Dispensing cap, insertable cartridge, dispensing container, dispensing system, and methods for manufacture and use

A cartridge for a dispensing cap, the cartridge comprising:

• a body removably attachable to a dispensing cap, the body defining at least a portion of a cavity comprising a first fluid, an internal cylindrical wall of the body defining at least a portion of a central opening of the body;
• a valve element attached to an outer surface of the body, wherein a tube portion of the valve element extends within the central opening of the body, the tube portion having a first end to receive a second fluid flowing into the tube portion from the dispensing cap and a second end through which the first and second fluids are dispensed, the tube portion comprising at least one outlet opening in a wall of the tube portion through which the first fluid is able to be dispensed from the cavity to join the second fluid in the tube portion;
• a cartridge piston element disposed within the cavity of the body and about the central opening and movable between a first position and a second position to force the first fluid toward the at least one outlet opening.