The technical features of solid-electrode batteries (e.g., high energy density, relatively low capital cost ($/kWh)) and flow batteries (e.g., long cycle life, design flexibility) are highly complementary. It is therefore extremely desirable to integrate their advantages into a single storage device for large-scale energy storage applications where lifetime cost ($/kW-h/cycle) is an extremely important parameter. Here, we demonstrate a non-Li-based-flow battery concept that replaces the aqueous solution of redox-active molecules found in typical redox flow batteries with suspensions of hydrophilic carbon particles ("solid suspension electrodes") coated with earth-abundant redox-active metals. The solid suspension electrodes charge by depositing earth-abundant redox-active metals onto the carbon particle suspension, which are then stripped during discharge operation. The electrical contact to the solid suspension electrodes is fed through fixed redox-inert hydrophobic carbon current collectors through "contact charge transfer" mechanism. The hydrophobicity of the current collectors prevents direct plating of redox-active metals onto their surfaces. The above concept was successfully used to demonstrate several non-Li-based battery chemistries including zinc-copper, zinc-manganese oxide, zinc-bromine, and zinc-sulfur, providing a pathway for potential applications in medium and large-scale electrical energy storage.