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We conducted a numerical investigation into droplet dynamics within a flexible constriction using the phase-field lattice Boltzmann method. Our study focused on constriction bending stiffness, Weber number, and constriction-to-droplet diameter ratio. Flexibility impedes droplet passage at low Weber numbers but significantly facilitates it at moderate and high Weber numbers. Passage times decrease with increasing Weber numbers and are proportional to the droplet's maximum deformed length. An anomalous phenomenon is observed: "more haste, less speed." The underlying mechanics arising from the interaction between the flexible constriction and the droplet are elucidated. The findings enhanced our understanding of droplet behavior in constrained environments. [ABSTRACT FROM AUTHOR]

The rheology of a capsule suspension in two-dimensional confined Poiseuille flow is studied numerically using an immersed-boundary lattice Boltzmann method. The effects of capsule volume fraction ϕ and bending stiffness Eb on the rheology of the suspension are investigated first. The apparent viscosity does not monotonically increase with ϕ: the variation curve can be divided into four flow regimes. In each regime, there is a distinct equilibrium spatial configuration. The overall lateral position of the capsules is directly connected with the apparent viscosity. Then, we propose to investigate the effect of inertia on the capsule configuration in dilute cases and the capsule transport in concentrated cases. For dilute cases, phase diagrams of flow regimes on the (ϕ, Eb) plane are plotted. It is found that, as the Reynolds number (Re) increases, the range of values for regime I, with a single-line configuration, reduces, while the range for regime II (transition configuration) increases. It is highly correlated with the equilibrium lateral position of a single capsule. For even larger Re, the range for regime IV (random configuration) increases rapidly and dominates because the larger inertia makes the arrangement more random. For concentrated cases, we observe that the optimal volume fraction, at which the transport of capsules is a maximum, increases with Re. This study may help to understand the collective behavior of capsules in Poiseuille flows. [ABSTRACT FROM AUTHOR]

• Boiling process on structured surfaces was simulated using our developed LBM. • The geometric parameters effects are investigated in detail. • It is ideal that the heated area is large while the convection is not hindered. Pool boiling heat transfer enhancement on structured surfaces with columns is investigated by a thermal two-phase lattice Boltzmann model. The effects of geometrical parameters, including column height (H), width (W) and gap spacing (D), are discussed in detail. The size of columns is comparable to the diameter of a typical detached bubble ( d b ). It is found that the heat transfer performance mainly depends on two factors: the heated surface area A and local convective flow field. When W and D are properly chosen as about W = D ≈ 4 d b , increasing H enhances the heat transfer solely due to the increase of the surface area. When W and D are small, it is observed that the top of the columns and the channels are mostly covered by a layer of vapor, respectively, which weaken the convection. Under the circumstances, although surface area A increases, heat transfer enhancement is not so significant. For the surface tension effect, the enhancement of the structured surface decreases with the increase of capillary number compared to that of the plain surface. The mechanism is that at larger capillary number, the convection close to the channel may be partially blocked, which hinders the heat transfer. An optimal enhancement could be achieved when A is as large as possible and meanwhile the convection is not hindered by the bubbles behaviors. The finding here may shed some light on mechanism of heat transfer enhancement on structured surfaces with columns. [ABSTRACT FROM AUTHOR]

In contrast to typical applications of the pseudopotential Lattice Boltzmann model to two components, quantitative validations and applications for three-component Shan-Chen model are performed here. First, the qualitative and quantitative validations for the following three cases were performed, i.e., three-phase separation, meniscus-induced bubble movement, and the three-phase layered flow. A scheme to control the simulated contact angle of droplets on the interface is provided for the three fluid phase Lattice Boltzmann model. The effects of droplet shape, the strength of gravity, droplet size, and meniscus curvature for the spontaneous motion of droplets and bubbles are investigated in detail. It is found that without gravity, droplets tend to move to the wall on a concave upwards meniscus when they have a big “head” and a small “belly”. Gravity may enhance rather than inhibit the motion towards the wall when the density of the droplet or bubble is relatively small. Finally, smaller droplet size and larger meniscus curvatures enhance the spontaneous movement towards a wall. The conclusions are relevant to practical applications such as water treatment, oil spill remediation, and droplet-based microfluidics. [ABSTRACT FROM AUTHOR]

Abstract: In many lattice Boltzmann studies about bubble rising, mass conservation is not satisfactory and the terminal bubble rising shape or velocity is not so consistent with experimental data as those obtained through other CFD techniques. In this paper, based on the multiphase model (He et al., 1999 [1]), a mass-conserving axisymmetric multiphase lattice Boltzmann model is developed. In the model, a mass correction step and an effective surface tension formula are introduced into the model. We demonstrate how the macroscopic axisymmetric Cahn–Hilliard equation and Navier–Stokes equation are recovered from the lattice Boltzmann equations through Chapman–Enskog expansion. The developed model is applied to simulate the bubble rising in viscous fluid. The mass correction step in our scheme significantly improves the bubble mass conservation. The surface tension calculation successfully predicts the terminal bubble shapes and reproduces the effect of initial bubble shape. The terminal bubble rising velocities are very consistent with experimental and numerical data in the literature. Qualitatively, the wakes behind the bubbles also agree well with experimental data. This model is useful for predicting the axisymmetric two-phase flows. [Copyright &y& Elsevier]

