Boundaries in lattice gas flows

Lavallée, Paul; Boon, Jean‐Pierre; Noullez, A.

doi:10.1016/0167-2789(91)90294-j

Cited by 61 publications

(38 citation statements)

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“…(21) reduces to two equations with three unknown variables. To close the system of equations the bounce-back rule [49,50] is adopted for the distribution functions normal to the boundary. This corresponds to impose that f 4 (t) = f 2 (t).…”

Section: B the Equilibrium Propertiesmentioning

confidence: 99%

Phase-separating binary fluids under oscillatory shear

Gonnella

Lamura³

2003

Phys. Rev. E

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We apply lattice Boltzmann methods to study the segregation of binary fluid mixtures under oscillatory shear flow in two dimensions. The algorithm allows to simulate systems whose dynamics is described by the Navier-Stokes and the convection-diffusion equations. The interplay between several time scales produces a rich and complex phenomenology. We investigate the effects of different oscillation frequencies and viscosities on the morphology of the phase separating domains. We find that at high frequencies the evolution is almost isotropic with growth exponents 2/3 and 1/3 in the inertial (low viscosity) and diffusive (high viscosity) regimes, respectively. When the period of the applied shear flow becomes of the same order of the relaxation time TR of the shear velocity profile, anisotropic effects are clearly observable. In correspondence with non-linear patterns for the velocity profiles, we find configurations where lamellar order close to the walls coexists with isotropic domains in the middle of the system. For particular values of frequency and viscosity it can also happen that the convective effects induced by the oscillations cause an interruption or a slowing of the segregation process, as found in some experiments. Finally, at very low frequencies, the morphology of domains is characterized by lamellar order everywhere in the system resembling what happens in the case with steady shear. 05.70.Ln, 47.20.Hw, 47.11.+j, 83.10.Tv

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Section: B the Equilibrium Propertiesmentioning

confidence: 99%

Phase-separating binary fluids under oscillatory shear

Gonnella

Lamura³

2003

Phys. Rev. E

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“…Various types of boundary conditions have been used for LB simulations of finite-Knudsen flows [10,11,12,13]. In this work, we confine our attention to bounce back (BB) [14] and kinetic, as recently introduced by Ansumali and Karlin (AK) [15].…”

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confidence: 99%

Lattice Boltzmann method at finite Knudsen numbers

2005

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A modified lattice Boltzmann model with a stochastic relaxation mechanism mimicking "virtual" collisions between free-streaming particles and solid walls is introduced. This modified scheme permits to compute plane channel flows in satisfactory agreement with analytical results over a broad spectrum of Knudsen numbers, ranging from the hydrodynamic regime, all the way to quasifree flow regimes up to Kn ∼ 30. PACS numbers:The dynamic behaviour of flows far from hydrodynamic equilibrium is an important subject of nonequilibrium thermodynamics, with many applications in science and engineering. The non-hydrodynamic regime is characterized by strong departures from local equilibrium which are hardly handled on analytical means. Consequently, much work is being devoted to the development of computational techniques capable of dealing with the aforementioned non-perturbative and non-local effects. Recently, the lattice Boltzmann (LB) method has attracted considerable interest as an alternative to the discretization of the Navier-Stokes equations for the numerical simulation of a variety of complex flows [1]. Extending LB methods to non-hydrodynamic regimes is a conceptual challenge on its own, with a variety of microfluidic applications, such as flows in micro and nano electro-mechanical devices (NEMS, MEMS) [2]. Departures from local equilibrium are measured by the Knudsen number, namely the ratio of molecular mean free path, l m , to the shortest hydrodynamic scale, l h : Kn = l m /l h . Ordinary fluids feature Kn < 0.01, while high Knudsen numbers are typically associated to rarefied gas dynamics, where l m is large because density is small, typical case being aero-astronautics applications. More recently, however, the finite-Kn regime is becoming more and more relevant for a variety of microfluidics applications in which the Knudsen number is large because of the increasingly smaller size of the devices. It is also worth emphasizing that the finite-Knudsen regime may also bear relevance to the problem of modeling fluid turbulence [3,4]. Recent work indicates that LB may offer quantitatively correct information also in the finite-Kn regime [5]. This hints at the possibility that LB may complement or even replace expensive microscopic simulation techniques such as kinetic Monte Carlo and/or molecular dynamics. On the other hand, this is also puzzling because finite-Knudsen flows are in principle expected to receive substantial contributions from highorder kinetic moments, whose dynamics is arguably not quantitatively correct because of lack of symmetry of the discrete lattice [6,7]. In this work we point out that, irrespectively of symmetry considerations, any LB extension aiming at describing non-hydrodynamic flows in

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“…The same 'bounce back' principle as described above is applied to fixed walls at the lattice boundaries (for this and other possible boundary conditions see [17]). All particles tending to leave the lattice are reflected towards their incoming direction (see Figure 9), resulting in a zero mean velocity at the boundary (no-slip boundary condition).…”

Section: Realization Of Boundary Conditionsmentioning

confidence: 99%