Mixed transport control in gas-liquid metal reactions
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T H E interpretation of kinetic data on gas-liquid m e t a l reactions controlled by mass transfer depends on a knowledge of whether the control lies in the liquid phase, the gas phase or whether t h e r e is m i x e d control. In the case of a s w a r m of bubbles r i s i n g in a liquid t h e r e is also the possibility of consecutive control,x Here the control changes from one mode to another as the gas composition in each bubble changes as a result of the transfer process involving the bubbles and the melt. During the course of work on gas-liquid m e t a l reactions it b e c a m e c l e a r that the c r i t e r i a for understanding the mechanism of the rate process controlled by mass transport had not previously been worked out and published for all classes of gas-liquid m e t a l reactions. The p u r p o s e of this paper is t o examine the rate of reactions controlled by transport which are of the type A(gas) + B(dissolved) = AB(gas)
[1]
in o r d e r t o establish an unequivocal criterion for the determination of the rate controlling s t e p . An example of this type of reaction is CO + O(dissolved)
=
CO2
[2]
d u r i n g the deoxidation of molten copper by CO prior t o casting into anodes. Another c l a s s of reactions behaves in a r a t h e r s i m i l a r way to reactions of the type given in Eq. [1]. These are reactions of the type A(gas) + B(dissolved) = 2D(gas)
[4]
The equilibrium of such a reaction is pressure dependent but the g e n e r a l features in interpreting kinetic data for the two types of reactions are the s a m e . DEFINITIONS For any gas-liquid m e t a l reaction where the rate is controlled by transport the concentration g r a d i T. DEB ROYand N. H. EL-KADDAH are Post-Doctoral Research Assistants, and D. G. C. ROBERTSON is Lecturer, all with the Department of Metallurgy and Materials Science, Imperial College of Science and Technology, London SW7, England. Manuscript submitted May 6, 1976. METALLURGICAL TRANSACTIONS B
J = klov(CA e
-
CAb).
-
An instructive graph can be drawn3 to demonstrate the relationship between the various concentrations and this is done in Fig. 2(a) for an absorption proc e s s . The surface concentrations are obtained by drawing a line of slope - l / k * from the point A (defining the two bulk concentrations) onto the equilib r i u m line. This construction is valid for the more complex c a s e s considered l a t e r . We now define the quantity 77l, which is the r a t i o of the actual rate to the rate calculated assuming liquid phase control. Ol is a convenient dimensionless quantity which indicates the extent t o which the liquid phase resistance is controlling the r a t e . When ~/l is close to unity the reaction is controlled by
[3]
an example b e i n g the decarburization of molten iron by CO2. CO2 + C(dissolved) = 2CO.
ents in the gas and liquid phases are as sketched in Fig. 1 for an absorption process. Chemical equilib r i u m will be achieved at the surface so that XA s and C A s are related through the equilibrium constant for the reacti
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