Momentum exchange

There are n Stefan-Maxwell relations in an n-component mixture, but they are not independent since each side of (2.16) yields zero on summing over r from 1 to n. Physically this is not surprising, since they describe only momentum exchange between pairs of species, and say nothing about the total momentum of the mixture. In order to complete the determination of the fluxes N.... N the Stefan-Maxwell relations must be supple-I n... 

Most of the commercial gas—air premixed burners are basically laminar-dow Bunsen burners and operate at atmospheric pressure. This means that the primary air is induced from the atmosphere by the fuel dow with which it mixes in the burner passage leading to the burner ports, where the mixture is ignited and the dame stabilized. The induced air dow is determined by the fuel dow through momentum exchange and by the position of a shutter or throtde at the air inlet. Hence, the air dow is a function of the fuel velocity as it issues from the orifice or nozzle, or of the fuel supply pressure at the orifice. With a fixed fuel dow rate, the equivalence ratio is adjusted by the shutter, and the resulting induced air dow also determines the total mixture dow rate. 

From Tolmin s theory and experimental data (e.g., Reichardtthe relationship between velocity profile and temperature profile in the jet cross-section can be expressed using an overall turbulent Prandtl number Pr = v /a, where Vf is a turbulent momentum exchange coefficient and a, is a turbulent heat exchange coefficient ... 

Black, J. R., Etch Pit Formation in Silicon at Al-Si Contacts Due to the Transport of Silicon in Aluminium by Momentum Exchange with Conducting Electrons , J. Electrochem. Soc., 115, 242c (1968)... 

We recall that e, f are the vibration-rotation energies of the molecule in the anion and neutral molecule states, E denotes the kinetic energy carried away by the ejected electron, and the density of translational energy states of the ejected electron is p(E). Also recall that we use the short hand notation to symbolize the multidimensional derivative operators that arise in non BO couplings and that embody the momentum-exchange between the vibration/rotation and electronic degrees of fieedom ... 

Figure 17 Kinetic theory and viscosity A schematic illustrating momentum exchange in a flowing gas.

Figure 20 Mass transfer and momentum exchange during free molecular flow in a long tube.

From the position of each particle, we can calculate its contribution to the local solid volume fraction es in any specified fluid cell. This local void fraction, e = 1 - es, is one of the key parameters that controls the momentum exchange between the phases and should be determined with care. 

Returning to the momentum equations, the third term on the right-hand side of Eqs. (145) and (146) contains the gas-solid momentum-exchange models Likewise, the fourth term on the right-hand side of Eqs. (146) contains the solid-solid momentum-exchange model fsm . Note that because solid-solid interactions conserve momentum, the latter must be defined such that... 

Determination of accurate models for fm and fsm is nontrivial (Drew and Passman, 1999), and no consensus exists on the exact forms needed to describe particular flows. Nevertheless, it is generally acknowledged that the momentum-exchange model must include drag terms with forms similar to... 

A spray is a turbulent, two-phase, particle-laden jet with droplet collision, coalescence, evaporation (solidification), and dispersion, as well as heat, mass and momentum exchanges between droplets and gas. In spray modeling, the flow of gas phase is simulated typically by solving a series of conservation equations coupled with the equations for spray process. The governing equations for the gas phase include the equations of mass, momentum and energy... 

Stewart, R. W. (1974). The air-sea mass momentum exchange. Boundary Layer Meteorol. 6, 151-167. 

E. Other Correlation Models 1. Momentum-Exchange Model... 

A similar equation to that of Eq. (43) was proposed by Bankoff (B6) on the basis of a bubble-flow model for vertical flow. His derivations are discussed in the following section (Section V, B). Finally, it should be mentioned that the momentum exchange model of Levy (L4), and the slip-ratio model of Lottes and Flinn (L7) are more readily applied for the determination of void fractions than for pressure drops. In general, these methods seem to give rather poorer accuracy than those already discussed. 

Consider a gas, near ambient pressure and temperature, forced by a small pressure gradient to flow through the channels of a packed bed of powder. At room temperature, a gas molecule can be adsorbed on a solid surface for an extremely short time but not less than the time required for one vibrational cycle or about 10 sec. When the adsorbed molecule leaves the surface it will, on the average, have a zero velocity component in the direction of flow. After undergoing one or several gas-phase collisions it will soon acquire a drift velocity equal to the linear flow velocity. These collisions and corresponding momentum exchanges will occur within one,... 

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