Integrating a parameter in openfoam/paraview, to find a 1-D equation from a 2D flow
 

Dear colleagues!
Consider a 2D, xy rotating mixer, which is used to disperse to liquids in each other. A simple shape is attached below. Obviously, the volume fraction of phases is a function of time, x and y.
My data for validation is the side view of this mixer. Let's say the phase one is transparent. So, imaging is used to give the dispersion of phases in different horizontal lines.
I want to integrate the alpha with respect to y, in order to achieve alpha=f(x) and report it automatically in each time step.
The integration of paraview seems to perform int(int.dy)dx.
What should I do?
Thank you in advance!https://www.researchgate.net/profile...ection_004.jpg