Abstract: Provided is a pump system that includes a primary pump and a secondary pump. The primary pump pumps a primary fluid. A first pump unit of the primary pump includes a first inner liner defining a first primary fluid chamber and also includes a first outer liner disposed around the first inner liner. The interior of the first outer liner defines a secondary fluid chamber. The secondary pump pumps a secondary fluid and is in fluid communication with the first secondary fluid chamber to operably pump the secondary fluid into and out of the first secondary fluid chamber, resulting in the compression and expansion of the first inner liner. A first valve is disposed proximate the primary fluid chamber inlet, and a second valve disposed proximate the primary fluid chamber outlet. The first and second valves allow fluid flow in one direction through the primary fluid chamber.