In this paper, we develop a three-dimensional multiple-relaxation-time lattice Boltzmann method (MRT-LBM) based on a set of non-orthogonal basis vectors. Compared with the classical MRT-LBM based on a set of orthogonal basis vectors, the present non-orthogonal MRT-LBM simplifies the transformation between the discrete velocity space and the moment space and exhibits better portability across different lattices. The proposed method is then extended to multiphase flows at large density ratio with tunable surface tension, and its numerical stability and accuracy are well demonstrated by some benchmark cases. Using the proposed method, a practical case of a fuel droplet impacting on a dry surface at high Reynolds and Weber numbers is simulated and the evolution of the spreading film diameter agrees well with the experimental data. Furthermore, another realistic case of a droplet impacting on a super-hydrophobic wall with a cylindrical obstacle is reproduced, which confirms the experimental finding of Liu et al. [“Symmetry breaking in drop bouncing on curved surfaces,” Nat. Commun. 6, 10034 (2015)] that the contact time is minimized when the cylinder radius is comparable with the droplet radius.

We present a mesoscale kinetic model for multicomponent flows, augmented with a short range forcing term, aimed at describing the combined effect of surface tension and near-contact interactions operating at the fluid interface level. Such a mesoscale approach is shown to (i) accurately capture the complex dynamics of bouncing colliding droplets for different values of the main governing parameters, (ii) predict quantitatively the effective viscosity of dense emulsions in micro-channels and (iii) simulate the formation of the so-called soft flowing crystals in microfluidic focusers.

Fluid flows hosting electrical phenomena are the subject of a fascinating and highly interdisciplinary scientific field. In recent years, the extraordinary success of electrospinning and solution-blowing technologies for the generation of polymer nanofibers has motivated vibrant research aiming at rationalizing the behavior of viscoelastic jets under applied electric fields or other stretching fields including gas streams. Theoretical models unveiled many original aspects in the underpinning physics of polymer solutions in jets and provided useful information to improve experimental platforms. This review examines advances in the theoretical description and numerical simulation of polymer solution jets in electrospinning and solution blowing. Instability phenomena of electrical and hydrodynamic origin, which play a crucial role in the relevant flow physics, are highlighted. Specifications leading to accurate and computationally viable models are formulated. Electrohydrodynamic modeling, theories on jet bending instability, recent advances in Lagrangian approaches to describe the jet flow, including strategies for dynamic refinement of simulations, and effects of strong elongational flow on polymer networks are reviewed. Finally, the current challenges and future perspectives in the field are outlined and discussed, including the task of correlating the physics of the jet flows with the properties of relevant materials, as well as the development of multiscale techniques for modeling viscoelastic jets.