Lattice Boltzmann across scales: from turbulence to DNA translocation

The capability of the lattice Boltzmann (LB) method to describe complex flow behaviour across a wide range of scales of motion is discussed. This capability is illustrated by means of three examples, straddling across over ten decades of fluid motion, from macroscopic turbulence, to microfluidics, all the way down to nanoscopic flows of biological interest. It is pointed out that each of these applications requires extensions of the original LB scheme, beyond the realm of Navier-Stokes hydrodynamics for which the method was originally designed. The main qualitative ideas behind such extensions are discussed and commented on, with special emphasis on their direct ties with modern non-equilibrium statistical mechanics.

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