Gas-liquid critical state

Fig. 3. PF diagram for a pure fluid (not to scale) point c is the gas—liquid critical state, is the constant pressure at which phase transition occurs at...

Fig. 2. PT diagram for a pure substance that expands on melting (not to scale). For a substance that contracts on melting, eg, water, the fusion curve, A, has a negative slope point /is a triple state point is the gas—liquid critical state (—) are phase boundaries representing states of two-phase equilibrium ...

The two satnration fines—c-a representing satnrated gas and c-b representing saturated liquid— meet at c, which is the highest point of the L+G two-phase area. Point c is the gas-liquid critical state. As temperature is increased from below to approach the critical, the flat gas-liquid coexistence segment of the isotherm shrinks to the point c at the critical temperature. The critical point is a point of inflection of the isotherm. At c. 

Ground State Recovery of Phenol Blue in Fluids near the Gas-Liquid Critical Density Yoshifumi Kimura and Noboru Hirota... 

We have made a sub-picosecond pump-probe transient absorption study on Phenol Blue at 308 K in trifluoromethane near the gas-liquid critical density and at the high density (about twice of the critical density) where small amount of 2,2,2-trifluoroethanol is added as cosolvent. The ground state hole created by the pump pulse is mostly broadened by about 1 ps, and we could not detect any meaningful density effect on this process. 

We start with gas-liquid equilibrium (gle). For simple mixtures of similar components, gas-liquid coexistence states are observed at a wide range of T and p that are bounded at the high-temperature side by the critical states and at the low-temperature side by the formation of solids. In mixtures of large difference in molecular attractive forces, liquid immiscibility takes place. On the high-temperature side, liquid-liquid equilibrium (lie) either merges into gas-liquid equilibrium (gle) or becomes bounded by separate critical states. With extremely dissimilar molecules, the liquid-liquid coexistence phenomenon persists without limit to high temperature, where it turns into gas-gas equilibrium (gge). 

In order to understand the utility of this picture, let us now consider the gas-liquid critical point in the (P,T) plane. While there exists only a fluid state beyond the critical point, one can still find that across the line that extends straight above the Tq the density fluctuation in the system shows a maximum when this line is crossed at different pressures. Thus across this line, the response functions show a maximum. This line is widely known as the Widom line. Now if one assumes that there exists a similar Widom line in the supercooled region corresponding to the second critical point, then one expects the maximum in response function across the line (see Figure 22.3) [6]. 

We have now introduced three semitheoretical equations of state van der Waals (vdW), Redlich-Kwong (RK), and the modified Redlich-Kwong (mRK). Each contains two parameters, a and b. For a particular pure gas, values for a and b can be obtained by fitting to two or more experimental PvT points. Traditionally, however, values have been obtained by matching the equation of state to the gas-liquid critical point, T, P, and Vc- At the critical point the critical isotherm passes through a point of inflection, so we have the two conditions... 

The conditions are often defined in other thermodynamic surfaces where the variables more closely match an equation of state or the experimental conditions. For example, a gas-liquid critical point in a pure fluid is usually defined by... 

Transition-state theory, that is treatment of chemical reactions as steady state processes, first devised by Evans and Polanyi [72] in 1935, has been widely used in modelling the absolute rate coefficients of reactions in both gases and liquids. Eyring s extension defining the volume of activation [73], has also been employed to interpret the pressure variation of rate coefficient data, often with mechanistic application. Activation volume is the particular facet of transition-state theory which has received application to reactions in supercritical fluids, especially in the immediate vicinity of the solvent gas-liquid critical point. Some of this work is reviewed below, beginning with a discussion of the validity of the use of transition-state theory in near-critical and supercritical fluids. 

John Prausnitz had mentioned the excellent agreement with experiment that Mollerup had obtained in the gas-liquid critical region of binary hydrocarbon mixtures. Mollerup s results were obtained with a good reference equation of state for methane (but one which is classical in form and so which does not describe accurately the known nonclassical singularities in the thermodynamic functions at the critical point), and with a one-fluid model based on a mole fraction average (or "mole fraction based mixing rules"). 

Critical Lines. The calculation of the thermodynamic conditions for critical points in even a binary system is a severe test of any method of prediction, because of the surprising variety of critical lines that can occur ( ). The Redlich-Kwong equation has been used by chemical engineers (33, 34, 35) to represent the simplest class of binary system, when there is but one critical line in p-T-x space. This joins the gas-liquid critical point of the two pure components. The treatment described above can represent, quantitatively for simple systems, and qualitatively for more complex systems, the critical lines of many binary mixtures (30). In the more complex of these, the lines representing liquid-liquid critical states Intrude into the gas-liquid critical region, giving rise to a topologically wide variety of behavior. 

The closeness of this and the van der Waals equation of state becomes even more clear if we compute the gas-liquid critical parameters via Ir = Ir = 0. We find... 

