Fractal cube-induced homogenisation of dual concentration microchannel flow in transitional Re: Lattice Boltzmann modelling

To date, the mixing of multiple species within microchannels relies primarily on infamously slow diffusive processes. Hence, the present study aims to numerically investigate the fundamental transportation and interaction of a dual-concentration fluid by employing fluid flow perturbations induced by a single instance of a 3D fractal geometry. In particular, a D3Q19 lattice-Boltzmann approach is employed to unravel the chaotic advection and the underlying flow dynamics of the multi-length-scale-induced mixing within the transitional flow regime at Reynolds number Re_D = 300. Four obstacle configurations are explored in depth, namely, a control regular cube (RC), two fractal cubes (FC₂^β) with varying blockage ratios (β), and a 45° tilted regular cube (RD). Results show that the FC₂^0.1312 with a reduced β still enhances the overall mixing performance by 10%, while the larger FC₂^0.2383 provides an augmentation of 59% compared to the RC. Furthermore, the effects of pertinent parameters: decay exponent, integral length scale, and energy spectra are studied. One key observation is that a higher decay exponent is correlated to a higher mixing index (MI) due to the precipitous collapse of turbulence intensity which dissipates energy to all scales of motion. The figure of merit (FoM) is employed to appraise the mixing performance of the obstacle relative to the penalty of blockage ratio, for which the FC₂^0.1312 yields the highest FoM. Through the rapid generation and subsequent decay of turbulence intensity, the multi-length scale FC₂^βs reshuffle the advective energy and express a preferred mixing mechanism transversely along the fluid interface, which attains a remarkable localized MI of 87% within ten obstacle diameters downstream from the obstacle position. Overall, this study may shed light on the underlying mechanism-of-action for the fundamental amplification of mixing within a microchannel, which allows for a potential application strategy that extracts highly homogenous mixtures from compact microchannel domains. Thermal mixing is also augmented using FC₂^0.2383 for a range of Reynolds number and shows that the method of assigning passive scalar quantities to the fluid provides a good two-way approximation for concentration/thermal mixing.