Micro Flows: Fundamentals and Simulation

Development of a model for high precursor conversion efficiency pulsed-pressure chemical vapor deposition (PP-CVD) processing

“…In this rarefied state, a molecular description of the reactor flow is required. Several methods exist for simulating rarefied flow including molecular dynamics (MD) simulations, where molecular motion and collisions are calculated deterministically, and the Lattice-Boltzmann method (LBM), which solves a simplified version of the Boltzmann equation over a grid [11]. However, the proceeding methods suffer respectively from enormous computational expense and poor physical reality, so the preferred technique for modelling rarefied flows has become the Direct Simulation Monte Carlo (DSMC) technique [12].…”

Gas Transport Characteristics through a Carbon Nanotubule

“…In the model employed, a first-order slip boundary condition was used, and a tangential-momentum accommodation coefficient (TMAC) of σ v ) 1 was found to successfully characterize transport through the pore, indicating that gas-wall interactions are described by diffusive reflection. Despite the theoretical elegance of molecular dynamics (MD), 2 direct simulation Monte Carlo (DSMC) 3 and Burnett equation 4 type models, they are yet to become applicable for practical micro/ nano flow simulation. Although our finite element hydrodynamic model was successfully applied to microchannels and nanopores, it is expected that the standard hydrodynamic model assumptions will run into difficulties as the media for transport reach nanometer sizes.…”

Integral equations for free-molecule ow in MEMS: recent advancements

“…A large-scale OpenMP parallel implementation [16] has been developed for three fundamental routines: point-to-point visibility test in Level 4 described in Section 2.1; iterative GMRES solution of the linear system obtained collocating Equation (3); force computation from Equation (5).…”

“…In Equations (3), (5) the velocity g of the deformable MEMS is assumed to be proportional to a given vector shape function: g(y, t) = ψ(y)q(t). Hence one has that t(x, t) = f (x)q(t), where f (x) is directly provided by Equation (5). The equivalent damping term in the 1D reduced order model finally becomes:…”

“…Anyway, among the different sources, gas damping often provides a meaningful contribution. The length scale and the working pressure are such that the collisions between molecules can be neglected; this regime is known as free-molecule flow [1][2][3][4][5][6]. The deterministic model implemented, proposed in [7,8], is an application of the collisionless Boltzmann equation which rests on the following assumptions: i) the mean free-molecule path is much larger than the typical dimension d of the flow (i.e.…”