The Eulerian and Lagrangian flow mixing characteristics in a two-dimensional (2D) micro wavy channels for low Reynolds number have been investigated using the Lattice-Boltzmann method (LBM) for solving the governing Boltzmann Transport Equation (BTE). Numerical simulations of a Newtonian compressible flow for Reynolds number flow regimes lower than Re = 0.505 are performed using a computational model of a symmetric wavy channel with many cavities and a geometrical aspect ratio of r = a/(2L) = 0.375, where a is the amplitude of the sinusoidal wall, and L is the cavity periodic length. The Eulerian flow characteristics are determined for different Knudsen numbers with the objective of characterizing time dependent velocity and flow patterns. Then, the Lagrangian characteristics are obtained by integrating the Eulerian velocity field. Thousands of massless fluid particles are used for determining fluid particle Lagrangian trajectories, stretching fields and Lagrangian Lyapunov exponents associated to possible evidences of flow mixing enhancement in different regions of the micro channel. The numerical results demonstrate that low Reynolds number compressible flows in micro wavy channels develop Lagrangian characteristics and stretching field that can lead later to flow mixing enhancement characteristics in an electroosmotic flow in microchannels with wavy, grooved and/or any other surface pattering on the channels walls.

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