Superheated-liquid theory

In this section, the phenomenon of BLEVE is discussed according to theories proposed by Reid (1976), Board (1975), and Venart (1990). Reid (1979, 1980) based a theory about the BLEVE mechanism on the phenomenon of superheated liquids. When heat is transferred to a liquid, the temperature of the liquid rises. When the boiling point is reached, the liquid starts to form vapor bubbles at active sites. These active sites occur at interfaces with solids, including vessel walls. 

Thus, the BLEVE theory predicts that, when the temperature of a superheated liquid is below T, liquid flashing cannot give rise to a blast wave. This theory is based on the solid foundations of kinetic gas theory and experimental observations of homogeneous nucleation boiling. It is also supported by the experiments of BASF and British Gas. However, because no systematic study has been conducted, there is no proof that the process described actually governs the type of flashing that causes strong blast waves. Furthermore, rapid vaporization of a superheated liquid below its superheat limit temperature can also produce a blast wave, albeit a weak... 

Reid s theory that a superheated liquid which flashes below its homogeneous nucleation temperature T i will not give rise to strong blast generation has not been verified. 

Thermodynamic and mechanical equilibrium on a curved vapor-liquid interface requires a certain degree of superheat in order to maintain a given curvature. Characteristics of homogeneous and heterogeneous nucleation can be estimated in the frame of classical theory of kinetics of nucleation (Volmer and Weber 1926 Earkas 1927 Becker and Doring 1935 Zel dovich 1943). The vapor temperature in the bubble Ts.b can be computed from equations (Bankoff and Flaute 1957 Cole 1974 Blander and Katz 1975 Li and Cheng 2004) for homogeneous nucleation in superheated liquids... 

Another theoretical basis of the superheated liquid-film concept lies on the irreversible thermodynamics developed by Prigogine [43]. According to this theory, irreversible chemical processes would be described (Equation 13.17) by extending the equation of De Donder, provided that simultaneous reactions were coupled in a certain thermodynamic model, as follows ... 

This comprehensive survey of the title topic is in three parts, the first dealing with the theoretical background and laboratory studies, with 29 references. The second part, with 21 references deals with case histories and experimental studies of industrial vapour explosions. These involved the systems molten titanium-water, molten copper-water, molten aluminium-water, smelt-water, water-various cryogenic liquids, molten salt-water and molten uranium dioxide-liquid sodium. In the third part (with a further 26 references) is discussion of the various theories which abound, and the general conclusion that superheated liquids most likely play a major role in all these phenomena [1]. A further related publication covers BLEVEs and pressure let-down explosions [2],... 

The second RPT criterion relates to the temperature of the hot liquid. That is, this temperature must exceed a threshold value before an RPT is possible. From one theory of RPTs, the superheated-liquid model (described later), this criterion arises naturally, and the threshold hot-liquid temperature is then equal to the homogeneous nucleation temperature of the colder liquid T. This temperature is a characteristic value for any pure liquid or liquid mixture and can be measured in independent experiments or estimated from theory. From alternate RPT theories, the threshold temperature may be equated, approximately, to the hot fluid temperature at the onset of stable film boiling. 

One experiment which does not seem to fit into the network of the salt-gradient theory was that of Wright and Humberstone (1966), who impacted water on molten aluminum and obtained explosions. These results are at variance with those of Anderson and Armstrong, but the latter worked at 1 bar whereas the former used a vacuum environment. It might be possible that, under vacuum, it is much easier to achieve intimate contact between the aluminum and water and, under these conditions, there may be sufficient reaction between the aluminum and water to allow soluble aluminum salts to form. This salt layer could then form the superheated liquid which is heated to the homogeneous nucleation temperature and explodes. 

This brief commentary on superheated liquids has indicated that they are readily formed if one prevents heterogeneous nucleation of vapor embryos. Also, there is a limit to the degree of superheat for any given liquid, pure or a mixture. This limit may be estimated either from thermodynamic stability theory or from an analysis of the dynamics of the formation of critical-sized vapor embryos. Both approaches yield very similar predictions although the physical interpretation of the results from both differ considerably. 

The above equation allows us to determine the values of the control parameters, p, T, for which a catastrophe, i.e. a spontaneous transition from the state of the superheated liquid to that of the vapour or from the state of the supercooled vapour to that of the liquid, may occur. Let us note at this point that the formalism of elementary catastrophe theory does not permit a description of evolution of the system on leaving the catastrophe surface until returning onto this surface. 

A classical set of experiments was performed by Dergarabedian (D2, D3) who irradiated water, carbon tetrachloride and other liquids, and photographed the asymptotic growth of minute bubbles originating within this uniformly superheated liquid. The superheat range was 2 to 10°C, and the pressure atmospheric, corresponding to Nj>l. The initial and boundary conditions corresponded to the theory, so that the results are susceptible of... 

