Systems and methods for containing and manipulating liquids, including vessels and unit operations or components of cell culture, cell containment, bioreactor, and/or pharmaceutical manufacturing systems, are provided. The apparatus may include a disposable, collapsible bag adapted for containing a liquid, the collapsible bag in fluid communication with a liquid-solids (e.g., cell) separation device. For example, an outlet of the collapsible bag may be connected to an inlet of the separation device, and an outlet of the separation device may be connected to an inlet of the collapsible bag for recycle. Accordingly, after separating the cells from the liquid in the separation device, the cells can be flowed back into the collapsible bag where they can be re-harvested. Meanwhile, product contained in the liquid can be collected in a separate container. The efficiency of product formation in such a system may be enhanced by using mixing systems described herein.