulation time distributions very similar to experimental ones (135, 140, 141). 

Figure 24 illustrates possible flocculation and chaining of particles in flow conditions. Larger particles close to the walls of the vessels experience greater shearing forces because of the nature of the flow patterns shown. Particles that adhere to er5dhrocytes move with them until detachment, often prolonging their own circulation times. Adhesion, seen as a prerequisite to cellular uptake from blood and interstitial fluids is not a foregone conclusion. The probability of adhesion, Padheaon can be written phenomenologically as in Figure 24. The factors include particle diameter, flow rate, the density of receptors, and the force of attraction between particle and receptor.

The time-based dose-response curve yielded a slow tissue time constant of 25.5 minutes. This is significantly greater than any circulation time constants previously reported in small animals (7). The experiments cannot indicate the anatomical location or the mode of transport responsible for this slow time constant. Flynns studies (7), which failed to show such a slow tissue, were performed on unanaesthetized mice so the conditions for comparison are not exact. Detection of this slow tissue by measurement of pulmonary gas washout is probably not feasible be-... 

Bile salts have been used for centuries as digestive aids and cathartics. Their use for these purposes has become more limited recently, and this is probably appropriate until better preparations become available and indications for their administration become more clearly defined. Most commercial bile salt preparations are desiccated or crude extracts of cattle bile containing mainly unconjugated bile salts with small amounts of pigment and lipids. They are generally supplied as 0.2- or 0.3-g tablets. The customary dose is 0.4-0.6 g three times daily with meals. This is probably an inadequate dose, as will be explained later. Dehydrocholic acid, 3,7,12-triketo-5j -cholanoic acid, is oxidized cholic acid and is supplied in pure form but does not form micelles and hence probably does not assist fat absorption significantly and would be of little value for replacement therapy. Sodium dehydrocholate is supplied as a 20 % solution in ampules and is widely used to measure blood circulation times. It does not appear to be conjugated by the liver (86). 

Namdev et al. (1991) simulated the fluctoating dissolved oxygen concentrations in large bioreactors in a 2 L vessel using a Monte Carlo approach. A lognormal distribution, described by a mean circulation of 20 s and a standard deviation of 8.9 s, was discretized into n elements of equal probability, each with a corresponding circulation time. A uniform random number was then used to select a circulation time. Therefore, a random circulation time was selected... 

As a specific example, consider oceanic sulfate as the reservoir. Its main source is river runoff (pre-industrial value 100 Tg S/yr) and the sink is probably incorporation into the lithosphere by hydrogeothermal circulation in mid-ocean ridges (100 Tg S/yr, McDuff and Morel, 1980). This is discussed more fully in Chapter 13. The content of sulfate in the oceans is about 1.3 X lO TgS. If we make the (im-realistic) assumption that the present runoff, which due to man-made activities has increased to 200 Tg S/yr, would continue indefinitely, how fast would the sulfate concentration in the ocean adjust to a new equilibrium value The time scale characterizing the adjustment would be To 1.3 X 10 Tg/(10 Tg/yr) 10 years and the new equilibrium concentration eventually approached would be twice the original value. A more detailed treatment of a similar problem can be found in Southam and Hay (1976). 

Although the general circulation patterns are fairly well known, it is difficult to quantify the rates of the various flows. Abyssal circulation is generally quite slow and variable on short time scales. The calculation of the rate of formation of abyssal water is also fraught with uncertainty. Probably the most promising means of assigning the time dimension to oceanic processes is through the study of the distribution of radioactive chemical tracers. Difficulties associated with the interpretation of radioactive tracer distributions lie both in the models used, nonconservative interactions, and the difference between the time scale of the physical transport phenomenon and the mean life of the tracer. 

A volumetric scaleup by a factor of 512 is quite large, and the question arises as to whether the large vessel wiU behave as a CSTR. The concern is due to the factor of 4 increase in mixing time. Does it remain true that tmix h/i and tmix t If so, the assumption that the large vessel wiU behave as a CSTR is probably justified. The ratio of internal circulation to net throughput—which is the internal recycle ratio—scales as the inverse of the mixing time and will thus decrease by a factor of 4. The decrease may appear worrisome, but if the increase in mixing time can be tolerated, then it is likely that the decrease in internal recycle ratio is also acceptable. 

Rimantadine in young adults), utilization of adamantane derivative carriers can probably prolong drug presence time in blood circulation. 

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