In this example, let us consider a binary liquid solution that is placed in a cylindrical cell in a high-speed centrifuge, as shown in Figure 1.  The mixture of A and B tends to separate by virtue of the pressure gradient produced in the centrifugal cell.  For the first part of the derivation, we will assume that the length of the cell (L) is short in comparison to the radius of rotation (Ro).  We will also assume that the solution density is a function of the composition only and neglect any changes in the partial molal volumes with composition.   Finally, we will assume that the activity coefficients are constant over the range of compositions existing in the cell.  We will determine the distribution of the two components at steady state in terms of their partial molal volumes, position in the cell and the pressure gradient for the following occurances (click on each to view):

1.) the mole fraction of A in the system, assuming L is negligible (Please click here).

2.) the mole fractions of A and B in the system, assuming L is negligible (Please click here).

3.) the two-compnent system where one component tends to zero, assuming L is negligible (Please click here).

4.) the mole fraction of A in the system, assuming L is NOT negligible (Please click here).

Finally, we will compute the error from neglecting the length, L, of the tube (Please click here).