### Co-Sedimenting solutes:

To adjust the s and D values in fvm, we need to know what the total density and total viscosity are at a particular radial spot in the cell at a particular scan time.

In order to know what the exact density is, we need to take into account that the gradient forming material is constantly changing its concentration profile until we reach the equilibrium condition of the gradient former.

We proceed as follows:

- from the database, we find the one analyte that is marked as gradient former and use its vbar and MW and, using the s and D from the model, to simulate a finite element solution for its concentration profile. Here, the concentration of the gradient former needs to be calculated in molar or millimolar units (whatever units the viscosity and density coefficients are valid for, which is listed in the buffer component database).

- In the finite volume method, we need to adjust the s and D for the other analytes based on the local density and viscosity values of the gradient former. To find these values, we need to recognize that as far as the overall velocity experiment is concerned, the density and viscosity of the gradient former keeps changing, but the other buffer components (TRIS, phosphate, NaCl?, etc.) are considered to be constant and not gradient forming. The calculation goes like this:

a) find the density and viscosity of the NON-gradient forming buffer components ONLY, say 1.1 and 1.005 respectively.

b) find the density and viscosity of gradient forming buffer component(s) at the given molar concentration from the fem calculation, say density=1.5 and viscosity=0.85 (all the while making sure that these values are calculated for molar concentrations that are actually within the range of the validity of the buffer component's coefficients)

c) subtract the density and viscosity of water (0.998234 and 1.00194) from the values of the gradient former, which gives:

1.5 - 0.998234 = 0.501766 and 0.85 - 1.00194 = -0.15194 (note: a negative value is acceptable here!)

d) add the density and viscosity calculated in a) to the values calculated in c), i.e.:

0.501766 + 1.1 = 1.601766 and 1.005 + (-0.15194) = 0.85306.

c) use density=1.601766 and viscosity=0.85306 to calculate the s and D corrections for any analytes.

- the concentration coming from the FEM calculation serves as the input (milli)molar concentration to the density and viscosity calculation, where density and viscosity are based on the gradient former's coefficients in the buffer component database, plus whatever the other buffer components contribute as a constant offset. The gradient former calculation is valid only for a certain range, which is listed in the database. This range may get exceeded in the FEM calculation. If the concentrations exceeds (in either direction), the program should be stopped and the output should be flagged as questionable. Negative densities or viscosities are not correct and should never occur.