Relationship between surface area of electrode and reaction rate of hydrogen in fuel cells
Any galvanic cell produces its equilibrium voltage at open-circuit.  Let's say your cell is at +3 V before you allow any current to flow through it.  As soon as you throw the switch, you allow that 3 V to push a current through the cell and some external load that you connect to it. There are several resistances within the cell that act to reduce the cell voltage from the initial 3 V.  The electrolyte resistance, concentration dependent resistances at the electrodes and electron transfer resistances all contribute to the total voltage drop in the cell, and hence, effectively limit the amount of current it can generate.  Typically, one of these resistances is much larger than any of the others depending on the exact configuration and operating conditions of the cell.  It is the electron transfer resistance that you are concerned with in your question.  The traditional way of expressing the voltage drop due to electron transfer resistance is the Tafel equation:

$$\eta _{a}=a+b\, log\, i$$

where $a$ and $b$ are empirical constants, $i$ is the current density and $\eta _{a}$ is what is called the activation overpotential.  We see from this expression that the amount of voltage drop in the cell due to electron transfer increases linearly with the logarithm of the current density.  It is desirable then to minimize $\eta _{a}$ for a battery or flow cell application so that we have the maximum amount of voltage available for pushing current through the load.  A very good way to do this, as you pointed out, is to simply increase the electrode area.  By doing so, we decrease the current density which decreases $\eta _{a}$.  

So, the exact mathematical relationship you seek would be the empirical Tafel expression given above, or even better, the Butler-Volmer equation which is really just a more fundamental way of expressing the Tafel relationship.  All you should need to do is locate some references on platinum polarization in aqueous solutions.  There just happen to be tons of papers on this subject.  Here is one to get you started:


  Sheng W. et al, Journal of The Electrochemical Society, 157 11
  B1529-B1536 2010