There are several materials that should work. Your situation isn't too different to loose-laid waterproofing membranes for potable water reservoirs, except you'd be suspending or floating it. Sealing seams and joints is always a problem, together with abrasion/ tearing, but you don't have long-term durability concerns. There are always points in concrete reservoirs where their loose liners finish, such as outlets. You just have a longer edge between liner and concrete.
Google "pond liner" or "waterproofing" and "potable" for some ideas and materials.
Interested to know why you want to divide a reservoir and have the same height of potable water on both sides. Are you doing something on one side and confining contamination?