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Register a new userContinuum Free-Energy formulation for a class of Lattice Boltzmann multiphase models
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Added by
Mauro Sbragaglia Dr
Publication date
2009
fields
Physics
and research's language is
English
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It is shown that the Shan-Chen (SC) model for non-ideal lattice fluids can be made compliant with a pseudo free-energy principle by simple addition of a gradient force, whose expression is uniquely specified in terms of the fluid density. This additional term is numerically shown to provide fairly negligible effects on the system evolution during phase-separation. To the best of our knowledge, these important properties of the SC model were not noted before. The approach developed in the present work is based on a continuum analysis: further extensions, more in line with a discrete lattice theory (X. Shan, {it Phys Rev E}, {bf 77} 066702 (2008)) can be envisaged for the future.
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We propose a novel approach to the numerical simulation of thin film flows, based on the lattice Boltzmann method. We outline the basic features of the method, show in which limits the expected thin film equations are recovered and perform validation tests. The numerical scheme is applied to the viscous Rayleigh-Taylor instability of a thin film and to the spreading of a sessile drop towards its equilibrium contact angle configuration. We show that the Cox-Voinov law is satisfied, and that the effect of a tunable slip length on the substrate is correctly captured. We address, then, the problem of a droplet sliding on an inclined plane, finding that the Capillary number scales linearly with the Bond number, in agreement with experimental results. At last, we demonstrate the ability of the method to handle heterogenous and complex systems by showcasing the controlled dewetting of a thin film on a chemically structured substrate.
We develop and implement a novel lattice Boltzmann scheme to study multicomponent flows on curved surfaces, coupling the continuity and Navier-Stokes equations with the Cahn-Hilliard equation to track the evolution of the binary fluid interfaces. Standard lattice Boltzmann method relies on regular Cartesian grids, which makes it generally unsuitable to study flow problems on curved surfaces. To alleviate this limitation, we use a vielbein formalism to write down the Boltzmann equation on an arbitrary geometry, and solve the evolution of the fluid distribution functions using a finite difference method. Focussing on the torus geometry as an example of a curved surface, we demonstrate drift motions of fluid droplets and stripes embedded on the surface of a torus. Interestingly, they migrate in opposite directions: fluid droplets to the outer side while fluid stripes to the inner side of the torus. For the latter we demonstrate that the global minimum configuration is unique for small stripe widths, but it becomes bistable for large stripe widths. Our simulations are also in agreement with analytical predictions for the Laplace pressure of the fluid stripes, and their damped oscillatory motion as they approach equilibrium configurations, capturing the corresponding decay timescale and oscillation frequency. Finally, we simulate the coarsening dynamics of phase separating binary fluids in the hydrodynamics and diffusive regimes for tori of various shapes, and compare the results against those for a flat two-dimensional surface. Our lattice Boltzmann scheme can be extended to other surfaces and coupled to other dynamical equations, opening up a vast range of applications involving complex flows on curved geometries.
Fluid motion driven by thermal effects, such as that due to buoyancy in differentially heated three-dimensional (3D) enclosures, arise in several natural settings and engineering applications. It is represented by the solutions of the Navier-Stokes equations (NSE) in conjunction with the thermal energy transport equation represented as a convection-diffusion equation (CDE) for the temperature field. In this study, we develop new 3D lattice Boltzmann (LB) methods based on central moments and using multiple relaxation times for the three-dimensional, fifteen velocity (D3Q15) lattice, as well as it subset, i.e. the three-dimensional, seven velocity (D3Q7) lattice to solve the 3D CDE for the temperature field in a double distribution function framework. Their collision operators lead to a cascaded structure involving higher order terms resulting in improved stability. In this approach, the fluid motion is solved by another 3D cascaded LB model from prior work. Owing to the differences in the number of collision invariants to represent the dynamics of flow and the transport of the temperature field, the structure of the collision operator for the 3D cascaded LB formulation for the CDE is found to be markedly different from that for the NSE. The new 3D cascaded (LB) models for thermal convective flows are validated for natural convection of air driven thermally on two vertically opposite faces in a cubic cavity enclosure at different Rayleigh numbers against prior numerical benchmark solutions. Results show good quantitative agreement of the profiles of the flow and thermal fields, and the magnitudes of the peak convection velocities as well as the heat transfer rates given in terms of the Nusselt number.
In this paper, an improved three-dimensional color-gradient lattice Boltzmann (LB) model is proposed for simulating immiscible multiphase flows. Compared with the previous three-dimensional color-gradient LB models, which suffer from the lack of Galilean invariance and considerable numerical errors in many cases owing to the error terms in the recovered macroscopic equations, the present model eliminates the error terms and therefore improves the numerical accuracy and enhances the Galilean invariance. To validate the proposed model, numerical simulation are performed. First, the test of a moving droplet in a uniform flow field is employed to verify the Galilean invariance of the improved model. Subsequently, numerical simulations are carried out for the layered two-phase flow and three-dimensional Rayleigh-Taylor instability. It is shown that, using the improved model, the numerical accuracy can be significantly improved in comparison with the color-gradient LB model without the improvements. Finally, the capability of the improved color-gradient LB model for simulating dynamic multiphase flows at a relatively large density ratio is demonstrated via the simulation of droplet impact on a solid surface.
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