Flow regime free molecular

TRANSITION FLOW AND FREE-MOLECULAR FLOW REGIME... 

In the free-molecular flow regime, the molecular mean free path is of the same order as the channel characteristic length. Because Newton s 2" Law should more or less be applied to each molecule, the analysis becomes extremely tedious and complicated. The current computational tools, the Molecular Dynamics (MD) and the Direct Simulation Monte Carlo, are still incapable of providing effective and efficient solutions. 

The current computational methods for analyses in transition flow and free-molecular flow regimes are ineffective and inefScient. Analyses in these two flow regime are still premature and require more extensive study. 

The Knudsen number (Kn) is used to determine the different regimes of the gas flow. These regimes can be divided into continuous flow, transitional flow and free molecular flow. This division is based on the understanding that the flow behaviour differs within each of the flow regimes. The Knudsen number is defined as... 

Internal rarefied gas flows Slip flow regime Transitional regime Free molecular regime... 

The Knudsen equation can only be applied to the viscous laminar flow regime, the molecular flow regime or the transition flow regime. For predominantly laminar flow, the calculated contribution for molecular flow becomes negligible, and similarly for predominantly molecular flow, the calculated contribution for laminar flow becomes negligible. The first part of this equation represents the viscous laminar flow component, Q, which is derived from Poiseuille s law for laminar flow, and the second part represents the molecular flow component, Q, which is derived from Knudsen s law for free molecular flow. 

Euler equation (negligible molecular diffusion) N-S equation with no-slip boundary condition N-S equation with slip flow boundary condition Transition regime Free molecular flow... 

Figure 3.19 shows the fluid flow regimes prevalent in different MEMS devices. It clearly demonstrates the limitation of the N-S equation for microscale flow modeling. It can be seen that most of the microsystems with gaseous flow works in the slip flow regime. Some flows inside microchannel, micropump, micronozzle, and microvalve operate in transitional regime. Free molecular flow is observed for Couette flow between hard disk and read-write head with a gap of about 100 nm. 

The change from a viscous to a molecular flow regime occurs when the mean free path L of the gas molecules in the system exceeds the minimum physical dimensions of the system. The mean free path is a measure of the average distance a molecule travels between collisions. The derivation of L involves a number of assumptions about the ideality of the gas and the nature of the collisions and by definition some 63.2% of the molecules in a particular gas collide with other molecules within the distance L. The mean free path for any gas can be calculated from Equation (1.1)... 

The value of T from Eq. 29 is 0.575 for y = 1.4 and doesn t vary by more than 10% for values of y from 1.1 to 1.67. At very large Kn the value of T is 0.399, the value for free molecular diffusion through an orifice [46]. In between the high and low Kn number limits the value of T assumes intermediate values [45]. Thus, it can be seen that using the low Kn limit expression in the transition regime is a conservative assumption when calculating gas flows for the purpose of sizing vacuum pumps. 

In the free molecular flow regime, where the molecular mean free path X is much larger than the orifice diameter, the speed of molecules exiting the reactor can be taken as the mean molecular speed, (v) = SRT/nMW, and the flux, FM, is given by... 

CVD reactors operate at sufficiently high pressures and large characteristic dimensions (e.g., wafer spacing) such that Kn (Knudsen number) << 1, and a continuum description is appropriate. Exceptions are the recent vacuum CVD processes for Si (22, 23) and compound semiconductors (156, 157, 169) that work in the transition to the free molecular flow regime, that is, Kn > 1. Figure 7 gives an example of SiH4 trajectories in nearly free molecular flow (Kn 10) in a very low pressure CVD system for silicon epitaxy that is similar to that described by Meyerson et al. (22, 23 Meyerson and Jensen, manuscript in preparation). Wall collisions dominate, and be-... 

In Chap. 2, Raz and Levine investigate a regime of dynamics where the motion along intermolecular coordinates is comparable or faster than that of intramolecular vibrational modes. These conditions exist momentarily when a large cluster impacts a surface at hyperthermal velocities ( 10 kms ). In Chap. 3, Boyd describes the challenges facing a direct simulation Monte Carlo modeler of hypersonic flows in a regime intermediate to the continuum and free molecular flow limits. Many of the lessons... 

According to reference [1] four flow regimes for gases exist continuum flow (0iKn<0.001), slip flow (0.00l Kn<0.1), transition flow (0.l SKn<10), and free molecular flow (lOsKn). Continuum equations are valid for Kn- >0, while kinetic theory is applicable for Kn>8. Slip flow occurs when gases are at low pressure or in micro conduits. The gas slip at the surface, while in continuum flow at the surface it is immobilized. 

As the flow enters the transition flow regime and eontinues into the free-molecular flow regime, the Knudsen number becomes significant enough that the molecular approach has to be utilized. Thus, the Boltzmann equation... 

One method which is known under the name of permeametry [131] or Poiseuille-Knudsen method [124] is based on the law of gas permeability in a porous media in the two flow regimes molecular flow (Knudsen) and laminar or viscous flow (Poiseuille). According to Darcy s law, the gas flux through a membrane with a thickness / can be written as / = KAP/l, where K is the permeability coefficient and AP (AP = Pi - P2) the pressure difference across the membrane. If the membrane pore diameter is comparable to the mean free path of the permeating gas, K can be expressed as a stun of a viscous and a non-vis-cous term... 

The asymptotic values of the flowrate for duct flows at high Knudsen number are constants depending on the duct aspect ratio. This offers the possibility of obtaining a model for the rarefaction coefficient Cr Kn) and in particular the coefficient a. The objective is to construct a unified expression for a Kn) that represents the transition of a from zero in the slip flow regime to its asymptotic constant value in the free-molecular flow regime. 

Deposition of nanoparticles was investigated in the free molecular regime approximation for thermophoretic force and the Brownian motion. The analytical solution was obtained by the Galerkin method for the heat transfer between gas flow and substrates and convective diffusion. Relative roles of two channels of nanoparticle deposition are discussed. 

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