Lattice Boltzmann-based microchannel concentration mixing with surface roughness-mediated flow dynamics

Efficient mixing at the microscales is essential for optimizing mass transfer and reaction rates in various microfluidic applications, underscoring the significance of comprehending and manipulating surface roughness to improve mixing performance. Surface morphology in microchannels is inherently influenced by fabrication and post-treatment. This study investigates the effects of three-dimensional (3D) Gaussian-generated random roughness on species homogenization. Nine roughness profiles, varying in (a) relative roughness (ε = 0.4%, 0.7%, 1.0%) and (b) correlation length (k = 10%, 20%, 30%), form the channel base at ReDh = 100. Using the lattice Boltzmann method, we examine the mixing efficiency (MI), velocity statistics, and spatial frequency. Higher ε enhances near-wall mixing, with a 5.7% MI increase for ε = 1.0% compared to 0.4%. Conversely, shorter correlation lengths create more rugged surfaces, increasing interfacial area for diffusion and thereby elevating the near-wall MI by 8.4% when k decreases from 30% to 10%. Spatial frequency analysis confirms that higher spatial frequencies (shorter spatial wavelengths, lower k) improve near-surface mixing. However, smoother surfaces (higher k) reduce global flow resistance, enhance central advective effects, and improve overall outlet mixing. Thus, for practical applications emphasizing outlet performance, lower ε and higher k yield superior results. This study not only advances our understanding of surface roughness parameters for fluid mixing in rough-walled microchannels and highlights the significance of spatial frequency characteristics but also offers valuable insights into optimizing mixing processes in diverse applications.