Energy saving in chaotic laminar mixing

Abstract

Chaotic mixing in laminar flows at high Schmidt numbers is considered: the time taken for molecular diffusion to erase the concentration gradient created by advection is estimated. The energy dissipated during mixing in a Stokes flow is calculated, and compared with that for a turbulent flow. It is shown that, at high Schmidt numbers, laminar mixing is more energy-efficient than turbulent mixing. A parameter is then introduced that takes into account both the time spent in mixingand the energy dissipated during this time: in fact, it is the product of time taken and energy dissipated. Again, at high Schmidt numbers, a Stokes flow is shown to be more efficient even when judged by this parameter.