A dynamic optimization strategy is presented to generate customized equations of state (EOS) for the numerical simulation of non-ideal fluids at high density ratio. While stable branches of the analytical EOS are preserved, the spinodal region is self-tuned during the simulation, in order to compensate for numerical errors caused by discretization in phase space. The employed EOS permits the readily setting of the sound speeds for the gas and liquid phases, thus allowing stable simulation with high density (1 : 10 to 1 : 1000) and compressibility ratios (250 : 1–25000 : 1). The present technique is demonstrated for lattice Boltzmann simulation of (free-space) multiphase systems with flat and circular interfaces.

It is shown that the cooperation between short and mid range attraction in Lattice Boltzmann (LB) models with multi-range pseudo-potentials, permits the achievement of phase-separation at liquid/vapor density ratios in excess of 1 : 500, nearly an order of magnitude above the current limits of standard single-range LB models. Inspection of the density configurations reveals that this favourable behaviour results from a sizeable reduction of spurious currents near the liquid/vapour interface. The aforementioned enhancement of the density ratio is obtained at virtually the same computational cost of the standard single-range models. As a consequence, the present results may open the way to a broader spectrum of LB applications, involving the dynamics of complex phase-separating flows with large density ratios.

Computational Fluid Dynamics (CFD) is currently used to design and improve the hydraulic properties of biomedical devices, wherein the large scale blood circulation needs to be simulated by accounting for the mechanical response of red blood cells (RBCs) at the mesoscale. In many practical instances, biomedical devices work on time-scales comparable to the intrinsic relaxation time of RBCs: thus, a systematic understanding of the time-dependent response of erythrocyte membranes is crucial for the effective design of such devices. So far, this information has been deduced from experimental data, which do not necessarily adapt to the broad variety of fluid dynamic conditions that can be encountered in practice. This work explores the novel possibility of studying the time-dependent response of an erythrocyte membrane to external mechanical loads via mesoscale numerical simulations, with a primary focus on the detailed characterisation of the RBC relaxation time t_c following the arrest of the external mechanical load. The adopted mesoscale model exploits a hybrid Immersed Boundary-Lattice Boltzmann Method (IB-LBM), coupled with the Standard Linear Solid (SLS) model to account for the RBC membrane viscosity. We underscore the key importance of the 2D membrane viscosity μ_m to correctly reproduce the relaxation time of the RBC membrane. A detailed assessment of the dependencies on the typology and strength of the applied mechanical loads is also provided. Overall, our findings open interesting future perspectives for the study of the non-linear response of RBCs immersed in time-dependent strain fields.

Lattice Boltzmann Methods for Multiphase Flow Simulations across Scales - Volume 9 Issue 2 - Giacomo Falcucci, Stefano Ubertini, Chiara Biscarini, Silvia Di Francesco, Daniele Chiappini, Silvia Palpacelli, Alessandro De Maio, Sauro Succi