Abstract: This study presents model extensions for a lattice Boltzmann (LB) approach to thermal axisymmetric flow including swirl or rotation. An incompressible axisymmetric lattice Boltzmann D2Q9 model was applied to solve the axial and radial velocities through inserting source terms into the two-dimensional lattice Boltzmann equation. The equations governing azimuthal (or swirling) velocity and the temperature were also solved by the LBM. It is found that this scheme is much more stable and consistent compared to previous hybrid schemes. It provides a significant advantage in simulation of melt flows with high Reynolds number and high Grashof number. The present scheme was validated by comparing the LB results with benchmark solutions for melt flow in Czochralski crystal growth. Unsteady flows with high Grashof numbers were studied in detail. The critical Grashof number for the onset of the oscillation is found to be about . The oscillation amplitude is proportional to for . The frequencies and flow patterns of the unsteady flows are also analyzed. The distributions of the mean quantities of the temperature and rms of temperature at Grashof number as high as is found to be similar to those obtained by 3D simulations. [Copyright &y& Elsevier]

Originally, the color-gradient model proposed by Rothman and Keller (R-K) was unable to simulate immiscible two-phase flows with different densities. Later, a revised version of the R-K model was proposed by Grunau et al. [D. Grunau, S. Chen and K. Eggert, Phys. Fluids A: Fluid Dyn. 5, 2557 (1993).] and claimed it was able to simulate two-phase flows with high-density contrast. Some studies investigate high-density contrast two-phase flows using this revised R-K model but they are mainly focused on the stationary spherical droplet and bubble cases. Through theoretical analysis of the model, we found that in the recovered Navier-Stokes (N-S) equations which are derived from the R-K model, there are unwanted extra terms. These terms disappear for simulations of two-phase flows with identical densities, so the correct N-S equations are fully recovered. Hence, the R-K model is able to give accurate results for flows with identical densities. However, the unwanted terms may affect the accuracy of simulations significantly when the densities of the two fluids are different. For the simulations of spherical bubbles and droplets immersed in another fluid (where the densities of the two fluids are different), the extra terms may not be important and hence, in terms of surface tension, accurate results can be obtained. However, generally speaking, the unwanted term may be significant in many flows and the R-K model is unable to obtain the correct results due to the effect of the extra terms. Through numerical simulations of parallel two-phase flows in a channel, we confirm that the R-K model is not appropriate for general two-phase flows with different densities. A scheme to eliminate the unwanted terms is also proposed and the scheme works well for cases of density ratios less than 10. [ABSTRACT FROM AUTHOR]

We propose a hybrid lattice-Boltzmann finite-difference method to simulate axisymmetric multiphase flows. The hydrodynamics is simulated by the lattice-Boltzmann equations with the multiple-relaxation-time (MRT) collision model and suitable forcing terms that account for the interfacial tension and axisymmetric effects. The interface dynamics is captured by the finitedifference solution of the convective Cahn-Hilliard equation. This method is applied to simulate a quiescent drop, an oscillating drop, a drop spreading on a dry surface and a drop accelerated by a constant body force. It is validated through comparisons of the computed results for these problems with analytical solutions or numerical solutions by other different methods. It is shown that the MRT-based method is able to handle more challenging cases than that with the single-relaxation-time collision model for axisymmetric multiphase flows due to its improved stability. [ABSTRACT FROM AUTHOR]

Abstract: A free energy (FE) model, the Shan–Chen (S–C) model, and the Rothman and Keller (R–K) model are studied numerically to evaluate their performance in modeling two-dimensional (2D) immiscible two-phase flow in porous media on the pore scale. The FE model is proved to satisfy the Galilean invariance through a numerical test and the mass conservation of each component in the simulations is exact. Two-phase layered flow in a channel with different viscosity ratios was simulated. Comparing with analytical solutions, we see that the FE model and the R–K model can give very accurate results for flows with large viscosity ratios. In terms of accuracy and stability, the FE model and the R–K model are much better than the S–C model. Co-current and countercurrent two-phase flows in complex homogeneous media were simulated and the relative permeabilities were obtained. Again, it is found that the FE model is as good as the R–K model in terms of accuracy and efficiency. The FE model is shown to be a good tool for the study of two-phase flows with high viscosity ratios in porous media. [Copyright &y& Elsevier]

Isothermal gas flow in microtubes with a sudden expansion or contraction is studied numerically by lattice Boltzmann method. An axisymmetric D2Q9 model is used to simulate gas slip flow in micro-circular pipes. With the boundary condition combined specular and bounce-back schemes, the computed results are in excellent agreement with analytical solution for straight microtube. For the gas flow in the expanded or constricted tubes, we carried out simulations of several Knudsen numbers with inlet/outlet pressure ratio 3. It is found the pressure drop in each section can be predicted well by the theory of straight tubes. For smaller Knudsen number, flow separation in the expanded tube is observed. While for large Knudsen number, there is no vortex at corner and the streamlines are attached to boundary. In the constricted tube, the vortex at corner is very weak. These results are consistent with some experimental conclusions. [ABSTRACT FROM AUTHOR]

