Hi Rasoul,

Thank you for the paper.  I will certainly go through this paper and will see whether it can serve my purpose.

Hi Bapin,

Did you try to apply the Kitamura's expression for the lime particles in the slag phase? As I remember, that expression includes the parameters such as : Viscosity, radius of particles, relative velocity of particles in the slag etc. - actually all these parameters must be defined applying Brooks approach for the area calculation.

Kitamura S., Shibata H. and Maruoka N., Kinetic model of hot metal dephosphorization by liquid and solid coexisting slags, Steel research, Vol. 79 (2008), No. 8, pp.586-590.

Dear Yuriy,

Thank you for your thoughtful reply.

I have gone through this paper. I think this correlation is for calculating the mass transfer coefficient of lime dissolution kinetics? Do you have any idea how this correlation is derived? is it from any experimental work?

Actually I am looking for calculating the mass transfer coefficient for chemical interaction of metal droplets while moving through slag-metal-gas emulsion . Here the metal droplets are internally stirred by CO gas bubbles and grows in size. In essence, it is a situation where the droplet surface is a function of time.  In my opinion the simple Higbie's penetration theory for calculating mass transfer coefficient may not work.

Looking froward on your thoughts in this regard.

Hi Bapin,

According to the references, the detailed explanation of Kitamura's correlation is in Japanese. This correlation is a modification of known expressions for the mass transfer coefficient such as: Sh=0.023Re^(1/2)*Sc(1/3) or Sh=2+0.6*Re^(1/2)*Sc(1/3)...

Lime dissolution is also chemical interaction, especially considering the dicalcium silicate formation in the slag. Therefore I suggested to try this approach.

Why the metal droplets grow in size in the slag-metal-gas emulsion? Their sizes should decrease because of chemical reactions (oxidation of metal phase impurities) during the residence time in the emulsions.

In the emulsion a metal droplet has the interracial areas with both slag and gas (CO bubbles). In the case of carbon oxidation you need both areas, but in the case of phosphorus you need only metal-slag area for chemical reaction . How are you going to define these areas?

I have seen a very interesting research performed by Korean scientists. The interaction of one metal droplet with the gas phase was simulated using CFD tools and compared with experimental results. Perhaps you can also make a simple multiphase CFD simulation for one droplet. An experimental investigation for one metal droplet can be done using the levitation melting.

 Hi Yuriy,

Thank you for your valuable suggestions

I am aware of this complication of separating area at slag-metal and metal-gas interface. Currently I don't have any answer for that.

Could you tell me the paper title you are talking about (by Korean Scientist)?

Hi Bapin,

Unfortunately I cannot find the title of that paper now. I'll let you know, when I'll find it. Perhaps this paper can help you as well: Haiping SUN, Reaction Rates and Swelling Phenomenon of Fe–C Droplets in FeO bearing Slag, ISIJ International, Vol. 46 (2006), No. 11, pp. 1560–1569

Good luck!

Hi Bapin, 

               Did you able to find the mass transfer co efficient of droplet stirred by gas bubbles???

Hi Regan, 

I could not fully solve this issue. However, I believe combining the surface renewal theory and CO nucleation theory can solve the issue. May be what you can try is apply surface renewal theory ( Km = 2 (Du/pi*d)^0.5) and replace the diameter d, by correlating with the surface tension of droplet. McMaster university ( Prof Ken Coley's group) has done some work . You can refer to their papers.

Good luck!

Hi Bapin,

I think this paper(recently published online, link attached below) will be very interesting in context of this discussion.

Article Dephosphorization Kinetics between Bloated Metal Droplets an...

Hi Bapin,

I'm out travelling at the moment and can't lay my hands on the book but I think the Poirier and Geiger book Transport Phenomena in Materials has a dimensionless analysis approach that may work for you.

The issue you will have is how do you represent the emulsion... 

Good luck

Brian

Hi Bapin,

I think our recent paper suggested by Ameya contains the answer.  With the very high rates of gas bubbling in bloated droplets, I think it is simplest to consider surface renewal to get mass transfer coefficients. Please note, there is an error in Table VI of the paper. The values we actually used for diffusivity of Phos in the metal are as presented below.

Parameter              Diffusivity*10^5 /(cm2/s) [37]

1813K(1540 oC)      1.86

1853K(1580 oC)      2.14

1913K(1640 oC)      2.62

I hope this helps.

Ken

Dear Brian,

Thank you for the suggestion. It is definitely worth of exploring. Are you talking about the Hughmark relationship to determine the liquid side mass transfer coefficient of a gas-bubble and liquid interface? However, I am interested in estimating the metal side mass transfer coefficient of bloated droplet (at the slag-metal interface ) which is thought to be  increased due to agitation by CO bubbles. If I am correct, this relationship is valid for gas-liquid interface mass transfer. 

Thanks

Bapin