A mixing apparatus including a kinetic energy source, a mixing tank, a pivot guide, and transfer shaft is used to drive a mixing paddle through a circular path within a tank without substantial shaft rotation. Sleeved and sleeveless mixing paddles are provided in combination with sealable mixing tanks. A volumetric compensation system responsive to tank wall deflection is used to maintain the internal volume of a mixing tank within predetermined limits. One mixing apparatus includes multiple mixing shafts and paddles coupled to at least one kinetic energy source. Methods for fabricating sleeved paddle-containing mixing apparatuses are further provided.