Boundary condition at material interface

andreasp · October 28, 2013, 05:38

Hi everyone!

I am stuck formulating the correct boundary condition at a material interface in a pure mass transport (diffusion) problem.

I have two domains with different diffusion coefficients. At their interface, I want to ensure both continuity of the concentration profile and of diffusive fluxes:

$\mathbf{n}_1 \cdot (D_1 \nabla c_1) = \mathbf{n}_2 \cdot (D_2 \nabla c_2)$

Currently I am pretty confused, so I have different questions:
1.) Are these conditions correct (in a physical sense)?
2.) Can I really enforce both at the same time? Wouldn't this result in an overdetermined system?
3.) Or does enforcing one of these automatically result in the other one being fulfilled as well?

Thanks in advance for any help!

Best,
Andreas

t.oliveira · March 11, 2016, 07:08

[it is an old discussion, but may be useful for someone]

Hi Andreas,

Shouldn't the conditions be the following?

$D_1 \nabla c_1 =D_2 \nabla c_2$

October 28, 2013, 05:38	Boundary condition at material interface	#1
andreasp New Member Andreas P Join Date: Sep 2010 Posts: 26 Rep Power: 16	Hi everyone! I am stuck formulating the correct boundary condition at a material interface in a pure mass transport (diffusion) problem. I have two domains with different diffusion coefficients. At their interface, I want to ensure both continuity of the concentration profile and of diffusive fluxes: $\mathbf{n}_1 \cdot (D_1 \nabla c_1) = \mathbf{n}_2 \cdot (D_2 \nabla c_2)$ Currently I am pretty confused, so I have different questions: 1.) Are these conditions correct (in a physical sense)? 2.) Can I really enforce both at the same time? Wouldn't this result in an overdetermined system? 3.) Or does enforcing one of these automatically result in the other one being fulfilled as well? Thanks in advance for any help! Best, Andreas

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March 11, 2016, 07:08		#2
t.oliveira Senior Member Thomas Oliveira Join Date: Apr 2015 Posts: 114 Rep Power: 12	[it is an old discussion, but may be useful for someone] Hi Andreas, Shouldn't the conditions be the following? $D_1 \nabla c_1 =D_2 \nabla c_2$