Application of high-order lattice Boltzmann for binary diffusive mixing in microfluidics: Comparison against fluorescent microscopy

Diffusive mixing between miscible fluids is an important process in many microfluidic applications, especially for biological studies. In microfluidic experiments it is common to observe microscopic fluid dynamics through fluorescence microscopy. Applying this technique to a hydrodynamic focusing device with a core-flow containing ferrofluid and fluorescence, an unexpected physical phenomenon referred to as the ‘saddle-like’ distribution was observed. Lattice Boltzmann (LB) methods have recently gained tremendous popularity as a numerical approach to model microfluidic dynamics. Despite the recent advancements in LB, reports on the application of high-order LB methods to single-phase miscible mixtures in microfluidics have been limited. The work presented here focuses on the application of high-order LB models to the simulation of single-phase binary miscible mixtures in microfluidic systems. We demonstrate the ability of our numerical simulation to capture the characteristics of the ‘saddle-like’ phenomenon and highlight the difficulties and limitations faced when comparing numerical results against experimental fluorescence microscopy with ferrofluids. This work sets the preliminary steps towards a LB model for simulating fluid mixtures in micro- and nanofluidics and allows for future advancements through higher order expansions.