Mixing (physics)

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In physics, there are several distinct notions of mixing, all of which try to capture the common-sense notion of mixing, but using rather disparate formal methods, techniques and definitions. One approach is to focus on mixtures of fluids, in three-dimensional space, described by differential equations suitable for fluids, such as the Navier–Stokes equations. The route to the final mixed state typically proceeds through turbulence created during mixing. A second approach considers the mixing of aggregates, such as rocks and sand, which are lumpy on the small scale; this is commonly seen in mixing in process engineering. A third approach uses the mathematical formalisms of measure theory and measure-preserving dynamical systems, to define mixing abstractly for generic dynamical systems in arbitrary dimensions. For example, by assigning a position and a velocity to each atom in a fluid, the mixing takes place in a ${\displaystyle 6^{N}}$-dimensional space, where ${\displaystyle N}$ is approximately the Avogadro number and ${\displaystyle 6=3+3}$ is the dimension of the phase space (position plus velocity) of a single atom.