Chapter 2

Fundamentals

Michael Türk

Abstract

Chapter 2 contains the concise description of the basic fundamentals pertaining to supercritical fluids and thermodynamics of binary and ternary mixtures with an emphasis on those systems that involve substances of interest for the various particle formation processes. Density-based models as well as equations of state and their use in modeling and description of binary and ternary vapor-liquid equilibria and the solubility of substances with low volatility are presented. High-pressure techniques as well as particle characterization techniques are also briefly reviewed.

Keywords

Phase behavior; complex mixtures; Equation of State Our human life takes place at so-called ambient pressure (0.1 MPa) and temperature (around 298 K). In opposite thereto, a large number of technical applications are carried out at elevated pressures and temperatures, e.g., coffee, hops and flavors extraction, or chemical production processes such as the ammonia synthesis. Under such process conditions, it is often not practical to distinguish between a liquid and a gas phase. This holds especially for the supercritical region that is characterized by a temperature and pressure above the fluid's critical values (e.g. in case of CO2, 7.4 MPa and 304 K). In this region, only a single homogenous phase exists due to the absence of phase boundaries. Therefore, the expression "fluid" is used for all aggregate states that are not solid.

2.1. Pure Supercritical Fluids

A simplified schematic p-T projection of the phase diagram for a pure substance is shown in Figure 2.1. The three solid lines divide the diagram into the gaseous, liquid, and solid state. At the triple point (TTP), the three phases coexist while along the lines, the two phases-gas-solid, liquid-solid, and liquid-gas-are in equilibrium with each other. The liquid-gas equilibrium pS = pS(T) line ends at the critical point (CP); above the critical temperature TC and the corresponding critical pressure pC, the pure substance is in its supercritical state and is described as a supercritical fluid (SCF). Table 2.1 lists some common SCFs and their corresponding critical data and the temperature at the triple point. Due to its low critical temperature, CO2 is the most common SCF for processes with heat-sensitive substances. At ambient pressure, CO2 is in the gaseous state that enables the formation of a solvent-free product without any thermal or mechanical postprocessing. Furthermore, it is nontoxic, nonflammable, and inexpensive. Compared to CO2, H2O is characterized by its high critical data but also by extraordinary physical-chemical properties. The unique properties of near- and supercritical H2O are the basis for new innovative technologies, in which supercritical H2O acts as a solvent or reactant or catalyst. The solvent behavior of H2O is controlled by its dielectric permittivity that decreases with increasing temperature and increases with increasing density. Therefore, H2O changes its character from a solvent for salt at ambient conditions to a solvent for nonionic species at supercritical conditions. More details about the multitude of applications for near- and supercritical H2O can be found in various articles (e.g., Refs [2-4]).
FIGURE 2.1 Schematic pressure-temperature diagram for a pure substance (left) and density-pressure plot for pure CO2 (right) [5].

TABLE 2.1

Critical Data and Triple Point Temperature for Some Selected Solvents [1]

CHF3
CO2
C2H6
H2O 299.0
304.2
305.4
647.3 4.80
7.38
4.88
22.1 7.52
10.6
6.81
17.4 118.15
216.55
90.07
273.15 The right-hand side of Figure 2.1 shows the density-pressure plot for pure CO2. It shows the liquid-gas saturation curve and the density at a subcritical temperature of 290 K and in the supercritical region at the two temperatures of 305 and 333 K. In this figure, l = g denotes the two-phase region in which both a liquid and a gaseous phase exist. CP stands for the CP of the fluid at which the distinction between a gaseous and a liquid phase disappears. It is obvious that above the fluid's CP, a low-density gas can be compressed into a dense fluid without a phase transition. In the region 1 < T/TC < 1.1, the SCF is highly compressible and minor changes in the temperature or pressure result in large changes in the fluid's density and hence, its solvent power. The comparison between the subcritical (290 K) and supercritical (305 K) isotherm clarifies descriptively that-e.g., at 15 MPa-the density of an SCF (ca 836 kg/m3) is very similar to that of a liquid (880 kg/m3).

TABLE 2.2

Orders of Magnitude for Density and Transport Properties in the Gaseous, SCF, and Liquid State [1]

Density
Viscosity
Diffusivity
Kinematic viscosity kg/m3
Pa s
cm2/s
cm2/s 1
10-5
10-1
10-5 5 × 102
10-4-10-5
10-3-10-4
10-7-10-8 103
10-3
10-6
1 Thus, the extraordinary properties of SCFs are mainly governed by the pressure and temperature dependence of the density. Especially close to the fluid's CP, small changes in either pressure or temperature lead to a dramatic change in the fluid's solvent power. This fact is crucial for SCF-based particle formation processes such as rapid expansion of supercritical solutions (RESS) (Section 4.1) since a nonvolatile solute can be dissolved at high pressure and subsequently recovered by expansion. In case of a very rapid expansion, very high supersaturations can be attained, leading to small and uniform particles. Table 2.2 shows that SCFs are characterized by liquid-like densities and mass transfer properties (viscosities and diffusivities) lying between those of gases and liquids. The viscosity of a gas is typically less than one order of magnitude lower than the viscosity of SCFs, but its density is at least two orders of magnitude higher. The ratio of these two quantities, the kinematic viscosity, is very low in the supercritical region. These specific characteristics are important for various applications in materials processing because natural convection effects are inversely proportional to the square of the kinematic viscosity. Similar to the density, the transport properties such as the viscosity of SCFs vary with changes in pressure and temperature. It is depicted in Figure 2.2 that the viscosity of CO2 increases at 313 K nearly to factor 6 as the pressure increases from 0.1 to 30 MPa. In opposite thereto, the kinematic viscosity decreases by two orders of magnitude as the pressure increases from 0.1 to 7 MPa. The viscosity of sc-CO2 is significantly lower than that of classical liquid solvents (e.g. H2O, 890 µPa/s) resulting in lower pressure drops in pipelines and packed beds columns. The optimization of the current and the development of new SCF-based processes require the knowledge of reliable T, p, and ? (incl. TC, pC, and ?C) data of pure substances and fluid mixtures under subcritical and supercritical conditions. Usually a static equilibrium apparatus, equipped with a view-cell, can be used for the determination of the critical state of pure substances and binary or ternary mixtures by observation of the critical opalescence (Figure 2.3). With carefully carried out decrease (50 mK/h) of the fluid's temperature from the supercritical to the subcritical state caused that the appearance of the fluid changes from colorless to yellowish and reddish tones. Exactly at the CP, the fluid is completely opaque (black). A further temperature reduction to the subcritical state caused that the fluid reaches its colorless appearance again. If the density of the fluid is carefully adjusted, the liquid-vapor interface occurs exactly in the middle of the equilibrium view cell. In this case, the critical density of the fluid can be determined from the known cell volume and the mass of the test fluid. More details about the apparatus and the experimental procedure, especially the determination of the critical data, can be found elsewhere [5,7,8].
FIGURE 2.2 Variation of the viscosity of CO2 with pressure at 313 K [6].
FIGURE 2.3 Observation of the critical opalescence of difluoromethane (CH2F2). The deviation from the critical temperature (351.23 K) and pressure (5.78 MPa) is given below the pictures [7].

2.2. Mixtures Consisting of an SCF and a Low Volatile Substance

For the design of SCF-based particle formation processes, namely RESS and particles from gas-saturated solution (PGSS), binary mixtures consisting of (1) an SCF and (2) a low volatile substance are of...