[25/11/20] Surface nanodrops and nanobubbles: a classical density functional theory study. Our recently published article in Journal of Fluid Mechanics presents a fully microscopic study of the interfacial thermodynamics of nanodrops and nanobubbles, adsorbed on flat substrates with first-order wetting. We show that both nanodrops and nanobubbles are thermodynamically accessible in regions, demarcated by the spinodals of planar wetting films, with nanobubbles occupying a relatively bigger portion of the phase space. While nanodrops can be described as near-spherical caps of Laplace radius, the radius of nanobubbles is very different from the Laplace value. Additionally, nanobubbles are accompanied by a thin gas film adsorbed on the substrate. By computing the interface binding potential, we relate the sphericity of nanodrops to the thin–thick liquid film coexistence (prewetting transition), whereas nanobubble shapes are determined only by the decay of the fluid–substrate forces.

[12/10/20] A theoretical framework to describe the dynamics of reacting multi-species fluid systems in-and-out of equilibrium. Our last study entitled "Memory effects in fluctuating dynamic density-functional theory: theory and simulations" has been published in Journal of Physics A: Mathematical and Theoretical. Our starting point is the system of generalised Langevin equations which describes the evolution of the positions and momenta of the constituent particles. One particular difficulty that this system of generalised Langevin equations exhibits is the presence of a history-dependent (i.e. non-Markovian) term, which in turn makes the system's dynamics dependent on its own past history. With the appropriate definitions of the local number density and momentum fields, we are able to derive a non-Markovian Navier–Stokes-like system of equations constituting a generalisation of the Dean–Kawasaki model. These equations, however, still depend on the full set of particles phase-space coordinates. To remove this dependence on the microscopic level without washing out the fluctuation effects characteristic of a mesoscopic description, we need to carefully ensemble-average our generalised Dean–Kawasaki equations. The outcome of such a treatment is a set of non-Markovian fluctuating hydrodynamic equations governing the time evolution of the mesoscopic density and momentum fields. Moreover, with the introduction of an energy functional which recovers the one used in classical density-functional theory and its dynamic extension (DDFT) under the local-equilibrium approximation, we derive a novel non-Markovian fluctuating DDFT (FDDFT) for reacting multi-species fluid systems. 

[30/03/20] Well-balanced finite-volume schemes for hydrodynamic equations with general free energy. Well-balanced and free energy dissipative first- and second-order accurate finite-volume schemes are proposed for a general class of hydrodynamic systems with linear and nonlinear damping. The variation of the natural Lyapunov functional of the system, given by its free energy, allows for a characterization of the stationary states by its variation. An analogous property at the discrete level enables us to preserve stationary states at machine precision while keeping the dissipation of the discrete free energy. This is the central idea of our latest published article in SIAM Multiscale Modeling & Simulation. By performing a careful validation in a battery of relevant test cases, we show that these schemes can accurately analyze the stability properties of stationary states in challenging problems such as phase transitions in collective behavior, generalized Euler--Poisson systems in chemotaxis and astrophysics, and models in dynamic density functional theories.