Time constant for

Figure C3.5.5. Vibronic relaxation time constants for B- and C-state emitting sites of XeF in solid Ar for different vibrational quantum numbers v, from [25]. Vibronic energy relaxation is complicated by electronic crossings caused by energy transfer between sites.

The exposure interval for the bed, T, is inversely proportional to the kiln rotation rate. Hence, equation 21 shows that the time constant for desorption is directly proportional to the bed depth and inversely proportional to the square root of the kiln rotation rate. However, the overriding factor affecting is the isotherm constant iC which in general decreases exponentially with increasing temperature as in equation 4. 

Problems are stiff when the time constants for different phenomena have very different magnitudes. Consider flowthrough a packed bed reactor. The time constants for different phenomena are ... 

Time constants. Where there is a capacity and a throughput, the measurement device will exhibit a time constant. For example, any temperature measurement device has a thermal capacity (mass times heat capacity) and a heat flow term (heat transfer coefficient and area). Both the temperature measurement device and its associated thermowell will exhibit behavior typical of time constants. 

Rapid Adsorption-Desorption Cycles For rapid cycles with particle diffusion controlling, when the cycle time is much smaller than the time constant for intraparticle transport, the LDF approximation becomes inaccurate. The generalized expression... 

In addition to the drift with time, step changes due to operating decisions, atmospheric changes, or other conditions result in additional time dependence. Not only is there a sudden change due to the actual decision, but also the plant changes due to the time constants. For example. Fig. 30-13 shows measurements with step changes in the operation. 

The spin-lattice relaxation time, T/, is the time constant for spin-lattice relaxation which is specific for every nuclear spin. In FT NMR spectroscopy the spin-lattice relaxation must keep pace with the exciting pulses. If the sequence of pulses is too rapid, e.g. faster than BT/max of the slowest C atom of a moleeule in carbon-13 resonance, a decrease in signal intensity is observed for the slow C atom due to the spin-lattice relaxation getting out of step. For this reason, quaternary C atoms can be recognised in carbon-13 NMR spectra by their weak signals. 

Thus, in the series of Ti measurements of 2-octanol (42, Fig. 2.27) for the methyl group at the hydrophobic end of the molecule, the signal intensity passes through zero at Tq = 3.8 s. From this, using equation 10, a spin-lattice relaxation time of Ti = 5.5 s can be calculated. A complete relaxation of this methyl C atom requires about five times longer (more than 30 s) than is shown in the last experiment of the series (Fig. 2.27) Tj itself is the time constant for an exponential increase, in other words, after T/ the difference between the observed signal intensity and its final value is still 1/e of the final amplitude. 

I would like a time constant for the R-C filter to be about 1 mS. Selecting the value of the capacitor to be 0.1 uF, the charging resistor should be... 

Time constant for open circuit voltage (when motor control will use delayed transfer to alternate sources on voltage loss). This value must include the effect of any capacitors applied on the load side of the motor controller. 

In Chapter 2 when the Maxwell and Kelvin models were analysed, it was found that the time constant for the deformations was given by the ratio of viscosity to modulus. This ratio is sometimes referred to as the Relaxation or Natural time and is used to give an indication of whether the elastic or the viscous response dominates the flow of the melt. 

FIGURE 8.1 Model of a central recirculating system used for calculating the connection between contaminant concentrations, airflow rates, contaminant source strength, q, and air cleaner efficiency, rj. Cj p is the concentration in the supply (outside) air, c is the concentration in the room, c is the concentration in the returned air, (JaMot the total flow rate through the room, ic is the ratio between recirculated airflow rate and total air flow rate, T is the time constant for the room, and V is the room volume. 

In order to have effective exchange of air in important locations in a room, the age of the air in those locations should be low. The basis for comparison is the complete mixing scenario. That scenario gives the same age for any air volume selected in the room, identical to the nominal time constant for the ventilation airflow,. A steady-state scenario is assumed. See Sutcliffe for an overview of definitions related to age of air. The various air exchange efficiency indices are presented in Table 8.6. 

In the case of a temperature probe, the capacity is a heat capacity C == me, where m is the mass and c the material heat capacity, and the resistance is a thermal resistance R = l/(hA), where h is the heat transfer coefficient and A is the sensor surface area. Thus the time constant of a temperature probe is T = mc/ hA). Note that the time constant depends not only on the probe, but also on the environment in which the probe is located. According to the same principle, the time constant, for example, of the flow cell of a gas analyzer is r = Vwhere V is the volume of the cell and the sample flow rate. 

A breakthrough curve with the nonretained compound was carried out to estimate the axial dispersion in the SMB column. A Peclet number of Pe = 000 was found by comparing experimental and simulated results from a model which includes axial dispersion in the interparticle fluid phase, accumulation in both interparticle and intraparticle fluid phases, and assuming that the average pore concentration is equal to the bulk fluid concentration this assumption is justified by the fact that the ratio of time constant for pore diffusion and space time in the column is of the order of 10. ... 

The meter will also have a control for the time constant for the display (i.e. the speed of the meter response), and the two common time constants are Fast and Slow . Others may have an impulse and peak hold facility. More complex meters incorporate Leq-measuring devices, and these are also available as hand-held Type 1 meters with filters as in the basic meter. 

From this mathematical treatment we properly conclude that ki + k- is the natural rate constant. The data workup does not give the sum because of an artful algebraic manipulation. Instead, the sum k-i + k is simply the inverse of the intrinsic time constant for the single exponential that defines the approach to equilibrium. 

For an ice sheet of thickness H in equilibrium with a climate supplying accumulation at a rate a (thickness of ice per imit time), the vertical velocity near the ice-sheet surface is a and this velocity decreases to zero at the ice-sheet bed. A characteristic time constant for the ice core is H/a. The longest histories are therefore obtained from the thick and dry interiors of the ice sheets (particularly central East Antarctica, where H/a = 2 X 10 yrs). Unfortunately, records from low a sites are also low resolution, so to obtain a high-resolution record a high a site must be used and duration sacrificed (examples are the Antarctic Peninsula (H/a = 10 ) and southern Greenland H/a = 5 x 10 )). 

These can be solved by classical methods (i.e., eliminate Sout to obtain a second-order ODE in Cout), by Laplace transformation techniques, or by numerical integration. The initial conditions for the washout experiment are that the entire system is full of tracer at unit concentration, Cout = Sout = L Figure 15.7 shows the result of a numerical simulation. The difference between the model curve and that for a normal CSTR is subtle, and would not normally be detected by a washout experiment. The semilog plot in Figure 15.8 clearly shows the two time constants for the system, but the second one emerges at such low values of W t) that it would be missed using experiments of ordinary accuracy. 

However, even with the most advanced measuring and simulation tools, the most efficient methods are simple calculations that give an order-of-magnitude estimation of the influence of a phenomenon. Time constants for diffusion, heat conduction, and acceleration are very useful. For example, the time constant for diffusion Td = f/D is the time it takes to fill a cube of size I by diffusion, and the time for a particle to accelerate from zero velocity to approximately two-third of the velocity of the surrounding fluids is 118/j, where p[Pg.331]

Diffusion in liquids is very slow. Turbulent transport or very narrow channels are necessary for good contact between the phases. The droplets must also be very small to minimize transport hmitations within the drops. An estimation of the time constant for diffusion in a 1-mm drop is (f (10-3)2... 

Characteristic time constant for micromixing calculated and measured... 

---