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Unit of Ion mobility (Nernst Plank Equation)

Posted 06.07.2012, 15:14 GMT-4 Version 4.2 3 Replies

Dao Trinh (COMSOL)
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Hello,

In Nernst Plank equation, we must enter the mobility of one ion for the migration in electric field.
But in Comsol, the unit of the mobility is [S.mol/kg].
In the scientific articles, they use the mobility with unit [m^2/V/s]. [1]

So can Comsol staff explains me how to convert the mobility in science to the mobility in Comsol ?


[1] en.wikipedia.org/wiki/Electrical_mobility

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3 Replies Last Post 20.08.2012, 23:28 GMT-4
Oscar Vera
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Posted: 1 decade ago 09.07.2012, 09:36 GMT-4
Hi,


the migration term can also be written in function of the transference number, and then you can obtain a formula to calculate the mobility.

I think it is:

u=(t_i*i)/(c_i*delta_phi*F^2+z_i^2)

with
u: mobility [s.mol/kg]
t_i: transfer number of the ion i [1]
i: current density [A/m^2]
c_i: concentration of ion i [mol/m^3]
delta_phi: electric potential [V]
F: Faraday constant (96485 [(A*s)/mol]
z_i: elementary charge of the ion i [1]

i/delta_phi is equal to the conductivity K in [S/m] so,

u=(t_i*K)/(c_i*F^2*z_i^2)

Hope it is correct
Hi, the migration term can also be written in function of the transference number, and then you can obtain a formula to calculate the mobility. I think it is: u=(t_i*i)/(c_i*delta_phi*F^2+z_i^2) with u: mobility [s.mol/kg] t_i: transfer number of the ion i [1] i: current density [A/m^2] c_i: concentration of ion i [mol/m^3] delta_phi: electric potential [V] F: Faraday constant (96485 [(A*s)/mol] z_i: elementary charge of the ion i [1] i/delta_phi is equal to the conductivity K in [S/m] so, u=(t_i*K)/(c_i*F^2*z_i^2) Hope it is correct
John H.
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Posted: 1 decade ago 10.07.2012, 04:21 GMT-4
In Nernst Plank equation, we must enter the mobility of one ion for the migration in electric field.
But in Comsol, the unit of the mobility is [S.mol/kg].
In the scientific articles, they use the mobility with unit [m^2/V/s]. [1]

So can Comsol staff explains me how to convert the mobility in science to the mobility in Comsol ?


If anyone was Comsol staff around here, I would have thought it was you. That's because you have "COMSOL" written in parentheses right next to your user name, which would typically indicate that... People answering in the forum are (mostly) regular users. To get an answer from Comsol staff, you would have to (be paying for and) contact Support.

To try to answer your question... Assuming that by "[S.mol/kg]" you meant "[s.mol/kg]", I think the difference between the two definitions is just a factor of the Faraday constant (elementary charge times Avogadro's constant). To be sure, you have to look at the term that describes the migration of ions in the electric field in whichever Comsol module you use (see the documentation) and compare it to the definition used in other literature (like the Wikipedia article).
[QUOTE]In Nernst Plank equation, we must enter the mobility of one ion for the migration in electric field. But in Comsol, the unit of the mobility is [S.mol/kg]. In the scientific articles, they use the mobility with unit [m^2/V/s]. [1] So can Comsol staff explains me how to convert the mobility in science to the mobility in Comsol ?[/QUOTE] If anyone was Comsol staff around here, I would have thought it was you. That's because you have "COMSOL" written in parentheses right next to your user name, which would typically indicate that... People answering in the forum are (mostly) regular users. To get an answer from Comsol staff, you would have to (be paying for and) contact Support. To try to answer your question... Assuming that by "[S.mol/kg]" you meant "[s.mol/kg]", I think the difference between the two definitions is just a factor of the Faraday constant (elementary charge times Avogadro's constant). To be sure, you have to look at the term that describes the migration of ions in the electric field in whichever Comsol module you use (see the documentation) and compare it to the definition used in other literature (like the Wikipedia article).
DH Chang
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Posted: 1 decade ago 20.08.2012, 23:28 GMT-4
Let u_i be the mobility with the unit of [s.mol/kg]; and u_e for [m^2/(V.s)].
Their relationships are:

u_e=u_i*F

Let's check the units of the right hand side of above equation.

u_i*F=[s.mol/kg]*[C/mol]
=[s.C/kg]
=[s.C.(m/s^2)/N] , (Newton's Law F=M*a: [N]=[kg]*[m/s^2))
=[C.m/(N.s)]
=[m/((N/C).s)]
=[m/((V/m).s)] , (Definition of electric field: F=Q*E: [N]=[C]*[V/m])
=[m^2/(V.s)]=u_e
Let u_i be the mobility with the unit of [s.mol/kg]; and u_e for [m^2/(V.s)]. Their relationships are: u_e=u_i*F Let's check the units of the right hand side of above equation. u_i*F=[s.mol/kg]*[C/mol] =[s.C/kg] =[s.C.(m/s^2)/N] , (Newton's Law F=M*a: [N]=[kg]*[m/s^2)) =[C.m/(N.s)] =[m/((N/C).s)] =[m/((V/m).s)] , (Definition of electric field: F=Q*E: [N]=[C]*[V/m]) =[m^2/(V.s)]=u_e

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