The stretching and flow mixing enhancement characteristics in mini and micro wavy channels have been investigated by solving the Boltzmann Transport Equation (BTE) with the Lattice-Boltzmann method (LBM). The Eulerian and Lagrangian flow characteristics are obtained for a 2D symmetric wavy channel with the geometrical aspect ratios r = 0.375 and 0.1875, by performing numerical simulations of a Newtonian incompressible flow and a Newtonian compressible flow. Extended and reduced domain are used for determining the existence of spatial periodicity the Eulerian and Lagrangian characteristics for increasing Reynolds numbers. The Eulerian flow characteristics for micro channels configuration are determined for different Knudsen numbers, pressure ratio and accommodation coefficients with the objective of obtaining reliable velocity and flow patterns. The Lagrangian characteristics are obtained by integrating the Eulerian velocity field. Thousands of massless fluid particles are used to determine fluid particle Lagrangian trajectories, future and past stretching fields, and Lagrangian Lyapunov exponents, which are used for determining the channel regions with high stretching and flow mixing enhancement. The numerical results demonstrate that mini and micro wavy channels flows develop different Lagrangian characteristics. In mini wavy channels, flow mixing enhancement develops for time dependent 2D flows; whereas, in micro wavy channels, future and past stretching fields describe existence of flow mixing enhancement for very low, stable and time independent Reynolds number flow regime.

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