Proceedings of the Institution of Mechanical Engineers,Part C: Journal of Mechanical Engineering Science

A regularized lattice Bhatnagar–Gross–Krook model for flow and heat transfer in porous media at the representative element volume scale is presented. In the model, the regularization process is extended to the existing Darcy–Forchheimer-based lattice Bhatnagar–Gross–Krook scheme. Numerical results show good agreement between the present model and the previous ones. Also, the present model shows better numerical stability than its lattice Bhatnagar–Gross–Krook counterpart.

A zero-interfacial-force condition is derived and implemented to improve the wetting boundary scheme for a lattice Boltzmann color-gradient model. This new wetting boundary scheme is validated by two static problems, i.e. a droplet resting on a flat surface and a cylindrical surface, and one dynamic problem, i.e. the capillary filling in a two-dimensional channel. In these simulations, we observe that non-physical mass transfer is suppressed and spurious velocities become smaller. Meanwhile, accurate results including dynamic contact line movement are achieved for a broad range of contact angles. The model is then applied to study the displacement of immiscible fluids in a two-dimensional channel. Both the displacement velocity and the change rate of finger length are found to exhibit a linear dependence on the contact angle at the viscosity ratio of unity. The displacement velocity decreases but the change rate of finger length increases with increasing capillary number, while the displacement velocity tends to be constant, i.e. two-thirds of the maximum inlet velocity, at high viscosity ratios or low capillary numbers. In contrast to the displacement velocity, the change rate of finger length is negligible at high viscosity ratios or low capillary numbers, where the finger length is in an equilibrium state, while the equilibrium finger length itself is smaller at a higher viscosity ratio or a lower capillary number.

The coalescence between a free droplet and a sessile droplet on wettable substrate is numerically studied. The axisymmetric lattice Boltzmann method for two-phase flows is used in modeling. Here the contact angle hysteresis (prescribed by advancing angle θ A and receding angle θ R ) is taken into account. The effects of Ohnesorge number (Oh), contact angle and its hysteresis, and the radius of the free droplet on the coalescence dynamics are investigated in detail. The Oh numbers ranging from 0.02 to 0.15 here makes the radius of the liquid bridge r and the time t follow power law. Also, Oh has remarkable impact on the development of capillary wave and on the amount of kinetic energy released from coalescence. It is found that the curve of the wetting radius varying with time includes several plateau stages, which is a typical characteristic for the effect of contact angle hysteresis. The larger window of contact angle hysteresis would result in smaller steady wetting radius after coalescence. Compared with the existence of contact angle hysteresis, the absence of contact angle hysteresis makes the droplets system release more kinetic energy during the coalescence but the released kinetic energy decays more rapidly and soon reduces to zero. Oppositely, if the contact angle hysteresis exists, the released kinetic energy would oscillate for a period of time before approaching zero.

Understanding the dynamic characteristic of the cavitation bubble near a solid wall is a fundamental issue for the bubble collapse application and prevention. In the present work, an improved three-dimensional multi-relaxation-time pseudopotential lattice Boltzmann model is adopted to investigate the cavitation bubble collapse near the solid wall. With respect to thermodynamic consistency, Laplace law verification, the three-dimensional pseudopotential multi-relaxation-time lattice Boltzmann model is investigated. By the theoretical analysis, it is proved that the model can be regarded as a solver of the Rayleigh–Plesset equation, and confirmed by comparing the results of the lattice Boltzmann simulation and the Rayleigh–Plesset equation calculation for the case of cavitation bubble collapse in the infinite medium field. The bubble collapse near the solid wall is modeled using the improved pseudopotential multi-relaxation-time lattice Boltzmann model. We find the lattice Boltzmann simulation and the experimental results have the same dynamic process by comparing the bubble profiles evolution. Form the pressure field and the velocity field evolution it is found that the tapered higher pressure region formed near the top of the bubble is a crucial driving force inducing the bubble collapse. This exploratory research demonstrates that the lattice Boltzmann method is an alternative tool for the study of the interaction between collapsing cavitation bubble and matter.

The effects of initial conditions on the coalescence of two equal-sized air micro-bubbles (R₀) in water are studied using the lattice Boltzmann method. The focus is on effects of two initial set-ups of parent bubbles, separated by a small distance d and connected with a neck bridge radius r₀, on the neck bridge growth at the early stage of the bubble coalescence. A sophisticated free energy lattice Boltzmann method model based on the Cahn-Hilliard diffuse interface approach is employed. This lattice Boltzmann method model has been demonstrated suitable for handling a large density ratio of two fluids up to 1000 and capable of minimizing the nonphysical spurious current. In both initial scenarios, the neck bridge evolution exhibits a half power-law scaling, r / R 0 = A 0 ( t / t i ) 1 / 2 after a development time. The half power-law agrees with the recent analytical prediction and experimental results. It has been found that smaller initial separation distance or smaller initial neck bridge radius results in faster growth of neck bridge and bubble coalescence, which is similar to the effects of these two initial scenarios on droplet coalescence. The physical mechanism behind each behavior has been explored. For the initial connected case, faster neck growth and longer development time corresponding to smaller initial neck radius is due to the significant bias between the capillary forces contributed by the meniscus curvature and the neck bridge curvature, whereas in the case of initial separated scenario, faster growth and shorter development time corresponding to shorter separation distance is due to the formation of elongated neck bridge. The prefactor A₀ that represents the growth of neck bridge radius at the characteristic time t_i captured in each case is in good agreement with the experimental results.