Zhang and Chen proposed a lattice Boltzmann method for simulations of liquid-vapor thermal flows [Zhang and Chen, Phys. Rev. E 67, 066711 (2003)]. In their numerical test, the authors show simulation results with a temperature ratio of approximately 1.2 for a thermal two-phase flow with T < 0.8 Tc. However, we believe this to be erroneous and demonstrate the error to originate from a wrong choice of a parameter of critical importance in the Carnahan-Starling equation of state used in their work. Our numerical tests show that using the correct parameter choice, the scheme is only valid and robust to simulate temperature ratios below 1.10 and the lowest temperature in the flow field should be 0.85 Tc. [ABSTRACT FROM AUTHOR]

We develop a semi-analytical model to calculate the entry pressure in rough capillaries based on an energy balance principle and wetting theory on rough surfaces. During the drainage process, we assume fluids form arc menisci at corners of capillary cross-sections depending on the apparent angle, and that there is a wetting phase film adsorbed on the rough surface depending on the wetting condition. A Logistic model is proposed to explain the contact angle dependence on the structure of rough surfaces. Then the capillary entry pressure is calculated by extended MS-P (Mayer, Stowe and Princen) method. We verify the model using the pseudopotential Lattice Boltzmann model and obtain good agreement between the analytical and simulated pressures. Taking capillaries with triangular sections with pillar pillar-type rough surfaces as example, we discuss how rough structures and contact angles influence capillary behaviors. The results reveal that both the wetting phase saturation and entry pressure of rough capillaries are larger than those in smooth capillaries under the same conditions. Moreover, the entry pressure is not sensitive to the roughness factor under strong wetting conditions and is much more sensitive to the pillar asperity height than the other structure parameters. [ABSTRACT FROM AUTHOR]

A novel flexible forcing immersed boundary and lattice Boltzmann method (IB-LBM) is introduced in this paper. In the conventional IB-LBM scheme, explicit calculation of the force density term may not guarantee exact satisfaction of the no-slip boundary condition. This produces unphysical streamline penetration into the solid object. In this study, an implicit approach is followed where the force density is obtained from the unknown velocity correction with a unique single Lagrangian velocity correction term and flexible number of forcing steps. The proposed algorithm is computationally efficient and easy for new code development. Also the algorithm is found advantageous for unsteady flow case where no-slip condition is accurately satisfied. Flow past circular cylinder is studied for both steady and unsteady flow cases to validate the proposed scheme. [ABSTRACT FROM AUTHOR]

A combination of cyclostratigraphic, ichnologic, and borehole geophysical analyses of continuous core holes; tracer-test analyses; and lattice Boltzmann flow simulations was used to quantify biogenic macroporosity and permeability of the Biscayne aquifer, south-eastern Florida. Biogenic macroporosity largely manifests as: (1) ichnogenic macroporosity primarily related to postdepositional burrowing activity by callianassid shrimp and fossilization of components of their complex burrow systems (Ophiomorpha); and (2) biomoldic macroporosity originating from dissolution of fossil hard parts, principally mollusk shells. Ophiomorpha-dominated ichnofabric provides the greatest contribution to hydrologic characteristics in the Biscayne aquifer in a 345 km² study area. Stratiform tabular-shaped units of thalassinidean-associated macroporosity are commonly confined to the lower part of upward-shallowing high-frequency cycles, throughout aggradational cycles, and, in one case, they stack vertically within the lower part of a high-frequency cycle set. Broad continuity of many of the macroporous units concentrates groundwater flow in extremely permeable passageways, thus making the aquifer vulnerable to long-distance transport of contaminants. Ichnogenic macroporosity represents an alternative pathway for concentrated groundwater flow that differs considerably from standard karst flow-system paradigms, which describe groundwater movement through fractures and cavernous dissolution features. Permeabilities were calculated using lattice Boltzmann methods (LBMs) applied to computer renderings assembled from X-ray computed tomography scans of various biogenic macroporous limestone samples. The highest simulated LBM permeabilities were about five orders of magnitude greater than standard laboratory measurements using air-permeability methods, which are limited in their application to extremely permeable macroporous rock samples. Based on their close conformance to analytical solutions for pipe flow, LBMs offer a new means of obtaining accurate permeability values for such materials. We suggest that the stratiform ichnogenic groundwater flow zones have permeabilities even more extreme (∼2-5 orders of magnitude higher) than the Jurassic "super-K" zones of the giant Ghawar oil field. The flow zones of the Pleistocene Biscayne aquifer provide examples of ichnogenic macroporosity for comparative analysis of origin and evolution in other carbonate aquifers, as well as petroleum reservoirs. [ABSTRACT FROM AUTHOR]