A disposable material processing apparatus, useable as a bioreactor or fermenter, includes a hollow tank (101) and a mixing paddle (110) disposed within the interior of the tank and adapted to mix contents therein. The paddle may be isolated within a flexible sleeve (140). Various functional elements, such as a sparger, sensor, material extraction conduit, material addition conduit, and/or heat exchange element may be provided, and optionally arranged to travel with the paddle within the tank interior. Baffles may protrude into a mixing tank to enhance mixing. A tank and/or sleeve may comprise polymeric film materials.