slag and the crucible. This compares with the maximum gasification 29
rate of a graphite surface measured by Blyholder and Eyring to be
3.7 cm^.s ^ cm ^ at 1 $00 °C. Thus the desorption rate measured in the
experiments of Davies et alia would be achieved if the true area of the reaction interface were no more than 2.5 times the apparent area. Since,
_ o at a pressure of 1 atm, a slag with a surface tension of 500 x 10 N/m
and a contact angle of l40° would fill all surface cavities greater than
15 microns in diameter, this ratio between true and apparent reaction
areas could be easily achieved. Thus the desorption of CO would appear to be an attractive possibility as the rate controlling step, but it is difficult to reconcile such a rate controlling step with the linear dependency that has been found (see section 5-l) with the FeO content of the slag. The electron transfer reaction producing the molten iron product could not either be reconciled with this linear dependency, and in any case would occur extremely quickly once the iron phase had been nucleated. Thus it can be concluded that the chemical processes occurring at the slag-carbon interface are unlikely to be rate controlling.
It is worth considering at this stage the behaviour of the molten iron product. The molten iron may form as a thin film clinging to the gas bubbles or as small droplets at the reaction sites. If the iron formed as a thin film clinging to the gas bubbles it would be carried up in the
slag layer with the rising bubbles to collect as fine iron droplets on the upper surface of the slag. Eventually these droplets would coalesce and fall from the upper surface of the slag layer to settle out as an iron layer in the bottom of the crucible. However, such settlement could
never be complete and fine iron droplets would always be found at the upper surface of the slag layer. Although such droplets were sometimes found they were relatively rare. An almost complete covering of iron droplets was, however, always found over the surface of the crucible in contact with the slag, so it was concluded that the iron formed as fine droplets at reaction sites on the crucible surface. The occasional
droplets found on the upper slag surface were thought to have been carried there after being caught up in particularly large and vigorous gas bubbles. Since the iron droplets appeared to be formed on the crucible surface, sufficient heterogeneous nucleation sites would exist there for the nucleation of iron to be easily accomplished so that this step could not be considered as the rate controlling step either.
It is possible that the behaviour of the gas could give rise to the rate 30
controlling step. Indeed, X-ray studies of the reaction between spheres of carbon and iron containing slags in which they had been immersed
suggested that the spheres were shrouded in an apparently continuous gas g
film. Davies et alia considered the possibility that the counter
diffusion of CO and CO^ across this film could be the rate controlling
step, the reaction FeO + CO -- ^ Fe + CO taking place at the slag gas
atom of iron, so that the molar rate at which iron is produced would be
interface, and the reaction 2C0 at the carbon gas interface.
Obviously 1 molecule of CO would be produced by this mechanism for each
equal to the molar transport rate of CO . This latter rate would be given by Fick's first law:-
11 dX.CO2
n CO +
which can be rearranged to give:-
A + x ^ n = - C_D_, dX (7.5)
^ co2) 2 2 2
dx
since stoichiometric considerations at the carbon surface show:-
11 ^11
" CO = 2 " CO 2 (7-6)
However, the partial pressure, and hence the mole fraction, of CO would be extremely low in any gas film that could form at the carbon surface. Certainly the mole fraction of CO in equilibrium with the carbon surface would be <£l, and even that in equilibrium with the slag is unlikely to be greater than 0.1. Under these circumstances, the bracketed term on
the left hand side of equation 7 - 5 is little different from unity, and the
equation can be integrated across the thickness of the gas film to give:-
11 ' DC0/O) c 2 n = C - ^ r ~ y x„_ - x__ (7.7) I CO L 2 CO \ 2J ' ' 1 8
Since ^q q/CO varies as 0 ’ , and C is given by the gas laws as:-
c " ? ■ fe <7'8)
equation (7*7) can be rearranged in the form:-
11 - 11 n ft q
n Fe = n ^ = b CO xj* CO (7'.9)
2 2
where b becomes an empirical constant that must be determined from the reaction rate experimentally determined at one temperature. The results
predict reaction rates at higher temperatures, these rates being shown as line 1 in Figure 43- Also shown on this diagram are the results
obtained by Davies et alia at lower temperatures (line 2) and the results
obtained in this work at higher temperatures (line 3)-
The Figure shows that the rates predicted by equation (7-9) fall below the results obtained in this work and, even more significant, show a negative temperature coefficient at variance with both sets of experi
mental results. This negative coefficient arises because the CO mole
fraction in the gas phase in equilibrium with the slag in equation (7-9) decreases more rapidly with absolute temperature than the 0.8 power. These discrepancies between equation (7-9) and the experimental results lead to the conclusion that any mechanism involving gaseous transport across a continuous film at the reacting carbon surface cannot adequately describe the reaction mechanism.
2+
It is possible that the reaction is controlled by the transport of Fe 2-
and 0 through the slag phase to the reaction interface, in which case