MATTER Undergraduate web site
   
    MATTERSolidification | Site Map | Help | Contact us | Glossary | About  
 
     

Steady State Partitioning

  Derivation of equation      
 

Consider change in composition at x1 as front advances. From the Diffusion Equation:

As the profile is steady in the moving frame (x'=x-vDt), the new composition at x=x1 must be the same as the old value vDt behind

Substituting for DC(x1) and expressing in the moving frame  

The profile in the liquid must conform to this equation. The solution will depend on boundary conditions. Here we have CL(x'=0)=CL* and the condition equating the solute rejected at the front to that diffusing away into liquid.

Using these two equations to evaluate the two integration constants, the solution is

If the value of CL* (and hence CS*) is identified, then a specific solution can be given. For example, if CL*=C0/k (CS*=C0), then

 

 
  Kinetics | Redistribution | Cell, dendrite and grain structure | Eutectic

 

 

© 2000 MATTER, The University of Liverpool. All rights reserved.
    contact us   Last updated: July 25, 2000 commercial information