The study of how fluids interact with porous solids is itself an important area of research [6], The introduction of wall forces and the competition between fluid-fluid and fluid-wall forces, leads to interesting surface-driven phase changes, and the departure of the physical behavior of a fluid from the normal equation of state is often profound [6-9]. Studies of gas-liquid phase equilibria in restricted geometries provide information on finite-size effects and surface forces, as well as the thermodynamic behavior of constrained fluids (i.e., shifts in phase coexistence curves). Furthermore, improved understanding of changes in phase transitions and associated critical points in confined systems allow for material science studies of pore structure variables, such as pore size, surface area/chemistry and connectivity [6, 23-25],... 

The phenomenon of critical flow is well known for the case of single-phase compressible flow through nozzles or orifices. When the differential pressure over the restriction is increased beyond a certain critical value, the mass flow rate ceases to increase. At that point it has reached its maximum possible value, called the critical flow rate, and the flow is characterized by the attainment of the critical state of the fluid at the throat of the restriction. This state is readily calculable for an isen-tropic expansion from gas dynamics. Since a two-phase gas-liquid mixture is a compressible fluid, a similar phenomenon may be expected to occur for such flows. In fact, two-phase critical flows have been observed, but they are more complicated than single-phase flows because of the liquid flashing as the pressure decreases along the flow path. The phase change may cause the flow pattern transition, and departure from phase equilibrium can be anticipated when the expansion is rapid. Interest in critical two-phase flow arises from the importance of predicting dis-... 

The conditions that apply for the saturated liquid-vapor states can be illustrated with a typical p-v, or (1 /p), diagram for the liquid-vapor phase of a pure substance, as shown in Figure 6.5. The saturated liquid states and vapor states are given by the locus of the f and g curves respectively, with the critical point at the peak. A line of constant temperature T is sketched, and shows that the saturation temperature is a function of pressure only, Tsm (p) or psat(T). In the vapor regime, at near normal atmospheric pressures the perfect gas laws can be used as an acceptable approximation, pv = (R/M)T, where R/M is the specific gas constant for the gas of molecular weight M. Furthermore, for a mixture of perfect gases in equilibrium with the liquid fuel, the following holds for the partial pressure of the fuel vapor in the mixture ... 

Agitated vessels (liquid-solid systems) Below the off-bottom particle suspension state, the total solid-liquid interfacial area is not completely or efficiently utilized. Thus, the mass transfer coefficient strongly depends on the rotational speed below the critical rotational speed needed for complete suspension, and weakly depends on rotational speed above the critical value. With respect to solid-liquid reactions, the rate of the reaction increases only slowly for rotational speed above the critical value for two-phase systems where the sohd-liquid mass transfer controls the whole rate. When the reaction is the ratecontrolling step, the overall rate does not increase at all beyond this critical speed, i.e. when all the surface area is available to reaction. The same holds for gas-liquid-solid systems and the corresponding critical rotational speed. 

For temperatures below the vapor—liquid critical temperature, T, isotherms to the left of the liquid saturation curve (see Fig. 3) represent states of subcooled liquid isotherms to the right of the vapor saturation curve are for superheated vapor. For sufficiently large molar volumes, V, all isotherms are approximated by the ideal gas equation, P = RTjV. Isotherms in the two-phase liquid—vapor region are horizontal. The critical isotherm at temperature T exhibits a horizontal inflection at the critical state, for which... 

For a gas, the effect of pressure on the viscosity depends on the region of P and T of interest relative to the critical point. Near the critical state, the change in viscosity with T at constant pressure can be very large. The correlation of Uyehara and Watson [15] is presented for the reduced viscosity estimated from the corresponding-states method. The critical viscosities of a few gases and liquids are available [15]. These are necessary to calculate the... 

The results given by Fig. 3.4-2 relative to measured viscosities are about 10%. Fig. 3.4-2 shows that the viscosity tends to a minimum at the critical state. Near the critical point, at constant pressure, there are two branches, one in which viscosity increases with increasing temperature (gas-like behaviour), and the other branch where the viscosity decreases with increasing temperature (liquid-like behaviour). 

The interest in mass transfer in high-pressure systems is related to the extraction of a valuable solute with a compressed gas. This is either a volatile liquid or solid deposited within a porous matrix. The compressed fluid is usually a high-pressure gas, often a supercritical fluid, that is, a gas above its critical state. In this condition the gas density approaches a liquid—like value, so the solubility of the solute in the fluid can be substantially enhanced over its value at low pressure. The retention mechanism of the solute in the solid matrix is only physical (that is, unbound, as with the free moisture), or strongly bound to the solid by some kind of link (as with the so-called bound moisture). Crushed vegetable seeds, for example, have a fraction of free, unbound oil that is readily extracted by the gas, while the rest of the oil is strongly bound to cell walls and structures. This bound solute requires a larger effort to be transferred to the solvent phase. 

At ihe critical point the molar volumes of the liquid and of the gas become equal. In general a critical state is characterized by the fact lhal the two coexistent phases (here the liquid and Ihe vapor) are identical. 

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