Lattice Boltzmann methods for soft flowing matter

Over the last decade, the Lattice Boltzmann method has found major scope for the simulation of a large spectrum of problems in soft matter, from multiphase and multi-component microfluidic flows, to foams, emulsions, colloidal flows, to name but a few. Crucial to many such applications is the role of supramolecular interactions which occur whenever mesoscale structures, such as bubbles or droplets, come in close contact, say of the order of tens of nanometers. Regardless of their specific physico-chemical origin, such near-contact interactions are vital to preserve the coherence of the mesoscale structures against coalescence phenomena promoted by capillarity and surface tension, hence the need of including them in Lattice Boltzmann schemes. Strictly speaking, this entails a complex multiscale problem, covering about six spatial decades, from centimeters down to tens of nanometers, and almost twice as many in time. Such a multiscale problem can hardly be taken by a single computational method, hence the need for coarse-grained models for the near-contact interactions. In this review, we shall discuss such coarse-grained models and illustrate their application to a variety of soft flowing matter problems, such as soft flowing crystals, strongly confined dense emulsions, flowing hierarchical emulsions, soft granular flows, as well as the transmigration of active droplets across constrictions. Finally, we conclude with a few considerations on future developments in the direction of quantum-nanofluidics, machine learning, and quantum computing for soft flows applications.