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...he boundary conditions becomes increasingly important. In this paper we set up a novel approach to the CFD of microflows. It is based on the recently developed Entropic Lattice Boltzmann Method (ELBM)=-=[10, 11, 12, 13, 14, 15, 16, 17, 18, 19]-=-. The choice of the ELBM for microflows is motivated by two reasons: • ELBM is an unconditionally stable simulation method for flows at low Mach numbers. • In contrast to Grad’s method, ELBM is much m...

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...ls become linearly unstable under certain conditions. (11) However, only very recently was a rigorous proof given. (12) There has also been an effort to construct LBE models which admit an H theorem. =-=(6,9,10)-=- This has been done in two ways. One is to analytically construct the equilibria which admit an H theorem. (6,9) The other is to construct an collision process which maximizes a given Lyapunov functio...

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... ELBM acts on the local equilibrium f eq because of if the local equilibrium is supported by some entropy function, then the Lattice Boltzmann method can be equipped with the H-theorem, (as refers in =-=[27]-=-, [26], [25], [28], [29]) and stability problem can be studied in a controlled way. Before giving more details about the model, let us briefly describe the theoretical motivations. 3.1. Theoretical mo...

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...gle relaxation time parameter which is related to kinematic viscosity. lattice Boltzmann method using the Bhatnagar-GrossKrook model becomes numerically unstable at low values of fluid viscosity. This is primarily due to the linear relation of bulk viscosity and the kinematic viscosity in lattice Bhatnagar-Gross-Krook models. When the kinematic viscosity is reduced at high Reynolds numbers, the bulk viscosity is also reduced which creates spurious density fluctuations due to insufficient dissipation. The causes of numerical instabilities are also attributed to the nonexistence of an H theorem [32]. There have been two main approaches introduced in order to find a remedy to the stability problem at low viscosities; entropic methods [32] and multiple-relaxation-time methods. A non-polynomial equilibrium distribution function is used in the entropic methods. Increased computational requirements, non-constant transport coefficients depending on the velocity field are some of the disadvantages of these methods in practical computer simulations with lattice Boltzmann method. The multiple-relaxation-time model permits adjustment of kinematic and bulk viscosities separately. This is achieved b...

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...pulsive interactions in MD simulations [8, 25, 30]). It should be emphasized that the contact angle can be computed also within the framework of the free-energy version of the lattice Boltzmann method for non-ideal fluids [10, 29]. Here, however, we prefer to stick to the Shan-Chen pseudo-potential formulation, because of its simplicity. In order to study the wetting/dewetting transition on micro/nano-patterned surfaces (see Fig. 1) we have integrated the LBE equation (1) in a 2D Lattice using the nine-speed 2DQ9 model (b = 9), one of the most used 2D-LBE scheme, due to its superior stability [9, 19]. We have used the two geometries described in Fig. 1. All simulations have been performed at fixed “inverse temperature” Gb = −6.0 i.e. beyond the critical value Gb = −4.0. The relaxation parameter is taken as τ = 0.8 in lattice units. The equation of state delivers the corresponding values of the liquid and vapor density, ρl = 2.65 and ρg = 0.07 respectively, while the surface tension is σlv = 0.105 ± 0.002 in lattice units. The value of the lattice spacing in physical units is obtained by matching the physical value of the liquid-vapor surface tension, with the one measured on the lattice, ...

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...nction is imposed through the following procedure: In the first step, populations are changed in the direction of the collision in such a way that the H function remains constant (Karlin et al. 1999; =-=Boghosian et al. 2001-=-). In the second step, dissipation is introduced and the magnitude of the H function decreases. Thus, [ fi(x, δt) = fi(x − ciδt, 0) + αβ f eq i (x − ciδt, ] 0) − fi(x − ciδt, 0) , (4.1) were β is the ...