The baffled cavity flow—the first representative of a class of chaotic flows produced by time-dependent changes of geometries—is introduced and extensions to spatially-periodic systems proposed. Both experimental and computational results are reported. The goal of the study is to put into evidence some of the steps and considerations when designing a new mixing flow; a related objective is to demonstrate the use of an efficient and accurate numerical technique (BIEM) suitable for mixing studies in time-dependent geometries. Several parameters that affect the degree of mixing are studied: the mixing protocol—how the baffles are alternated and how many baffles are used in the flow during each piecewise motion; baffle sizes and shapes; geometrical and flow parameters, such as the wall displacement per period; and details of the baffle's motions.