Time to approach steady state

Estimating the Diffusion Depth and Time to Approach Steady State... 

Topaz was used to calculate the time response of the model to step changes in the heater output values. One of the advantages of mathematical simulation over experimentation is the ease of starting the experiment from an initial steady state. The parameter estimation routines to follow require a value for the initial state of the system, and it is often difficult to hold the extruder conditions constant long enough to approach steady state and be assured that the temperature gradients within the barrel are known. The values from the Topaz simulation, were used as data for fitting a reduced order model of the dynamic system. 

Carry out simulations for differing tank volumes, flow rates and feed concentrations, in which the inlet and outlet flow rates are set equal, (F + P2 = F3) and observe the approach to steady state. Relate the time taken to approach steady state to the mean tank residence time (t = V/F3). 

Clearance is readily estimated from the dosing rate and mean steady-state concentration. Blood samples should be appropriately timed to estimate steady-state concentration. Provided steady state has been approached (at least three half-lives of constant dosing), a sample obtained near the midpoint of the dosing interval will usually be close to the mean steady-state concentration. 

Male Fischer 344/N rats were exposed via the nose only for 6 h to concentrations of vinylidene fluoride ranging from 27 to 16 000 ppm [71-42 000 mg/m. Tidal volume (mean, 1.51 mL/brcath) and respiratory frequency (mean, 132 breaths/min) were not influenced by exposure concentration. Steady-state blood levels of vinylidene fluoride increased linearly with increasing exposure concentration up to 16 000 ppm. Vinylidene fluoride tissue/air partition coefficients were determined experimentally to be 0.07, 0.18, 0.8,10, and 0.29 for water, blood, liver, fat and muscle, respectively. Previously published detenninations (Filser Bolt, 1979) for the maximum velocity of metabolism in mg/li/kg) and Michaelis Menten constant (K in mg/L) are 0.07 and 0.13, respectively. Time to reach steady-state blood levels of vinylidene fluoride was less than 15 min for all concentrations. After cessation of exposure, blood levels of vinylidene fluoride decreased to 10% of steady-state levels within 1 h. Simulation of the metabolism of vinylidene fluoride mdicated that although blood levels of vinylidene fluoride increased linearly with increasing exposure concentration, the amount of vinylidene fluoride metabolized per 6-h exposure period approached a maximum at about 2000 ppm [5240 mg/m vinylidene fluoride (Medinsky et al., 1988). 

Note that Eq. 4 can still be looked upon as a measure for the time needed to approach steady-state. 

The separation of enantiomers has become of particular importance in the production of pharmaceuticals. These separations are often difficult because the separation factors achieved on many chiral stationary phases (CSP) are low or moderate (often below 1.6) and the saturation capacities of most CSPs are low. The optimization of the experimental conditions of a separation is particularly important because most chromatographic separations of enantiomers are performed using the simulated moving bed process (SMB, see Chapter 17) and the complexity of this process, the long time that it needs to approach steady-state makes optimization by trial and error lengthy and costly. So, much attention has been devoted... 

With an adequate amount of desiccant In the structure, the EVOH Is not prone to Retort Shock and does not suffer from a prolonged lag time In approaching steady state. Oxygen permeation through EVOH barrier/desiccant containers Is controlled by the partition of water between the desiccant and the EVOH. Simply said, the desiccant keeps the EVOH dry. 

Those compounds that have higher values have a higher tendency to bioconcentrate, also have lower tendencies to be excreted, and will take longer times to achieve steady state. So, compounds that bioconcentrate will not only need to show high values, but will also have to persist to achieve Cf values approaching those predicted from Tb-2. Dissolved Organic Matter Natural waters will always contain a certain amount of DOM. It has been demonstrated that hydrophobic compounds can partition into this compartment (Section 2.2.5.3, Chapter 2). The analysis of water samples does not usually discriminate between the amounts of compound in free solution and that associated with the DOM and, hence, the amount detected, Ctot would be... 

Effect of temperature on the creep of NT154 (a) Strain as a function of exposure time (b) Minimum creep rate as a function of temperature. Transient creep effects are evident from the time required for the data to approach a common Arrhenius curve. Approximately 1500 hr of creep was required to approach steady state creep. Stress 100 MPa. 

The time-dependent KIEapp at 430 nm is illustrated in Figure 1.19 for the hydride transfer reactions between BNAH/BNAH-d2 and MA in acetonitrile at 298 K. The KIEapp values rise from near unity at zero-time to approach a constant value equal to 3.6 as steady state is reached. The KIEapp values with monitoring at wavelengths from 410 nm to 450 nm, at 10 nm intervals, are summarized in Table 1.26. In all cases the KIEapp values at short times are close to unity and increase with time to the steady-state KIEapp value. 

A discussion of the chronoamperometric feedback response is valuable, as potential step measurements have been used to obtain homogeneous kinetic parameters. Calculations of the chronoamperometric response also provide valuable information on the time taken to reach a true steady state, which is particularly important for approach curve measurements. It has been demonstrated that values of t in excess of 100 may be necessary to achieve steady-state conditions (within a few percent). For typical tip disk electrode radii of 12.5 and 2.5 pm, and a typical diffusion coefficient of 1X10 cm s , this corresponds to real times that are greater than 15 and 0.6 s, respectively. For the larger disk size, the time is longer than required for many other steady-state measurements with SECM. Furthermore, it is important to point out that this analysis is for the situation where A and B have the same diffusion coefficient. It has been demonstrated comprehensively that unequal diffusion coefficients of A and B greatly increase the time to true steady state even for simple electron transfer without homogeneous kinetics. ... 

Fig. 17.—The ratio of the radical concentration to its steady-state concentration as a function of the time during alternate dark and light periods of durations t and rt, respectively. Curve OABCD represents /ts = 1.5 and r = 3 curve OGH, with r = 3 and t/Ts = l/4i, approaches a condition of oscillation about an average radical concentration [M ] / [M ] = 1 /2.

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