Mixing Versus Stirring

Mixing is the operation by which a system evolves under stirring from one state of simplicity—the initial segregation of the constituents—to another state of simplicity—their complete uniformity. Between these extremes, patterns emerge, possibly interact, and die sooner or later. This review summarizes recent developments on the problem of mixing in its lamellar representation. This point of view visualizes a mixture as a set of stretched lamellae, or sheets, possibly interacting with each other. It relies on a near-exact formulation of the Fourier equation on a moving substrate and allows one to bridge the spatial structure and evolution of the concentration field with its statistical content in a direct way. Within this frame, one can precisely describe both the dynamics of the concentration levels in a mixture as a function of the intensity of the stirring motions at the scale of a single lamella and the interaction rule between adjacent lamellae, thus offering a detailed representation of the mixture content, its structure, and their evolution in time.