The lattice Boltzmann method (LBM) is an alternative method to the conventional computational fluid dynamic (CFD) methods. It gained popularity due to its simplicity in coding and dealing with a complex fluid flow such as the multiphase flow. The method is based on the kinetic theory, which is mesoscopic scale. Hence, applying the LBM method for macroscopic problems requires a proper conversion from the physical scale (conventional units) to the mesoscopic scale (lattice units) and vice versa. The Buckingham π theorem and the principle of corresponding states are the popular methods used for data reductions and unit conversion processes in the LBM. Nevertheless, those methods have some issues, such as difficulty in converting specific quantities, such as thermo-physical properties. The current work uses a novel dimensional analysis method systematically for mapping properties’ units between scales. Moreover, the approach has the flexibility in selecting parameters to ensure the stability of the method of solution. Several benchmark examples are used to evaluate the feasibility and accuracy of the proposed approach. In conclusion, the proposed approach showed the flexibility of the mapping between meso-scale to macro-scales and vice versa on solid bases rather than ad-hoc methods.

Multiple Emulsions (MEs) contain a drop laden with many micro-droplets. A single-step microfluidic-based synthesis process of MEs is presented to provide a rapid and controlled generation of monodisperse MEs. The design relies on the interaction of three immiscible fluids with each other in subsequent droplet formation steps to generate monodisperse ME constructs. The design is within a microchannel consists of two compartments of cross-junction and T-junction. The high shear stress at the cross-junction creates a stagnation point that splits the first immiscible phase to four jet streams each of which are sprayed to micrometer droplets surrounded by the second phase. The resulted structure is then supported by the third phase at the T-junction to generate and transport MEs. The ME formation within microfluidics is numerically simulated and the effects of several key parameters on properties of MEs are investigated. The dimensionless modeling of ME formation enables to change only one parameter at the time and analyze the sensitivity of the system to each parameter. The results demonstrate the capability of highly controlled and high-throughput MEs formation in a one-step synthesis process. The consecutive MEs are monodisperse in size which open avenues for the generation of controlled MEs for different applications.