The simulation of multiphase flows is an outstanding challenge, due to the inherent complexity of the underlying physical phenomena and to the fact that multiphase flows are very diverse in nature, and so are the laws governing their dynamics. In the last two decades, a new class of mesoscopic methods, based on minimal lattice formulation of Boltzmann kinetic equation, has gained significant interest as an efficient alternative to continuum methods based on the discretisation of the NS equations for non ideal fluids. In this paper, three different multiphase models based on the lattice Boltzmann method (LBM) are discussed, in order to assess the capability of the method to deal with multiphase flows on a wide spectrum of operating conditions and multiphase phenomena. In particular, the range of application of each method is highlighted and its effectiveness is qualitatively assessed through comparison with numerical and experimental literature data.
We point out a formal analogy between the Dirac equation in Majorana form and the discrete-velocity version of the Boltzmann kinetic equation. By a systematic analysis based on the theory of operator splitting, this analogy is shown to turn into a concrete and efficient computational method, providing a unified treatment of relativistic and nonrelativistic quantum mechanics. This might have potentially far-reaching implications for both classical and quantum computing, because it shows that, by splitting time along the three spatial directions, quantum information (Dirac-Majorana wave function) propagates in space-time as a classical statistical process (Boltzmann distribution).
The phenomenon of Anderson localization in expanding one-dimensional Bose-Einstein condensates is investigated by numerically solving the Gross-Pitaevskii equation with a random speckle potential. To this purpose, a quantum lattice Boltzmann (QLB) method is used, and compared with a standard Crank-Nicolson scheme. The QLB simulations show evidence of Anderson localization even for relatively low-energy condensates, with a healing length as large as one-tenth of the Thomas-Fermi length. Moreover, very long-time simulations, lasting up to 15 000 optical confinement periods, indicate that the Anderson localization degrades in time, although at a very slow pace. In particular, the inverse localization length is found to decay according to a t;{-1/3} law. This lends support to the idea that localized wave functions, although not strictly ground states, represent extremely long-lived metastable states of the expanding condensate.
Numerical simulations with previous formulations of the quantum lattice Boltzmann (QLB) scheme in three spatial dimensions showed significant lack of isotropy. In two or more spatial dimensions the QLB approach relies upon operator splitting to decompose the time evolution into a sequence of applications of the one-dimensional QLB scheme along coordinate axes. Each application must be accompanied by a rotation of the wave function into a basis of chiral eigenstates aligned along the relevant axis. The previously observed lack of isotropy was due to an inconsistency in the application of these rotations. Once this inconsistency is removed, the QLB scheme is shown to exhibit isotropic behavior to within a numerical error that scales approximately linearly with the lattice spacing. This establishes the viability of the QLB approach in two and three spatial dimensions.
Flows in microcapillaries and associated imbibition phenomena play a major role across a wide spectrum of practical applications, from oil recovery to inkjet printing and from absorption in porous materials and water transport in trees to biofluidic phenomena in biomedical devices. Early investigations of spontaneous imbibition in capillaries led to the observation of a universal scaling behavior, known as the Lucas-Washburn (LW) law. The LW allows abstraction of many real-life effects, such as the inertia of the fluid, irregularities in the wall geometry, and the finite density of the vacuum phase (gas or vapor) within the channel. Such simplifying assumptions set a constraint on the design of modern microfluidic devices, operating at ever-decreasing space and time scales, where the aforementioned simplifications go under serious question. Here, through a combined use of leading-edge experimental and simulation techniques, we unravel a novel interplay between global shape and nanoscopic roughness. This interplay significantly affects the early-stage energy budget, controlling front propagation in corrugated microchannels. We find that such a budget is governed by a two-scale phenomenon: The global geometry sets the conditions for small-scale structures to develop and propagate ahead of the main front. These small-scale structures probe the fine-scale details of the wall geometry (nanocorrugations), and the additional friction they experience slows the entire front. We speculate that such a two-scale mechanism may provide a fairly general scenario to account for extra dissipative phenomena occurring in capillary flows with nanocorrugated walls.
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