  Redox flow batteries (RFBs) are potential solutions for grid-scale energy
storage, and deeper understanding of the effect of flow rate on RFB performance
is needed to develop efficient, low-cost designs. In this study we highlight
the importance of modeling tanks, which can limit the charge/discharge capacity
of redox-active polymer (RAP) based RFBs. The losses due to tank mixing
dominate over the polarization-induced capacity losses that arise due to
resistive processes in the reactor. A porous electrode model is used to
separate these effects by predicting the time variation of active species
concentration in electrodes and tanks. A simple transient model based on
species conservation laws developed in this study reveals that charge
utilization and polarization are affected by two dimensionless numbers
quantifying (1) flow rate relative to stoichiometric flow and (2) size of flow
battery tanks relative to the reactor. The RFB's utilization is shown to
increase monotonically with flow rate, reaching 90% of the theoretical value
only when flow rate exceeds twenty-fold of the stoichiometric value. We also
identify polarization due to irreversibilities inherent to RFB architecture as
a result of tank mixing and current distribution internal to the reactor, and
this polarization dominates over that resulting from ohmic resistances
particularly when cycling RFBs at low flow rates and currents. These findings
are summarized in a map of utilization and polarization that can be used to
select adequate flow rate for a given tank size.
