Flow batteries having a pressure-balanced electrochemical cell stack and associated methods

A method comprising:

• (a) placing an insert in an outflow channel of a flow battery, the insert having a variable width along a length of the outflow channel, the insert having larger widths at locations in the outflow channel that are more removed from an outlet and smaller widths at locations nearer the outlet at one end of the outflow channel;
• the flow battery comprising:
• (i) an electrochemical cell stack comprising a plurality of electrochemical cells in electrical communication with one another, each electrochemical cell configured to circulate an electrolyte solution laterally therethrough;
• (ii) an inlet manifold comprising an inflow channel having a length that is substantially constant in width and cross-section along the length and fluidically connected to an inflow side of each of the plurality of electrochemical cells and positioned longitudinally with respect to the plurality of electrochemical cells, the inflow channel being configured to supply the electrolyte solution to the plurality of electrochemical cells;
• and
• (iii) an outlet manifold having a length, and comprising the outflow channel fluidically connected to an outflow side of each of the plurality of electrochemical cells and positioned longitudinally with respect to the plurality of electrochemical cells, the outflow channel being configured to withdraw the electrolyte solution from the plurality of electrochemical cells through the outlet manifold and out the outlet at the one end of the outflow channel;
• and
• (b) circulating the electrolyte solution through the electrochemical cell stack via the inlet manifold and the outlet manifold.