Storing short, small, intermittent pulses of energy
Disclaimer : i am no physicist, but here is my best guess :

Build a battery

I think that harnessing 40mV would not be very efficient, you should try generating more than that before.

From the paper you linked, i understand that a drop moving on graphene behaves like a current source in parallel with a resistor :


image taken from http://www.nature.com/nnano/journal/v9/n5/full/nnano.2014.56.html?foxtrotcallback=true

For clarity, I will from now on call the resistance in parallel with the drop the intra-cell resistance. 

To allow/improve the energy harnessing, you have two angles of attack : You can either increase the  intra-cell resistance, generating a higher voltage (Ohm's law) and wasting less energy, and add more sources in serie, effectively increasing the voltage, making it easier to harvest.  

Increase the resistance

From Wikipedia, we know that for a given material, resistance is inversely proportional to the cross-section, which means that if you use a thin strip of graphene instead of a sheet, you should obtain better results (higher voltage and longer pulses) around the drop, but worse results between drops, which brings us to my second point :

Connect your "cells" is series

From the same paper (and intuitively), we learn that drops following each other behave like such source-resistor pairs in serie (adding the resistance of the graphene between the drops, which we will call inter-cell resistance). 

Of course, if we want to improve our battery's performance, we have to minimize the  inter-cell resistance, which is directly proportional to the distance between drops and inversely proportional to the graphene strip's width. 

There is some experimentation/optimization work here, to find the best combination between graphene strip width, strip inclination (and thus drop speed), drop frequency, etc.

Using medical devices, you can control your drop frequency, and conduct experiments to find your optimum.

Additional hypothesis

This is a wild guess, but what if instead of a graphene sheet, you used horizontal strip? or even dots? this way, the  intra-cell resistance would be much higher.