Is it the diffusion coefficient that varies spacially as a step function where the two regions are in contact or the boundary condition of the concentration that suddenly change from a value to another during your simulation?

in both cases you can define a step function in >>parameter >function>step, this will create a step function (lets say 'f') that goes from a value 'a' to a value 'b' at a point 'c', and wich you can smooth as you want to make it less sharp and twice derivative.

1/ If it is the diffusion coefficient that you want to model : a=diff_coeff in the first material, b=diff_coeff in the second material, c=the contact coordinate, then you write in the physic section that your diffusion coefficient is f(x).

2/ if it is the boundary condition: a=initial boundary condition, b=2nd boundary condition, c=the instant of transition, then you write in the physic section that your boundary condition is f(t).

Hi Suraksha Sharma,

if I got it right, you are trying to model diffusion in two materials, which means, that the second Fick's law is not applicable anymore. This is simply because the two materials have different solubility for the same element and the diffusion will rather follow the gradient of the chemical potential, than the concentration gradient. I wanted to warn you, just in case, but it would be interesting to share a bit more, if you are somehow modelling diffusion in inhomogeneous domains in COMSOL.

Best of luck!

Best regards,

Antoni

Idir Hamzaoui Thank you for the response. I really appreciate it.

Antoni Artinov I really appreciate your response.

But i have a little confusion here, as the two materials have different diffusion values, I have taken two transport properties in each, with different diffusion coefficients. Isn't it okay to model in that way?

Suraksha Sharma,

by the diffusion coefficients you describe the element transport, but to calculate concentration there is more needed. Consider for example the case of heat diffusion. You describe the heat transfer not only by the heat conductivity but also by the density and the heat capacity, turning this physical quantities into the so called thermal diffusivity. This you need, because the different materials or even more simple one material in its two phases, e.g. solid and liquid iron, have different heat capacities.This says simply, you can store more energy or more of element in the one material, than in the other! The second Fick's law you are using in COMSOL models the transport of the element but only if you have homogeneous materials. In such a case the concentration transport and distribution will depend only on the concentration gradient. The same would happen if you model heat transfer by describing the energy conservation by enthalpy. Here two practical examples for you:

1. Heat transfer: Imagine you have two materials with different heat capacities sharing a boundary with different temperatures on both sides, like if you heat them up and put them together. If you describe the heat transfer in homogeneous materials by using the enthalpy you will have no heat transfer. Why so? Just because you will have no enthalpy gradient (enthalpy = heat capacity*temperature). From this equation you see, you can have a small heat capacity value multiplied by a high temperature on the one side of the boundary and a bigger heat capacity value multiplied by a small temperature value on the other side of the boundary. Hence, there will be no enthalpy gradient and you will conclude that you have no energy/heat flow. But if you describe the heat transfer for inhomogeneous materials, which should be done using the potential, in this particular case the potential is the temperature, you will end with different temperature values on both sides of the boundary, resulting in a temperature gradient leading to a heat/energy flow.

2. Concentration: Imagine you have a glass half full with butter and water. And you have the same concentration of let's say sugar in both the butter and the water. This results in concentration gradient on the joint boundary equal to zero. So, one would conclude, there will be no diffusion. But this is wrong, very wrong and would be correct only in the case of homogeneous materials, which butter and water obviously are not! So what happens in such a case? You need to use another equation, which uses the potential to describe the diffusion, in this example this would be the chemical potential. Similarly to the heat transfer (enthalpy = heat capacity*temperature, where temperature is the potential), (concentration = solubility*chemical potential). From here you see, heat capacity plays the role of solubility and concentration this of enthalpy. Because you have different solubilities in butter and water, just like different heat capacities in the case of heat diffusion, you can save more sugar in the water, than in the butter. This means that by using concentration to describe the process, you end up with small solubility and a high potential value on the one side of the boundary and a higher solubility and a small potential value on the other side of the boundary, resulting in no concentration gradient, just like in the case of heat diffusion, no enthalpy gradient. So, in the case of heat diffusion, you need then to use the potential (temperature) and in the case of element diffusion you need to describe the system by the chemical potential.

I hope my long explanation helps!

Best of luck!

Antoni Artinov

dear Antoni Artinov

how do we calculate chemical potential in comsol?