''A higher current flow (amperage) through the cell means it will be passing more electrons through it at any given time. This means a faster rate of reduction at the cathode and a faster rate of oxidation at the anode. This corresponds to a greater number of moles of product. The amount of current that passes depends on the conductance of the electrodes and electrolyte, though it also depends on how much current the power source itself can generate.

Current also makes a difference in that it can shift chemical equilibria by sheer mass action.  For instance, metals plated at a certain current density might form a durable and shiny coating on the substrate, while some other current density might form an excessively grainy, dull coating. In some cases the "plated" metal can even fall away from the electrode as mossy clumps'' 

My conclusions so far:

1) In general, the higher is the current density, the smaller are the EP effects (i.e., higher Cep and smaller Rep, for a RC series representation of the interface impedance). The supporting papers: Historical Evolution of Circuit Models for the Electrode-Electrolyte Interface (L. Geddes, 1997) and Electrode polarization impedance: limits of linearity (H. Schwan and J. Maczuk, 1965).

2) Reducing the physical dimension of a probe may have competitive effects: a) the current density increases, then EP decreases, b) the surface area decreases, then EP increases, c) the increase of the current density may cause rapid deterioration of the electrode, d) the resulting EP effect may present non-linear behavior according to the value of the current density.

3) Increasing too much the current density has eventually a reverse outcome: the EP starts increasing.

4) As a rule-of-thumb, we can mitigate the EP effects by increasing the current density (i.e., by raising the source current for a given dielectric cell and specimen system). However, this action may be constrained by a) the item 3 above, b) the fact that a higher current density may destroy/impact the specimen, and c) the related measurements regulation which may limit the maximum current density (e.g., in vivo measurements).

During my dissertation work, Chapter 2 (http://digitallibrary.usc.edu/cdm/ref/collection/p15799coll3/id/595708), I had introduced a novel methodology that was expected to "control" the EP effects given two different dielectric cells maintaining all the remaining parameters the same (frequency, material, temperature, etc.).

Therefore, if the excitation voltage was the same for those two cells, I empirically proved that the EP effects were indeed different due to distinct current density regimes. By using a total harmonic distortion instrument (FFT Analyzer), I was able to show that the systems were subjected to different non-linearity regimes. However, by properly selecting different voltage-levels for each dielectric cell, we can identify what I call the "kink of the hysteresis".

By selecting a voltage level excitation which puts the system just before the "kink", the system may have its maximum current density while still under linear mode. Therefore, the subtraction method proposed by H. Fricke and H. Curtis to eliminate EP effect from the measurements (“The Dielectric Properties of Water-Dielectric Interphases,” Journal of Physical Chemistry, vol. 41, no. 5, pp. 729–745, 1937) can be successfully applied.

I succeeded in my tests with multiple samples of soils but the process was very cumbersome (we must maintain the temperature fixed during all the experiments with different excitation levels!!) and it took me weeks to perform tests with just very few samples and frequency points.

Currently, I am working on a more practical methodology for the application of those principles.