Liquid-phase density maximum

FIG. 5 The density of liquid and supercooled water as a function of temperature, illustrating the anomalous liquid phase density maximum of water (data from Lide, 2002-2003). 

Consider a bubble-free slurry. It is known that solid concentrations up to 10% can be handled in slurry reactors (Perry and Green, 1999). Thus, for particle densities of 1-3 g/cm3 and water as liquid phase, the maximum values of VS/VL are 0.1-0.03, which means that hs is 3.2-9.1%. However, for low ms, e.g. 2% (w/v) (g/100 cm3), these values drop to 0.6-1.9%, which is fairly low. Considering that on introducing the gas-phase, the total volume of the reactor will be even higher, the solid-phase holdup is decreased even more and becomes minimal in many practical applications. ... 

Water, both in the liquid and solid (ice) phase, is very peculiar, with properties that differ from most substances. A growing list of currently 69 anomalous properties has been compiled by Chaplin [1]. For example, water is the only substance that can be found in nature in the solid, liquid, and gas phases [2]. In the solid phase, it can exist in a wide variety of crystalline phases. Water is also well known for its density anomalies (such as the liquid s density maximum at 277.13K and the solid s density minimum at 70K [3]), diffusion anomalies... 

In the region of a first-order transition ip has equal minima at volumes V and V2, in line with the Maxwell construction. The mixed phase is the preferred state in the volume range between V and V2. It follows that the transition from vapour to liquid does not occur by an unlikely fluctuation in which the system contracts from vapour to liquid at uniform density, as would be required by the maximum in the Van der Waals function. Maxwell construction allows the nudeation of a liquid droplet by local fluctuation within the vapour, and subsequent growth of the liquid phase. 

Govier et al. (G5, G6, B14) have correlated flow patterns in terms of the location of the two minima and the maximum observed in the pressure drop vs. gas-liquid volumetric feed ratio (12 ) curves (cf. Fig. 2). Gas-liquid ratios, gas flow, liquid flow, pipe diameter and gas-phase density were investigated for the air-water system in isothermal flow. From the correlations presented (as against a function, when n varies... 

In the Gibbs model of an ideal interface there is one problem where precisely do we position the ideal interface Let us therefore look at a liquid-vapor interface of a pure liquid more closely. The density decreases continuously from the high density of the bulk liquid to the low density of the bulk vapor (see Fig. 3.2). There could even be a density maximum in between since it should in principle be possible to have an increased density at the interface. It is natural to place the ideal interface in the middle of the interfacial region so that T = 0. In this case the two dotted regions, left and right from the ideal interface, are equal in size. If the ideal interface is placed more into the vapor phase the total number of molecules extrapolated from the bulk densities is higher than the real number of molecules, N < caVa + c V13. Therefore the surface excess is negative. Vice versa if the ideal interface is placed more into the liquid phase, the total number of molecules extrapolated from the bulk densities is lower than the real number of molecules, N > caVa + surface excess is positive. 

Here ng is the density of the gas molecules, c is the average thermal velocity and 7 is the mass accommodation coefficient This is the maximum flux of gas into a liquid. In many circumstances, however, the actual gas uptake is smaller. It may be limited tty several processes, the most important of which are gas phase diffusion and Henry s Law saturation. The treatment of Henry s Law saturation in turn involves liquid phase diffusion and, in some cases, liquid phase chemical reactions. 

A variation of this technique, the maximum droplet pressure method, can be used to determine interfacial tensions. This technique is especially useful in situations for which the density contrast between the two liquid phases is very low, or non-existent [144,145],... 

Name Manufacturer" Surface Area (m2/g) Packed Density (g/cm3) Pore Size (p.m) Maximum % Liquid Phase... 

A high velocity of the flow, Wg, an elevated density of the fluid as well as a low viscosity of the liquid phase and a low interfacial tension between liquid and fluid represent favourable conditions for high pressure spraying. Pressurised gases evidently possess characteristics similar to those of liquids with respect to the atomisation so that the relationships which are valid for liquid/liquid spraying may lead to realistic results. In the case presented here, a modified Nukiyama-Tanasawa distribution [5] has been used to specify the maximum drop diameter in the spraying process ... 

Subsequently the pure extraction gas flows through a heat exchanger where it is indirectly cooled with water to rise its density. When possible, it is intended to get a liquid phase which is collected in a connected buffer vessel (KP). The installed membrane compressor is able to pump gas as well as highly compressible liquids, which are withdrawn from the buffer vessel To achieve a maximum flexibility with respect to extraction medium and operation parameters a cooler (WT6, for gas phase recompression) or a heater (WT4, for liquid phase recompression) can alternatively be used to bring the recompressed solvent back to extraction temperature Before it is entering the main column a side stream is removed for the feed presaturation. 

The regenerated extraction gas leaves the second regeneration column at its head and is cooled down in (WT3) to a temperature of approximately 20°C. Depending on the type of extraction solvent the buffer vessel (KP) contains liquid phase in equilibrium state with gas or merely gas of high density. In the last case a pressure controlled pneumatic pump feeds fresh solvent into the circular process. If a gas/liquid equilibrium is achieved in the buffer vessel the gas pressure remains constant until a minimal amount of liquid remains there. For this purpose two optical sensors are introduced into the buffer vessel registrating the minimum and maximum extraction liquid level If the level falls below minimum, fresh liquid extraction solvent is refilled. 

Figure 7.17 Left Fluctuating density in a liquid phase near a solid surface, relative to the bulk density p0. The first maximum occurs at the hard-sphere contact distance from the surface, at r = a the molecular diameter. Right Pair potentials for two molecules in the liquid calculated from p(r) - p0exp[-w/kT]...

Transferability from the solid state to the liquid state is equally problematic. A truly transferable potential in this region of the phase diagram must reproduce not only the freezing point, but also the temperature of maximum density and the relative stability of the various phases of ice. This goal remains out of reach at present, and few existing models demonstrate acceptable transferability from solid to liquid phases.One feature of water that has been demonstrated by both an EE model study and an ab initio study °° is that the dipole moments of the liquid and the solid are different, so polarization is likely to be important for an accurate reproduction of both phases. In addition, while many nonpolarizable water models exhibit a computed temperature of maximum density for the liquid, the temperature is not near the experimental value of 277 Eor example, TIP4P and... 

---