The theory of bubble nucleation in a superheated liquid was first applied to the concept of thermal inkjet by Allen et al. [7]. They were able to determine the minimum cmiditions for the first bubble nucleation by applying Hsu s theory [10]. Time dependent temperature profiles above a heater surface were obtained. By superimposing the activation curve with the thermal boimdary layer, the initial bubble size and the minimum temperature for nucleation were determined. Based on a one-dimensional model and by assuming the nucleation temperature to be the superheat limit of the liquid at 330°C transient temperature profiles for the heater structure and the bubble surface after nucleation were obtained. It was noticed that the decay time to ambient temperature from its initial state was only several microseconds after 6 ps heating pulse. The thermal effects of the passivation (protective coating) layer on the heater surface were also analyzed. The results showed that the effective pulse energy required for bubble nucleation increases with the thickness of the passivation layer. 

For droplet condensation in supercooled vapors or bubble formation in superheated liquids, density functional theory predicts that the free energy barrier to nucleation vanishes at the spinodal curve. This is an important improvement on classical nucleation theory, which predicts finite barriers irrespective of the depth of penetration into the two-phase region. Density functional theory is an extremely powerful technique for the rigorous calculation of free energies barriers to nucleation. Examples of calculations in non-ideal systems include bubble nucleation in the superheated Yukawa and Lennard-Jones liquids [55, 57] liquid nucleation in dipolar vapors [61] binary nucleation of liquids from vapors [58] and of bubbles from liquids [62] and crystal nucleation [59]. 

The embryos that trigger vapor formation in a superheated liquid are microscopic bubbles small regions where the density is smaller than in the bulk. To calculate the rate of homogeneous nucleation in a superheated liquid according to the classical theory, one must therefore consider the energetics of bubble formation. The contents of vapor embryos can be treated as an ideal gas except near the critical point. Let P be the pressure inside the critical nucleus. Then, P being the bulk pressure in the superheated... 

Equilibritun flash models for superheated liquids are based on thermodynamic theory. However, estimates of the aerosol fraction entrained in the resultant cloud are mostly empirical or semiempirical. Most evaporation models are based on the solution of time dependent heat and mass balances. Momentum transfer is typically ignored. Pool spreading models are based primarily on the opposing forces of gravity and flow resistance and typically assume a smooth, horizontal surface. 

As will be described later in this section, for several types of small-scale tests where RFTs would be expected, an increase in the absolute system pressure had a profound effect in suppressing such incidents. As often noted in previous sections, one current theory to explain RPTs invokes the concept of the colder liquid attaining its superheat-limit temperature and nucleating spontaneously. In an attempt to explain the pressure effect on the superheating model, a brief analysis is presented on the dynamics of bubble growth and how this process is affected by pressure. The analysis is due largely to the work of Henry and Fauske, as attested to by the literature citations. 

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. 

Fig. 18. Application of rate theory and equation-of-state theory to Wismer s data for ether superheated in glass. Horizontal displacements represent superheating vertical displacements represent the liquid in tension. Wismer s original Van der Waals plot was different above is the corrected form as given by Volmer (VI).

As indicated in Sec. IIB, ordinary nucleate boiling is a two-step process. First, nuclei must appear. Second, the nuclei must grow into bubbles large enough to move away from the nucleation sites. The rate of heat absorption by the liquid may be controlled by either one or both of these two processes. The growth of a nucleus (tiny bubble) into ordinary bubbles has received attention recently. The theoretical attack of Forster and Zuber was discussed in Sec. IIB2. Inasmuch as the theory of Zwick and Plesset (P3, P4, Zl, Z2) represents another attempt to obtain exact expressions for bubble growth, and since the theory fits well with the few data for steam bubbles in superheated water, their theoretical method is summarized below. 

Thus, melting of a crystalline substance without superheating is a superficial effect. Pre-melting phenomena are apparently also related to the formation of liquid films on the surfaces of crystals, if not to other incidental causes (for example, impurities), and are not pertinent to Frenkel s theory. Heterophase fluctuations are quite large where the difference between two phases and the surface tension between them tend to zero—near the critical point and near the Curie point. The first case is commonly known, the second was earlier investigated quantitatively in Landau s fine work [13, 14]. 

According to the hot-spot theory (Neppiras Noltingk 1950), the homogeneous ultrasound reaction takes place in the collapsing cavitation bubble and in the superheated (ca. 2,000 K) liquid shell around it. Species with sufficient vapor pressure diffuse into the cavity, where they undergo the effect of adiabatic collapse. 

Another popular concept has been the idea that the hysteresis is caused at the single pore level by the existence of metastable states analogous to the supercooled liquid and superheated vapor states which can be encoimtered in bulk systems when nucleation of condensation or evaporation is delayed. Hysteresis loops of this type will emerge from any theory of the van der Waals or mean field t3q)e. This idea dates back to... 

Light water was superheated in tubes of optieal quartz or pyrex glass. Experiments were made in the pressure ranges 0.1-3.3 MPa (H2O) and 0.1-2.1 MPa (D2O) at nueleation rates 3-10 -5 10 s m. On experimental isobars (Fig. 1) there are no flattened seetions and sections with curvature of different sign characteristic of other liquids. The maximum value of an experimental temperature of superheat in light water at atmospheric pressure is 521.4 K, which is 55 K lower than the theoretical value. For heavy water these values are 531.4 K and 44 K, respectively. With increasing pressure, discrepancies between theory and experiment decrease, which is mainly connected with a decrease in the dimensions of the metastable region. 

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