a function of bubble radius r and volume fraction ϕ of bubbles."/>
Figure 8 Rising velocity vSLIP of bubble swarms in a melt at a viscosity of 150 dPa·s as a function of bubble radius r and volume fraction ϕ of bubbles.
(8)
where ϕmax = 0.64 is the maximum value of ϕ as given by random close spherical packing. But the density decrease caused by the presence of bubbles, which is proportional to 1 − ϕ/ϕmax, must also be taken into account. The rising velocity vSLIP of an individual bubble within a bubble swarm of volume fraction ϕ thus is
(9)
The situation is illustrated in Figure 8 for a viscosity of 150 dPa·s, which is that of a typical float glass melt near 1400 °C. Up to a volume fraction of 0.4, bubbles bigger than 0.5 mm in radius safely escape during the available process time, whereas those smaller than 0.1 mm hardly reach any noticeable rising velocity. They rather rest relative to the environment. An especially critical situation occurs when the volume fraction approaches the limit ϕmax. In this case, bubbles of any size become stagnant so that a foam forms on top of the melt in the fining area as observed in a glass of beer. Hence, this problem calls for utmost care in the design of the chemical part of the fining process, and especially of the amount of fining agent used.
5.2 Chemical Fining
As indicated by old glass specimens, bubbles cannot be completely eliminated with only physical fining. In a somewhat paradoxical way, better results are achieved if additional bubbles are produced within the melt at a sufficiently high, yet not too high, volume fraction to coalesce with the bubbles formed or entrapped during melting. The process is known as chemical fining as it involves reactions with gas‐releasing substances.
For reasons of cost, chemical compatibility, and effectiveness, the most widely used agent is sodium sulphate (Na2SO4). By experience, 4 kg of Na2SO4 are added per ton of produced glass. During the early stages of batch melting, the sulfate dissolves in the melt. Under oxidizing conditions, it decomposes at 1400–1450 °C according to the reaction
(10)
where the braces {−} denote the state “dissolved in the melt.” Under reducing conditions, sodium sulphate reacts with the Na2S formed during primary batch melting as follows:(11)
The latter reaction already occurs at temperatures slightly below 1400 °C.
Oxygen fining is an alternative option. The agent typically used is Sb2O3; it is added to the batch in amounts of 3–5 kg per 1000 kg of sand, in combination with a four‐ to eightfold amount of NaNO3 [5]. At the moderately low temperatures of primary batch melting, Sb2O3 converts to {Sb2O5} provided that a sufficiently high oxygen partial pressure in the batch is established (Figure 4, stage b). This is achieved by the action of NaNO3, which decomposes at batch melting temperatures to release oxygen:
(12)
At increasing temperatures, the higher valences of polyvalent ions become increasingly unstable (see Chapter 5.6) so that the fining reaction actually reads
(13)
The release of oxygen bubbles reaches its maximum at about 1300 °C and extends beyond 1400 °C. The negative side effect of this procedure is the formation of the NOx pollutant.
A simple calculation will finally explain why experience and empirical knowledge still play the predominant role in the allotment of fining agents. As used in the batch in Table 4, a mass of 4 kg of Na2SO4 represents 56.3 mol of SO2, which, at 1400 °C, 1 bar, would fill a volume of 7.6 m3. Now, 1 ton of melt, by contrast, fills 0.4 m3 only. Obviously, only a very minor part of the nominal SO2 ends up in gas bubbles otherwise a foam instead of a clear melt would be obtained. The major part of SO2 is in fact lost during batch melting, by evaporation from the melt surface, or is retained in the glass. Thus, the proper allotment of fining rests on the small difference between sulfate input and the above losses. One of the rare attempts to perform a detailed sulfur balance of a glass furnace revealed that approximatively 0.25–0.3 kg of the sulfate added per t of glass are released in the form of fining bubbles [6].
5.3 Homogeneization
After the fining process, the melt is cooled down and homogenized thermally in a steady way. Small residual bubbles resorb themselves because the solubilities of most volatile species strongly decrease with increasing temperatures (Chapter 5.5). For this reason, care has to be taken to prevent local temperature rises from happening during the homogenization process otherwise the so‐called reboil bubbles would form in the melt and could not be removed in any way. Among dissolved gases, N2 distinguishes itself by its decreasing solubility with decreasing temperatures. Thus, N2‐containing bubbles escaping the fining process appear as very tiny bubbles called seeds in the final glass. Their number per unit mass of glass represents an important quality criterion. In container glass, a few tens of seeds per 100 g of glass are accepted. Float glass requires a much higher quality (one visible defect per 20 m2 already is considered a high defect density) and hence, much longer dwell times (approx. 1.5–2 days vs. 1 day for container glass) in the melting compartment.
6 Energetics of Glass Melting
The amount of energy involved in the fusion of glass is an issue of great interest to the glass industry. Referring to comprehensive quantitative treatments ([7, 8] and Chapter 9.8), we will give only a brief sketch of this issue within the scope of this chapter. The approach rests on the fact that, at constant pressure, the heat (enthalpy) transferred to or drawn from a system is thermodynamically the variation of a state function: as such, the intrinsic energy demand depends only on the initial and final states of the system and it can be determined without any consideration of what is going on along the process road.
The initial enthalpy state is given by the sum of standard enthalpies H°i at 25 °C, 1 bar, of the individual raw materials i, weighted by their respective amounts mi in the batch:
(14)
The final enthalpy is given by the standard enthalpies of the batch gases g, H°GASES = ∑ mg·H°g, and of the glass,
