Superheated liquids existence

Figure 2.9 Representation of pressure-temperature relationship that exists during the growth period of a spherical bubble in a superheated liquid of infinite extent. (From Dwyer, 1976. Copyright 1976 by American Nuclear Society, LaGrange Park, IL. Reprinted with permission.)...

Superheated liquids are liquids which exist at temperatures above their equilibrium boiling point at the system pressure. These liquids are metastable in a thermodynamic sense, i.e., they are stable with respect to small perturbations on the system, but if the perturbation is sufficiently large, superheated liquids will partially vaporize and form a final, more stable state, usually consisting of vapor and residual liquid. 

The basic reason why superheated liquids can exist is that the nucleation step requires that a vapor embryo bubble of a minimum size must be achieved. Vapor embryos less than the critical size are unstable and tend... 

It is not obvious how AF varies with the size of a cluster, because vv depends on the size, but an indirect scheme is available for determining the desired information. For one particular size, R0, there is assumed to be a value of AF for a condition of stability. This means that for a superheated liquid at a stated temperature and pressure, one and only one cluster size is capable of existence for long. This cluster is called a nucleus. A stable cluster is really in a metastable state, as discussed later. However, for any degree of equilibrium, AF must be unaffected by infinitesimal changes in the cluster size. So d(AF)/dR = 0. If vv is defined as the volume occupied by one vapor molecule, then ny = 47r.fi o8/(3ty)- These two manipulations produce a solution for the quantity r v — vl in Eq. (40)... 

The constancy of the critical AT agrees with the equation-of-state explanation of superheated liquids and with the reaction-rate view of nucleation. It means there is an upper temperature limit above which a superheated liquid cannot exist (at a stated pressure) regardless of agitation. 

Any liquid can exist in three thermodynamic states with regard to the phase diagram stable, metastable, and unstable. When it is metastable with respect to its vapour, the so-called superheated liquid persists over the more stable vapour owing to the nucleation barrier related to the cost to create the liquid-vapour interface. Practically speaking, a superheated liquid undergoes any P-T conditions located between the saturation and the spinodal curves (Fig. 1). It should be noted that the term superheating does not refer to a particular... 

PRIMARY NUCLEATION. In scientific usage, nucleation refers to the birth of very small bodies of a new phase within a supersaturated homogenous existing phase. Basically, the phenomenon of nucleation is the same for crystallization from solution, crystallization from a melt, condensation of fog drops in a supercooled vapor, and generation of bubbles in a superheated liquid. In all instances, nucleation is a consequence of rapid local fluctuations on a molecular scale in a homogenous phase that is in a state of metastable equilibrium. The basic phenomenon is called homogeneous nucleation, which is further restricted to the formation of new particles within a phase iminfluenced in any way by solids of... 

We have recently been able to obtain a correlation of the data so that void fractions (volume fractions vapor) can be predicted empirically from the heat fluxes and mass velocities. But in order to determine the qualities, the fluid temperatures must be known because we have seen that in film boiling a superheated vapor exists simultaneously with the liquid at its boiling point. 

A theoretical model for the heterogeneous nucleation was proposed by Hsu [10] for the growth of pre-existing nuclei in a cavity on a heated surface. The model included the effect of nmi-uniform superheated liquid. The equation for the activation curve of bubble nucleation was derived by combining the Clausius-Qapeyron and the Young—Laplace equations. Then, by substituting the linear temperature profile into the equation, the range of active cavity sizes on the heated surface was obtained. 

Experiments with rapid decompression of superheated liquids and droplets exploding near the superheat hmit reveal the existence of steady evaporation waves. An idealized model for steady evaporation waves has been analyzed. A evaporation wave is treated as a jump or discontinuity between metastable liquid and an equilibrium vapor or liquid-vapor mixture. 

These experimental observations of high and low speed waves have naturally led to the suggestion that evaporation waves are analogous to combustion waves and both subsonic (deflagration) and supersonic (detonation) waves may exist in superheated liquids. Indeed, as we discuss below, this analogy is exact in that two such solution branches do exist for steady waves in superheated liquids. This analogy has further suggested the special role of solutions with sonic (relative to the wave) flow downstream ... 

When a vessel bursts in a BLEVE explosion, the mechanical energy contained inside is released (note that toe units of pressure are energy per unit volume). The substance contained in the vessel instantaneously increases in volume due to toe expansion of toe vapor already existing in the vessel at toe moment of toe explosion and the superheated liquid, which undergoes a partial vaporization practically instantaneously (flash). 

If a small ball were balanced exactly on the top of a very large ball, then any displacement of any measurable size in any direction would cause it to roll down the surface of the larger ball. This is an unstable equilibrium. We may think of this as the limiting case of a metastable equilibrium, in which the indentation in which the baU rests in the second part of the figure becomes shallower and shallower, eventually becoming flat and then curved upward. This situation exists in many nucleation phenomena. For example, as the temperature of a superheated liquid droplet is increased, eventually a critical superheat temperature is reached at which the drop boils spontaneously. At this temperature the drop is unstable and its own internal vibrations are apparently enough to cause it to boil. 

The boiling point is limited by the critical temperature at the upper end, beyond which it cannot exist as a liquid, and by the triple point at the lower end, which is at the freezing temperature. Between these two limits, if the liquid is at a pressure higher than its boiling pressure, it will remain a liquid and will be subcooled below the saturation condition, while if the temperature is higher than saturation, it will be a gas and superheated. If both liquid and vapour are at rest in the same enclosure, and no other volatile substance is present, the condition must lie on the saturation line. 

It was found that the steam supply to the reactor was often superheated (just prior to shutdown to 330°C) [10], Although this degree of superheat would not grossly increase the temperature of the inner reactor wall in contact with the liquid (or the bulk liquid temperature) [11], it seems probable that any reaction material splashed onto and dried out at the top of the coil-heated wall would have become heated to a much higher temperature. Further detailed work on the thermal stability of the mixture showed that a previously unsuspected very slow exothermic decomposition existed, beginning at 180°C and proceeding at an appreciable rate only above 200°C, so that the exotherm was insufficient to heat the contents of the reactor from the last recorded temperature of 158°C to the decomposition temperature of 230°C in 7.5 h [12,13,14], It was concluded that an alternative (effectively an external) source of heat was necessary to account for the observed effect, and the residual superheat from the steam at 330°C seems to have been that source. 

A given phase may persist beyond the point at which transition to another phase should properly occur. On the T5 isotherm, for instance, it is possible to compress the vapour in clean conditions beyond point V, as shown by the dots, without condensation occurring. This vapour is supercooled, and Pv > Pl- When disturbed, the supercooled vapour condenses at once. In the same way, clean liquid may be superheated without boiling, in which case Pl > Pv Supercooled or superheated phases are metastable. They appear to be stable, but are thermodynamically unstable, since another state of lower chemical potential exists. 

A few of the many contributors to the classical rate theory of boiling nucleation are Volmer (VI), Becker and Doring (B2), Frenkel (F7), Fisher (F3), and Bernath (B4). All agree that a prime requirement for nucleation to occur in a liquid is that the liquid must be superheated. The bubbles formed are cooler than the liquid therefore nucleation is strictly irreversible. Because of the superheat, a temperature driving force exists between liquid and bubble. However, because surface tension forces are immense for tiny bubbles, a collapsing tendency exists which may counteract the tendency of a bubble to grow by absorbing heat. One problem faced by any theory of nucleation is to explain the formation of a bubble which will not collapse. 

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