Solidification Processing

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Solidification Processing

• Lecture 6 Mass transfer

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Solidification of binary alloy
T
Ca
Cb
Ta
Tb
C
Solidifying temperature relates on solute
concentration
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Modes of mass transfer

• Fluid flows
• Pressure difference, density difference, etc
• Diffusion
• Chemical potential

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Mass diffusion

• Ficks first law

J the diffusion flux D the diffusion
coefficient or diffusivity C the concentration
x is the position
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Mass diffusion

• Ficks first law

• D depends on the temperature, viscosity of the
  fluid and size of the particles.
• D??2/6
• ? atom jump frequency
• atom jump distance
• At melting temperature, diffusivity of carbon in
  liquid steel is about 4x10-9 m2/s.

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Mass diffusion

• 1D steady state

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Ficks second law of diffusion

• From continuum equation and Ficks first law

• Three dimensional system

• Constant D

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Diffusion in multicomponent system
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Diffusion in multicomponent system
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Diffusion in multicomponent system
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Diffusion in multicomponent system
Second law of thermodynamics can be satisfied by
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Diffusion in multicomponent system
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Application
T
C0
C
CS
CI
C0
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Solute diffusion around interface
Local solute change
Solute change due to interface moving
Ficks diffusion
R
solid
liquid
interface
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Solute diffusion around interface
Solution
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Steady state solute distribution in moving
interface
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Question

• Unsteady state solute diffusion