Immiscible gas–liquid two-phase flows with an initial stochastically distribution, which are driven by a constant body force in a period microchannel of 5 - 20 μ m in width, are studied using the lattice Boltzmann method under various conditions. Continuous dynamic behaviors of bubbles and droplets including breaking up, coalescence, deformation, and mass exchange between them are observed. The flows reach to their steady state when the rate of breaking up and coalescence are in balance, and no mass exchange occurs. The simulation results show that the steady-state flow regimes depend strongly on the viscous force, surface tension, inertial force, channel width, and wettability of the solid surface. Specially, it is found that slug flow is more probable to occur for the small channel width at the same volume fraction. And the shape of bubble in the slug flow is determined by the wettability of the solid wall. Furthermore, the shape and number of bubbles at steady state are related to surface tension, viscous force, and inertial force. It is also found that the initial bubble distributions have slight effects on the flow regimes at steady state.

We present a series of three-dimensional discrete Boltzmann models for compressible flows in and out of equilibrium. The key formulating technique is the construction of discrete equilibrium distribution function through inversely solving the kinetic moment relations that it satisfies. The crucial physical requirement is that all the used kinetic moment relations must be consistent with the non-equilibrium statistical mechanics. The necessity of such a kinetic model is that, with increasing the complexity of flows, the dynamical characterization of non-equilibrium state and the understanding of the constitutive relations need higher order kinetic moments and their evolution. The discrete Boltzmann models at the Euler and Navier–Stokes levels proposed by this scheme are validated by several well-known benchmarks, ranging from one-dimension to three-dimension. Particularly, when the local Mach number, temperature ratio, and pressure ratio are as large as 10², 10⁴, and 10⁵, respectively, the simulation results are still in excellent agreement with the Riemann solutions. How to model deeper thermodynamic non-equilibrium flows by discrete Boltzmann is indicated. Via the discrete Boltzmann method, it is convenient to simulate nonequilibrium flows without knowing exact form of the hydrodynamic equations.

The micro-scale effect occurs because of the gas flows in shale reservoirs containing small organic pores. In this study, based on a lattice Boltzmann model incorporating the bounce-back and specular-reflection boundary conditions, the gas flow through two parallel plates driven by differential pressures is simulated, which in turn verifies the model. Considering the effects of the slippage, surface diffusion, and adsorption, the gas flow in the organic channels is simulated based on the proposed lattice Boltzmann model. It is shown that the micro-scale effect is significant in the gas flows in the micro-scale channels. The compression effect leads to a nonlinear distribution of pressures along the centreline of the flow channels, and the nonlinearity increases with an increase in the pressure difference between the two sides of the flow channel. In case of gas flows in organic pores, the adsorption effect decreases the free-gas velocities, and with a decrease in pore sizes, the average free-gas velocity is reduced owing to the increased adsorption effect. The slippage effect and surface diffusion have a significant impact on the free-gas velocity of the mass flow. Compared to the slippage effect, surface diffusion contributes more to the mass flow of gas in organic pores. An increase in the Knudsen number intensifies the slippage effect and surface diffusion and enhances the mass flow.

The deformability of cells has been used as a biomarker to detect circulating tumor cells from patient blood sample using microfluidic devices with microscale pores. Successful separations of circulating tumor cells from a blood sample require careful design of the micropore size and applied pressure. This paper presented a parametric study of cell squeezing through micropores with different size and pressure. Different membrane compressibility modulus was used to characterize the deformability of varying cancer cells. Nucleus effect was also considered. It shows that the cell translocation time through the micropore increases with cell membrane compressibility modulus and nucleus stiffness. Particularly, it increases exponentially as the micropore diameter or pressure decreases. The simulation results such as the cell squeezing shape and translocation time agree well with experimental observations. The simulation results suggest that special care should be taken in applying Laplace–Young equation to microfluidic design due to the nonuniform stress distribution and membrane bending resistance.

This work presents thermal lattice Boltzmann method simulation of magneto-hydrodynamic, buoyancy-driven convection in a partially differentially heated cavity (aspect ratio = 1) subjected to a magnetic field along the vertical direction, i.e. at 90°. Lattice Boltzmann method simulations are performed for three different cooler lengths (L_c = H/4, H/2, H) placed along the middle of one vertical wall for a wide range of Rayleigh and Hartmann numbers (10³≤ Ra ≤ 10⁵; Ha = 0, 60, 120) at fixed Prandtl number (Pr = 0.71, air). A partial heater is placed at the center of other vertical walls and its size is kept as half of the characteristic length (H/2). The physical insights of the systems are delineated by systematic analysis of stream function and temperature contours. Heat transfer characteristics of the cavity are elucidated by using averaged values of the Nusselt number. It is noted that average Nusselt number has a proportional dependence with cooler length and Rayleigh number, while it varied inversely with Hartmann number. Further, the functional dependence of average Nusselt number with cooler size, Rayleigh number, and Hartmann number is established for possible use in engineering design purpose.