## sorbed equilibrium concentration

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Mahmoda
Posts: 19
Joined: Sat Jan 22, 2022 9:51 am
Location: Egypt

### sorbed equilibrium concentration

hi Dr.jirka
i hope you are well
1- i have aproblem with calculation sorbed equilibrium concentration
when using freindlich non linear isotherm s_eq = K_d * C ^ (beta)
= L^ (3beta ) M_s^( -beta) * M_c ^(beta) L^(-3 beta)
= M_c ^(beta) M_s^( -beta) =( Mc/Ms)^ beta
so s_eq will be with unit ( Mc/Ms)^ beta not Mc/Ms , am i Right, if so what i should do to get it into Mc/Ms unit

when using Langmuir isotherm s_eq = (K_d * C ) / ( 1+ eta C)
it will be = (Mc/Ms)/2 am i Right , if so should i doubled the result to get it into Mc/Ms

2- when using non Equilibrium transport with f = 0.1 , the initial conditions still in total concentration (Ms/Ls) or i will check on ( non equilibrium phase is initially at equilibrium with equilibrium phase ) , and if i have to enter soebed non Equilibrium conc. value in the initial conditions , if so how i can calculate it from total concentration.

3 - when calculating total solute mass in the solid phase with tow site sorption = row (f *K_d *C^beta+ s_k) in the manual
but i found it in the forum = row (f *K_d *C^beta+(1-f)* s_k)
where s_k the Sorbed non Equilibrium Conc. from out but files .
which formula i must use

Jirka
Posts: 5522
Joined: Sat Mar 16, 2002 3:47 pm
Location: USA
Location: Riverside, CA

### Re: sorbed equilibrium concentration

For Freundlich sorption, K_d has the following units [L^3Beta M^-beta], and then it should all work out well. See the explanation in the technical manual after eq. 3.3.

For Langmuir sorption, K_d has the following units [L^3 M^-1].

For Chemical Nonequilibrium, you should look at Chapter 3.1.1 for all definitions. Always use definitions from the technical manual, unless we specifically state elsewhere that they are wrong.

J.

Mahmoda
Posts: 19
Joined: Sat Jan 22, 2022 9:51 am
Location: Egypt

### Re: sorbed equilibrium concentration

thank you Dr. jirka

2- when using non Equilibrium transport with f = 0.1 , the initial conditions still in total concentration (Ms/Ls) or i will check on ( non equilibrium phase is initially at equilibrium with equilibrium phase ) , and if i have to enter soebed non Equilibrium conc. value in the initial conditions , if so how i can calculate it from total concentration.

Jirka
Posts: 5522
Joined: Sat Mar 16, 2002 3:47 pm
Location: USA
Location: Riverside, CA

### Re: sorbed equilibrium concentration

Is there some particular reason why you do not consult the Technical Manual? How the initial conditions for solute transport can be specified (including liquid phase concentration or the total information) is described in Section “3.2. Initial and Boundary Conditions”.

One has to, obviously, make some assumption about the nonequilibrium phase (i.e., the sorbed concentration at kinetic sorption sites) when the two-site sorption model is used. The code thus assumes that the nonequilibrium phase is initially in equilibrium with the equilibrium phases. If you choose to specify the initial concentration in terms of the total concentration for the two-site model, you should also check the option that the nonequilibrium phase is initially in equilibrium with the equilibrium phase.

I will be traveling in Italy for the entire month of August and not respond to emails and questions in the forum.

J.