Forcing scheme in pseudopotential lattice Boltzmann model for multiphase flows

The pseudo-potential lattice Boltzmann (LB) model is a widely used multiphase model in the LB community. In this model, an interaction force, which is usually implemented via a forcing scheme, is employed to mimic the molecular interactions that cause phase segregation. The forcing scheme is therefore expected to play an important role in the pseudo-potential LB model. In this paper, we aim to address some key issues about forcing schemes in the pseudo-potential LB model. Firstly, theoretical and numerical analyses will be made for Shan-Chen's forcing scheme and the exact-difference-method (EDM) forcing scheme. The nature of these two schemes and their recovered macroscopic equations will be shown. Secondly, through a theoretical analysis, we will reveal the physics behind the phenomenon that different forcing schemes exhibit different performances in the pseudo-potential LB model. Moreover, based on the analysis, we will present an improved forcing scheme and numerically demonstrate that the improved scheme can be treated as an alternative approach for achieving thermodynamic consistency in the pseudo-potential LB model.Comment: 7 figure

Numerical simulation of viscous fingering phenomenon in immiscible displacement of two fluids in porous media using Lattice Boltzmann method

This paper was presented at the 2nd Micro and Nano Flows Conference (MNF2009), which was held at Brunel University, West London, UK. The conference was organised by Brunel University and supported by the Institution of Mechanical Engineers, IPEM, the Italian Union of Thermofluid dynamics, the Process Intensification Network, HEXAG - the Heat Exchange Action Group and the Institute of Mathematics and its Applications.In the present study, viscous fingering phenomenon, which occurs when a less viscous fluid (e.g. supercritical carbon dioxide) is injected into simplified porous media to displace a more viscous fluid (e.g. crude oil), is investigated by a mesoscopic approach-the lattice Boltzmann method (LBM). Due to its convenience in dealing with complex fluids of different viscosities, the pseudo-potential model is employed to study the effects of the capillary number, Bond number and viscosity ratio between the displaced fluids and displacing fluid; as such effects reflect the competition of viscous force and surface tension and gravity forces during viscous fingering. The numerical procedure is validated against a series of droplet tests, in which surface tension can be determined. By changing the injecting velocity of the displacing fluid and gravitational acceleration, the displacement processes under conditions of different capillary number and Bond number are investigated. The finger pattern is presented in this paper. The effects of capillary number, Bond number and viscosity ratio are discussed in detail. The ability and suitability of the lattice Boltzmann method for simulating multi-component fluids displacement in porous media are proved in our work.This work is supported by China Scholarship Council (CSC)

Modern Lattice Boltzmann methods for multiphase micro-flows

This paper was presented at the 2nd Micro and Nano Flows Conference (MNF2009), which was held at Brunel University, West London, UK. The conference was organised by Brunel University and supported by the Institution of Mechanical Engineers, IPEM, the Italian Union of Thermofluid dynamics, the Process Intensification Network, HEXAG - the Heat Exchange Action Group and the Institute of Mathematics and its Applications.During the last decade, the Lattice Boltzmann (LB) method has captured an increasing attention as an efficient tool for the numerical simulation of complex fluids, particularly multi-phase and multi-component flows. In this paper, we revisit the basic features of two modern variants of lattice Boltzmann models for non-ideal fluids, which offer promising perspectives for the numerical simulation of complex micro- flows.This study is funded from the European Project INFLUS, NMP3-CT-2006-031980

Lattice Boltzmann Models with Mid-Range Interactions \ud \ud

An extension of the standard Shan-Chen model for non ideal-fluids, catering for mid-range, soft-core and hard-core repulsion, is investigated. It is shown that the inclusion of such mid-range interactions does not yield any visible enhancement of the density jump across the dense and light phases. Such an enhancement can however be obtained by tuning the exponents of the effective interaction. The results also indicate that the inclusion of soft-core repulsion can prevent the coalescence of neighborhood bubbles, thereby opening the possibility of tailoring the size of multi-droplet configurations, such as sprays and related phase-separating fluids. \ud \u

Generalized Lattice Boltzmann Method with multi-range pseudo-potential

The physical behaviour of a class of mesoscopic models for multiphase flows is analyzed in details near interfaces. In particular, an extended pseudo-potential method is developed, which permits to tune the equation of state and surface tension independently of each other. The spurious velocity contributions of this extended model are shown to vanish in the limit of high grid refinement and/or high order isotropy. Higher order schemes to implement self-consistent forcings are rigorously computed for 2d and 3d models. The extended scenario developed in this work clarifies the theoretical foundations of the Shan-Chen methodology for the lattice Boltzmann method and enhances its applicability and flexibility to the simulation of multiphase flows to density ratios up to O(100)

Lattice Boltzmann models for non-ideal fluids with arrested phase-separation

The effects of mid-range repulsion in Lattice Boltzmann models on the coalescence/breakup behaviour of single-component, non-ideal fluids are investigated. It is found that mid-range repulsive interactions allow the formation of spray-like, multi-droplet configurations, with droplet size directly related to the strength of the repulsive interaction. The simulations show that just a tiny ten-percent of mid-range repulsive pseudo-energy can boost the surface/volume ratio of the phase- separated fluid by nearly two orders of magnitude. Drawing upon a formal analogy with magnetic Ising systems, a pseudo-potential energy is defined, which is found to behave like a quasi-conserved quantity for most of the time-evolution. This offers a useful quantitative indicator of the stability of the various configurations, thus helping the task of their interpretation and classification. The present approach appears to be a promising tool for the computational modelling of complex flow phenomena, such as atomization, spray formation and micro-emulsions, break-up phenomena and possibly glassy-like systems as well.Comment: 12 pages, 9 figure

Mesoscopic model for soft flowing systems with tunable viscosity ratio

We propose a mesoscopic model of binary fluid mixtures with tunable viscosity ratio based on the two-range pseudo-potential lattice Boltzmann method, for the simulation of soft flowing systems. In addition to the short range repulsive interaction between species in the classical single-range model, a competing mechanism between the short range attractive and mid-range repulsive interactions is imposed within each species. Besides extending the range of attainable surface tension as compared with the single-range model, the proposed scheme is also shown to achieve a positive disjoining pressure, independently of the viscosity ratio. The latter property is crucial for many microfluidic applications involving a collection of disperse droplets with a different viscosity from the continuum phase. As a preliminary application, the relative effective viscosity of a pressure-driven emulsion in a planar channel is computed.Comment: 14page