In this paper, we compare two families of Lattice Boltzmann (LB) models derived by means of Gauss quadratures in the momentum space. The first one is the HLB (N;Qx,Qy,Qz) family, derived by using the Cartesian coordinate system and the Gauss–Hermite quadrature. The second one is the SLB (N;K,L,M) family, derived by using the spherical coordinate system and the Gauss–Laguerre, as well as the Gauss–Legendre quadratures. These models order themselves according to the maximum order N of the moments of the equilibrium distribution function that are exactly recovered. Microfluidics effects (slip velocity, temperature jump, as well as the longitudinal heat flux that is not driven by a temperature gradient) are accurately captured during the simulation of Couette flow for Knudsen number (kn) up to 0.25.
Abstract:Colloidal dispersions are known to undergo phase transition in a number of processes. This often gives rise to formation of structures in a flowing medium. In this paper, we present a model for flow of a colloidal dispersion with phase change. Two distribution functions are used. The colloid is described as a non-ideal fluid capable of phase change, but rather than taking the dispersion medium as the second fluid, a better choice is the dispersion (water plus colloid) which can be considered as an incompressible fluid. This choice allows a standard Lattice Boltzmann (LB) model for incompressible fluids to be used in combination with for the 'free-energy' LB model for the colloid. The coupling between the two fluids is the drag force on the colloid and the dependence of the viscosity of the overall fluid on the particle volume fraction. The problems raised by characteristic times and lengths have been treated. The main application considered is the growth dynamics or domain structuration of protein dispersions during dead-end filtration on a membrane surface.
An unsteady model of condensation flow in capillary regime inside a cylindrical tube was developed, based on a two-fluid approach. The model takes into account the coupling between the liquid film zone (where the quality is low) and the nearly hemispherical meniscus which is present at the end of the condensation region. Numerically, a major difficulty is that this type of problem has a free boundary condition. Indeed the end location of the two-phase zone is the result of all the heat exchanges occurring upstream of this area. To overcome this difficulty a mathematical representation was specifically developed. The unsteady model presented is based on five dimensionless numbers characterizing this type of flow. A comparison between the results of this model and those of a previously developed stationary model is made. An excellent agreement is obtained. The presence of self-sustaining oscillations due to the intrinsic mechanisms of condensation are also obtained numerically. The variation of the Nusselt number with the boiling number is then determined and presented. These results complement the previous study by determining the frontier between the stable and unstable situations. The atypical behaviour of the Nusselt number preceding the onset of instability is also analyzed.
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