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The suspension of porous particles in fluids occurs widely in various natural and industrial processes. However, the sedimentation behavior of porous particles is not extensively understood as the solid impermeable counterparts. In this work, the drafting–kissing–tumbling (DKT) phenomenon in a narrow channel containing porous particles is investigated by the multi-relaxation-time (MRT) lattice Boltzmann method (LBM). The initial particle spacing L p * (1.5 ∼ 6) and Darcy number Da (8 × 10 − 6 ∼ 6 × 10 − 2 ) are examined on the sedimentation process of two particles under three initial arrangements, i.e., the trailing particle is porous (case 1), the leading particle is porous (case 2), and both the particles are porous (case 3). The results show that the presence of porous particles can enhance the interactions between two particles, and increasing the penetrability reduces the particle drag force to accelerate sedimentation. The drafting time is insensitive to Da at small L p * , and it decreases with Da at large L p * in cases 1 and 3 while it changes to increase with Da in case 2. A phase diagram with respect to Da and L p * is further extracted to identify three sedimentation modes of particle pairs. It is found that the transition between the one-off DKT and repeated DKT modes is not affected by L p * in cases 2 and 3, while the critical condition for the non-DKT and one-off DKT modes depends strongly on Da and L p * in case 2. [ABSTRACT FROM AUTHOR]

In this work, a phase-field-based lattice Boltzmann method with reduced spurious velocity is developed for axisymmetric incompressible two-phase flows. Two sets of lattice Boltzmann equations with multiple-relaxation-time collision operators are used to, respectively, recover the conservative Allen–Cahn equation for interface capturing and the hydrodynamic equations. To reduce the spurious velocity, a novel correction term is introduced into the hydrodynamic lattice Boltzmann equation so that the leading truncation error related to the third derivatives of pressure can be partially removed. Simultaneously, the radius-weighted mirror symmetric boundary is applied to the axis of symmetry because all the moments of the distribution functions are proportional to the radial coordinate. Furthermore, the bulk viscosity is able to be changed independent of the shear viscosity through redefining the source term. A series of classical numerical experiments, including stationary droplet, oscillation of an elliptical droplet, bubble rising, drop splashing, have been conducted to test the performance of the proposed model. Numerical results agree well with the analytical solution and published data in literature, which demonstrates the improved accuracy and numerical stability. [ABSTRACT FROM AUTHOR]

The interfacial instability between miscible fluids in a channel is determined by many factors, such as viscosity contrast and the inclination angle. Considering the effect of the gravity field, we investigate the displacement phenomenon between two miscible fluids with different viscosities in an inclined channel. The results show that when the concentration Rayleigh number Ra C < 10 5 , the inclination angle θ ranges from 0 ° to 90 ° , and the natural logarithm of the viscosity ratio R > 0; there are three fluid–fluid interfacial instability regions, namely, viscous fingering, "Kelvin–Helmholtz" (K–H) instability, and "Rayleigh–Taylor" (R–T) instability. A scaling analysis is developed to describe the time evolution of the displacement as described by the displacement efficiency at a fixed viscous ratio. Our analysis indicates that in the viscous fingering region, the time evolution of the displacement efficiency gradually increases with t scaling due to fingering formations; in the K–H and R–T regions, the displacement efficiency rapidly increases with t 1 + Ra C / 10 6 . When considering the effect of the viscosity ratio in the K–H instability region, the displacement efficiency scales as η ∼ t 1 + Ra C / 10 6 R 0.1 . In addition, when the inclination angle is negative or R < 0, the instability phenomenon is not obvious, and the displacement efficiency decreases as the inclination angle or R decreases. [ABSTRACT FROM AUTHOR]

In this paper, a well-balanced discrete unified gas-kinetic scheme (WB-DUGKS) is developed to capture the physical equilibrium state for two-phase fluid systems. Based on the strategies adopted in the well-balanced lattice Boltzmann equation (WB-LBE) [Z. Guo, "Well-balanced lattice Boltzmann model for two-phase systems," Phys. Fluids 33, 031709 (2021)], a novel equilibrium distribution function and a modified force term are employed in the DUGKS framework. Unlike the LBE model, the time step in DUGKS is decoupled from the mesh size such that the numerical stability can be enhanced. First, the well-balanced properties of the method are validated by simulating a stationary droplet. The numerical results show that the WB-DUGKS can successfully reach an equilibrium state and exhibits superior numerical stability at low viscosity compared with the WB-LBE model. Then, the dynamic process of the coalescence of two droplets is simulated. The time scaling predicted by the present model is in good quantitatively agreement with the previous numerical results and experimental data. Overall, the proposed model provides a promising tool for simulating two-phase systems. [ABSTRACT FROM AUTHOR]

Spurious velocities and inaccurate density properties arising from the imbalance of discretized forces at discrete level are frequently observed in numerical simulation of multiphase flows based on lattice Boltzmann equation (LBE) models. In this paper, an improved well-balanced free-energy LBE model is proposed for two phase flows with high Reynolds numbers and large viscosity differences based on the well-balanced LBE [Guo et al., Phys. Fluids 33, 031709 (2021)]. To this end, a free parameter associated with the shear rate is introduced into the equilibrium distribution function. This results in a fluid viscosity that is dependent not only on the relaxation time but also on the introduced parameter. The relaxation time can be chosen to improve the numerical stability and accuracy, while the viscosity is mainly determined by the new parameter. To test the capability of the present model in capturing discrete equilibrium states, both one-dimensional flat interface and two-dimensional stationary droplet are simulated. Numerical results show that the present model is capable of eliminating spurious velocities and maintaining a constant chemical potential when the system reaches an equilibrium state. To further validate the performance of the present LBE for dynamic problems, both binary droplet collision and single bubble rising are performed, which demonstrates that the present model has the capability to deal with two phase flows with high Reynolds number and large viscosity ratio. [ABSTRACT FROM AUTHOR]

Based on the phase-field theory, we present an improved lattice Boltzmann (LB) method for simulating droplet dynamics with soluble surfactants. This method takes advantage of three sets of particle distribution functions for solving the coupled system of two Cahn–Hilliard-like equations and incompressible Navier–Stokes equations. The phase-field model is formulated from the perspective of the Ginzburg–Landau free energy functional, where some modifications introduced circumvent unphysical behavior of the interfacial layer and improve the well-posedness of the model. We also give a comprehensive review on the existing surface tension force formulations and demonstrated that the popular potential form is artificial; instead, an alternative potential surface tension force is deduced. The equation of state accounting for the influence of the surfactant concentration on interfacial tension can be directly incorporated into the present approach, further improving the flexibility of the method. Besides, a linear equilibrium distribution function and a proper source term are introduced into the LB method for surfactants such that it can recover the correct physical formulations for a surfactant-laden multiphase system. An abundance of numerical experiments is carried out to validate the LB method, and the numerical performances of the tensor and potential surface tension forces are also evaluated. It is reported that the potential scheme achieves a better accuracy in solving interfacial dynamics at low surfactant concentrations and also is in favor of lower spurious velocities. In addition, the numerical predictions of surfactant-laden droplet dynamics show good agreement with the literature data. [ABSTRACT FROM AUTHOR]