Hydrodynamic behavior of the pseudopotential lattice Boltzmann method for interfacial flows

A filter inspired by deep-sea glass sponges for oil cleanup under turbulent flow

Oil spill disasters lead to widespread and long-lasting social, economical, environmental and ecological impacts. Technical challenges remain for conventional static adsorption due to hydrodynamic instability under complex water-flow conditions, which results in low oil-capture efficiency, time delay and oil escape. To address this issue, we design a vortex-anchored filter inspired by the anatomy of deep-sea glass sponges (E. aspergillum) by mimicking their exceptional skeletal features and filter-feeding patterns. Results demonstrate that the vortex-anchored filter can retain external turbulent-flow kinetic energy in low-speed vortical flow with small Kolmogorov microscale (85 μm) in the cavity of skeleton, leading to enhanced interfacial mass transfer and residence time by physical field synergy. It improves hydrodynamic stability by reducing Reynolds stresses in nearly quiescent wake flow. The vortex-anchored filter can realize >97% capture of floating, underwater and emulsified oils stably at Reynolds numbers ranging from subcritical to supercritical regimes. This study not only highlights the importance of vortex-anchored mechanism in enhancing interfacial mass transfer and hydrodynamic stability during oil capture beyond previously known benefits of increased residence time, but also represents a paradigm shift to advance biophysically inspired strategies for in-situ, dynamic and robust cleanup of spilled oil, environmental remediation and resource recovery.

Improved hybrid Allen-Cahn phase-field-based lattice Boltzmann method for incompressible two-phase flows

In this work we develop an improved phase-field based lattice Boltzmann (LB) method where a hybrid Allen-Cahn equation (ACE) with a flexible weight instead of a global weight is used to suppress the numerical dispersion and eliminate the coarsening phenomenon. Then two LB models are adopted to solve the hybrid ACE and the Navier-Stokes equations, respectively. Through the Chapman-Enskog analysis, the present LB model can correctly recover the hybrid ACE, and the macroscopic order parameter used to label different phases can be calculated explicitly. Finally, the present LB method is validated by five tests, including the diagonal translation of a circular interface, two stationary bubbles with different radii, a bubble rising under the gravity, the Rayleigh-Taylor instability in two-dimensional and three-dimensional cases, and the three-dimensional Plateau-Rayleigh instability. The numerical results show that the present LB method has a superior performance in reducing the numerical dispersion and the coarsening phenomenon.

Phase-field lattice Boltzmann model for two-phase flows with large density ratio

In this work, a lattice Boltzmann (LB) model based on the phase-field method is proposed for simulating large density ratio two-phase flows. An improved multiple-relaxation-time (MRT) LB equation is first developed to solve the conserved Allen-Cahn (AC) equation. By utilizing a nondiagonal relaxation matrix and modifying the equilibrium distribution function and discrete source term, the conserved AC equation can be correctly recovered by the proposed MRT LB equation with no deviation term. Therefore, the calculations of the temporal derivative term in the previous LB models are successfully avoided. Numerical tests demonstrate that satisfactory accuracy can be achieved by the present model to solve the conserved AC equation. What is more, the discrete force term of the MRT LB equation for the incompressible Navier-Stokes equations is also simplified and modified in the present work. An alternative scheme to calculate the gradient terms of the order parameter involved in the discrete force term through the nonequilibrium part of the distribution function is also developed. To validate the ability of the present LB model for simulating large density ratio two-phase flows, series of benchmarks, including two-phase Poiseuille flow, droplet impacting on thin liquid film, and planar Taylor bubble are simulated. It is found that the results predicted by the present LB model agree well with the analytical, numerical, and experimental results.

A lattice Boltzmann study of particle settling in a fluctuating multicomponent fluid under confinement

We present mesoscale numerical simulations based on the coupling of the fluctuating lattice Boltzmann method for multicomponent systems with a wetted finite-size particle model. This newly coupled methodologies are used to study the motion of a spherical particle driven by a constant body force in a confined channel with a fixed square cross section. The channel is filled with a mixture of two liquids under the effect of thermal fluctuations. After some validations steps in the absence of fluctuations, we study the fluctuations in the particle's velocity at changing thermal energy, applied force, particle size, and particle wettability. The importance of fluctuations with respect to the mean settling velocity is quantitatively assessed, especially in comparison with unconfined situations. Results show that the expected effects of confinement are very well captured by the numerical simulations, wherein the confinement strongly enhances the importance of velocity fluctuations, which can be one order of magnitude larger than what expected in unconfined domains. The observed findings underscore the versatility of the proposed methodology in highlighting the effects of confinement on the motion of particles in the presence of thermal fluctuations.

A unified lattice Boltzmann model and application to multiphase flows

In this work, we develop a unified lattice Boltzmann model (ULBM) framework that can seamlessly integrate the widely used lattice Boltzmann collision operators, including the Bhatnagar-Gross-Krook or single-relation-time, multiple-relaxation-time, central-moment or cascaded lattice Boltzmann method and multiple entropic operators (KBC). Such a framework clarifies the relations among the existing collision operators and greatly facilitates model comparison and development as well as coding. Importantly, any LB model or treatment constructed for a specific collision operator could be easily adopted by other operators. We demonstrate the flexibility and power of the ULBM framework through three multiphase flow problems: the rheology of an emulsion, splashing of a droplet on a liquid film and dynamics of pool boiling. Further exploration of ULBM for a wide variety of phenomena would be both realistic and beneficial, making the LBM more accessible to non-specialists. This article is part of the theme issue 'Progress in mesoscale methods for fluid dynamics simulation'.

Structure and isotropy of lattice pressure tensors for multirange potentials

We systematically analyze the tensorial structure of the lattice pressure tensors for a class of multiphase lattice Boltzmann models (LBM) with multirange interactions. Due to lattice discrete effects, we show that the built-in isotropy properties of the lattice interaction forces are not necessarily mirrored in the corresponding lattice pressure tensor. This finding opens a different perspective for constructing forcing schemes, achieving the desired isotropy in the lattice pressure tensors via a suitable choice of multirange potentials. As an immediate application, the obtained LBM forcing schemes are tested via numerical simulations of nonideal equilibrium interfaces and are shown to yield weaker and less spatially extended spurious currents with respect to forcing schemes obtained by forcing isotropy requirements only. From a general perspective, the proposed analysis yields an approach for implementing forcing symmetries, never explored so far in the framework of the Shan-Chen method for LBM. We argue this will be beneficial for future studies of nonideal interfaces.