Volume depletion

FIGURE 12.10 Illustration of the depletion of polymer molecules, radius of gyration rg, from a layer around spherical particles, radius rp, and of the decrease in depletion volume resulting from particle aggregation. 

In summary, we first of all have used TEM results to determine that rp 20 nm and Np 5 x 1015 cm-3, and thus have been able to calculate the sample porosity P = (4/3)jrrp3Np s= 0.2. That is, about 20 % of the free-carrier loss in our sample is due to the removal of material. Then, an analysis of DLTS results has shown that acceptorlike surface states on the pores produce a depleted volume of radius w 34 nm around each pore. Therefore, the total fractional volume depleted of free electrons is (4/3)nw3Np 0.8. This means that about 60 % of the carrier depletion is due to traps on the pore surfaces, not the pores themselves. The calculated carrier depletion (80%) is quite consistent with C-V measurements (Figure 9.2), which indicate that n (averaged over the depleted regions [3]) has fallen from mid-1018 to about 1017 cm-3 in the region sampled by the DLTS experiment. 

The probability of y-interaction is so small in the small depletion depth of the surface barrier detectors that they are not very useful for y-spectroscopy. Large depleted volumes can be created by drifting lithium atoms into a silicon or germanium crystal. Lithium does not occupy a crystal site in the crystal, but is small enough to go into interstitial sites. The ease of ionization of Li to Li makes it a donor impurity. The lithium is drifted from one side of the crystal using an electric field. Its concentration at the "entrance" side becomes high and then decreases towards the other end of the crystal. The amount of lithium in the... 

When a potential is applied over such a crystal, with the positive terminal at the high lithium side, three volumes are created, one of p-type, a middle "intrinsic" one, and an n-type one (p-i-n detectors). In the intrinsic volume the lithium donor electrons neutralize any original impurities, which are of acceptor p-type. The intrinsic volume becomes depleted and thereby sensitive to nuclear radiation, and detectors with depleted volumes up to more than 100 cm are commercially available. Figure 8.14 shows the arrangement of the Dewar vessel with liquid N2, cold-finger, detector, and preamplifier. 

For hard spheres as depletants, this issue was first addressed by Mao in a numerical study to second order in density. At constant depletant volume fraction, the depth of the depletion potential was found to decrease with increasing depletant polydispersity, while the repulsive part of the potential, which occurs for large number densities, was found to be rather robust against polydispersity and flattens only for very lar widths of the size distribution. 

Deep depletion Increasing the depleted volume near the surface increases the depth of the well. Because the long-wavelength photons travel farther before being absorbed, the QE in the far red is enhanced. 

Polymeric amphiphiles, even when they are not adsorbed to the droplet interfaces, provide an entropic effect that can expressed as a change in viscosity. Depletion flocculation occurs because the center of mass of the depleting agent (the polymers) will not approach the droplet more closely than its effective radius (as mentioned before). Hence there is an area around the droplet that is not accessible to the polymer because of its reduced entropy. If the total depletion volume of the droplets is reduced by the overlap of their depletion zones, the excluded volume is decreased, and the volume accessible to the polymer is increased, increasing its entropy. The attractive force that appears... 

In contrast to bridging flocculation, depletion flocculation occurs when the added polymer cannot adsorb to the surfaces of the droplets. Under these conditions a layer around the droplets exists where the polymer concentration is depleted as compared to the bulk solution (see the depleted volume in Figure 4.3). The origin of the depleted volume lies with a geometrical restraint imposed by the finite voliune of the polymer molecule. This may be understood by modelling the polymer molecule as a sphere of radius r, whose position is defined by its centre. Since the polymer may not adsorb to the droplet surface, the closest it may approach the droplet is to touch the surface. In this arrangement the centre of the polymer will be a distance rg from the droplet surface. It follows that polymer centres cannot get closer than this to the droplet surface and consequently do not contribute to the segment density there. 

Starting at condition A with the ethane in the liquid phase, and assuming isothermal depletion, then as the pressure is reduced so the specific volume increases as the molecules move further apart. The relationship between pressure and volume is governed by the compressibility of the liquid ethane. 

The initial temperature of a gas condensate lies between the critical temperature and the cricondotherm. The fluid therefore exists at initial conditions in the reservoir as a gas, but on pressure depletion the dew point line is reached, at which point liquids condense in the reservoir. As can be seen from Figure 5.22, the volume percentage of liquids is low, typically insufficient for the saturation of the liquid in the pore space to reach the critical saturation beyond which the liquid phase becomes mobile. These... 

Pressure depletion in the reservoir can normally be assumed to be isothermal, such that the isothermal compressibility is defined as the fractional change in volume per unit change in pressure, or... 

The typical compressibility of gas is 500 10 psi, compared to oil at 10 10 psr, and water at 3 10 psi When a volume of gas is produced (8V) from a gas-in-place volume (V), the fractional change in pressure (8P) is therefore small. Because of the high compressibility of gas it is therefore uncommon to attempt to support the reservoir pressure by injection of water, and the reservoir is simply depleted or blown down . 

Reservoir pressure is measured in selected wells using either permanent or nonpermanent bottom hole pressure gauges or wireline tools in new wells (RFT, MDT, see Section 5.3.5) to determine the profile of the pressure depletion in the reservoir. The pressures indicate the continuity of the reservoir, and the connectivity of sand layers and are used in material balance calculations and in the reservoir simulation model to confirm the volume of the fluids in the reservoir and the natural influx of water from the aquifer. The following example shows an RFT pressure plot from a development well in a field which has been producing for some time. 

The principal mechanism of the hypotensive effect of diuretics (qv) is salt and fluid depletion, leading to reduction in blood volume (200,240). Acute effects lead to a decrease in cardiac output and an increase in total peripheral resistance. However, during chronic adrninistration, cardiac output and blood volume return toward normal and total peripheral resistance decreases to below pretreatment values. As a result, the blood pressure falls. The usual reduction in blood volume is about 5%. A certain degree of sustained blood volume contraction has to occur before the blood pressure decreases. The usual decrease in blood pressure achieved using a diuretic is about 20/10 mm Hg (2.7/1.3 kPa) (systoHc/diastoHc pressures. 

Trichloroethylene is being evaluated by the industry as a precursor in the production of hydrochlorofluorocarbons (HCEC), the replacement products for the chlorofluorocarbons impHcated in the depletion of the stratospheric ozone. At this time it is too early to project any estimates or probabihties for potential volume changes as a result of this opportunity (23). 

The other analytical methods necessary to control the typical specification given in Table 5 are, for the most part, common quality-control procedures. When a chemical analysis for purity is desired, acetylation or phthalation procedures are commonly employed. In these cases, the alcohol reacts with a measured volume of either acetic or phthalic anhydride in pyridine solution. The loss in titratable acidity in the anhydride solution is a direct measure of the hydroxyl groups reacting in the sample. These procedures are generally free from interference by other functional groups, but both are affected adversely by the presence of excessive water, as this depletes the anhydride reagent strength to a level below that necessary to ensure complete reaction with the alcohol. Both procedures can be adapted to a semimicro- or even microscale deterrnination. 

The terms may be quantities or rates of flow of material or enthalpy. Inputs and outputs are streams that cross the vessel boundaries. A heat of reaction within the vessel is a. source. A depletion of reactant in the vessel is a. sink. Accumulation is the time derivative of the content of the reference quantity in the vessel of the volume times the concentration, 3V C /df, or of the total enthalpy of the vessel contents, d[WCfT-T,i)]/dt. 

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