I have a problem with the thermodynamic factors in regular solution model in r-component system. I have analytical expressions for chemical potentials μi for i=1,...,r. I want to calculate thermodynamic factors defined as Φij=(nj/RT)*dμi/dnj, where ni is the molar fraction of i-th element. The problem occurs when it comes to derivatives dμi/dnr as the r-th component is a dependent one, since nr=1-sum of other ni. How can it be done? I need these values to calculate the values of partial intrinsic diffusion coefficients from known tracer diffusivities. All values of interactions parameters are known (Miedema's scheme). More details in the attached files. I would be grateful for help.
I suppose what you actually need is Φij=(Nj/RT)*dμi/dNj, where Nj is the number of particles of species, not the mole fraction. If so, make the replacement nk=Nk/N, where N=Sumk Nk is the total number of particles. When taking the derivative with respect to Nj, note that dN/dNj=1. After having proceeded in that way you can return to the mole fractions by the change Nj=N nj.
I once worked on a project involving fish kills below a dam. The fish were getting something like the bends that divers get from decompression. The fish had gas bubbles in their tissue. I'm not a biologist. I got the job because of my experience analyzing mass transfer. Conventional mass transfer analysis (pure single-component diffusion) presumes there is no interaction between the diffusing species (in this case nitrogen and oxygen into water), but this is not always true. Conventional analysis indicated the conditions killing the fish were not physically possible, but examination by the biologists indicated that they were. A lot of experimental data was collected and I was able to show that the diffusion process was subject to both preferential and limited molecular site interactions that resulted in the fish kills. The correct mass transfer analysis confirmed the conclusion of the biologists. The fish were indeed killed by the bends. Sometimes simplifications that result in neat solutions don't accurately represent reality. There is a logical explanation to such things, but it may not be a simple one.
I published some papers for multi-solute systems separated by a membrane, see my publications. Practically all systems in cryobiology consider there is NO interaction between the solute species. It is especially true when they are diluted and you then consider the system of LINEAR equations. However, when you got the total molar concentration not
- Badges
- Science topic
- Similar topics
- Physical Sciences
- Thermodynamics