Molecular collision parameter

As a practical method, designers have employed other methods such as / -pentane conversion as a key component, kinetic severity factor (31), or molecular collision parameter (32) to represent severity. Alternatively, molecular weight of the complete product distribution has been used to define conversion (A) for Hquid feeds. 

Molecular Collision Parameter. For high severity cracking, especially in the case of heavy feed stocks, hydrocarbon partial pressure and short residence time are necessary to get high yields and economic running times. Hydrocarbon partial pressure and residence time are interrelated for a fixed coil design. The molecular collision parameter combines these parameters to a single number (2) (see Equation 1),... 

Figure 3a. Methane yields as a function of molecular collision parameter. Feedstock naphtha.

Process licensors have tried to supplant this overall assessment by a finer analysis of the severity of operation of a pyrolysis furnace operating on a complex feed. Among the values thus determined are the MCP (Molecular Collision Parameter) for the treat ment of naphthas, based on considerations stemming from the kinetic theory of gases and developed by Wall and Witt of the Selas Corporation, and especially the KSF (Kinetic Severity Function) proposed by Zdonik et al of Stone ami Webster Engineering. 

The Chapman-Enskog equation (see Chapman and Cowling, 1970) is semi-empirical because it uses equation (3.11) and adjusts it for errors in the observations of diffusivity in gases. It also includes a parameter, S2, to account for the elasticity of molecular collisions ... 

As discussed by M. Shapiro and R Brumer in the book Quantum Control of Molecular Processes, there are two general control strategies that can be applied to harness and direct molecular dynamics optimal control and coherent control. The optimal control schemes aim to find a sef of external field parameters that conspire - through quantum interferences or by incoherent addition - to yield the best possible outcome for a specific, desired evolution of a quantum system. Coherent control relies on interferences, constructive or destructive, that prohibit or enhance certain reaction pathways. Both of these control strategies meet with challenges when applied to molecular collisions. 

Figure 1. Electric field, E(t), and corresponding frequency spectrum, I(v), associated with distant collision of fast electron and molecular target (a) collision parameters—t), electron velocity and b, impact parameters (b) idealized case for very fast electron (c, d) realistic picture.

At once, the previous discussion explains why the polar molecules do not exhibit a polarization effect at all the strong anisotropy of the CO-Na potential leads to a complete mixing of 2 and II states. Somewhat less easily explained is the dependence of the polarization effect on CM and its disappearance at larger scattering angles. One possibility is to ascribe small quenching cross sections to small collision parameters and thus to deeper penetration, where the molecular anisotropy is dominant and thus mixes the initial state preparation as discussed previously. 

We have examined the nature of LIFS in some detail. The response of an atomic or molecular system is described in terms of appropriate rate (or balance) equations whose individual terms represent the rate at which individual quantum states are populated and depopulated by radiative and collisional processes. Given the response of a system to laser excitation, one may use the rate equations to recover information about total number density, temperature and collision parameters. 

Rather than consider the absolute rate of atomisation, it is sometimes more convenient to employ a parameter which expresses the efficiency of the process in terms of the probability that a molecular collision with the surface results in the atomisation of the molecule involved. Such a parameter is, a defined by the relation... 

The concept of potential-energy surface (or just potentials) is of major importance in spectroscopy and the theoretical study of molecular collisions. It is also essential for the understanding of the macroscopic properties of matter (e.g., thermophysical properties and kinetic rate constants) in terms of structural and dynamical parameters (e.g., molecular geometries and collision cross sections). Its role in the interpretation of recent work in plasmas, lasers, and air pollution, directly or otherwise related to the energy crisis, makes it of even greater value. 

From the above outline, the mass-transport problem is seen to consist of coupled boundary value problems (in gas and aqueous phase) with an interfacial boundary condition. Cloud droplets are sufficiently sparse (typical separation is of order 100 drop radii) that drops may be treated as independent. For cloud droplets (diameter 5 ym to 40 pm) both gas- and aqueous-phase mass-transport are dominated by molecular diffusion. The flux across the interface is given by the molecular collision rate times an accommodation coefficient (a 1) that represents the fraction of collisions leading to transfer of material across the interface. Magnitudes of mass-accommodation coefficients are not well known generally and this holds especially in the case of solute gases upon aqueous solutions. For this reason a is treated as an adjustable parameter, and we examine the values of a for which interfacial mass-transport limitation is significant. Values of a in the range 10 6 to 1 have been assumed in recent studies (e.g.,... 

Liu and Ruckenstein [Ind. Eng. Chem. Res. 36, 3937 (1997)] studied self-diffusion for both liquids and gases. They proposed a semiem-pirical equation, based on hard-sphere theory, to estimate self-diffusivities. They extended it to Lennard-Jones fluids. The necessary energy parameter is estimated from viscosity data, but the molecular collision diameter is estimated from diffusion data. They compared their estimates to 26 pairs, with a total of 1822 data points, and achieved a relative deviation of 7.3 percent. 

G. Duration of a Collision. The hard sphere model is very useful because it permits us to describe molecular collisions in terms of a single, simple, molecular parameter, the collision diameter. It is, however, insufficient to permit a detailed description of a chemical reaction, which is an event that transpires during a collision between two molecules, because the duration in time of a hard sphere collision is precisely zero. 

The dependence of natural convection heat transfer on the aforementioned parameters can be established based on the physics of the process. Let us assume that a vertical wall is in contact with a fluid. The wall temperature Tw is higher than the fluid temperature T. When a unit volume of fluid contacts the hot wall, the fluid receives energy from the wall due to molecular collisions. The fluid molecules begin to move with a higher velocity. The initial fluid volume expands. From this description one can conclude that energy transfer should depend on the parameters T, Tw, P, and cp. 

The parameter the diffusion collision integral, is a function of k T/e, where is the Boltzmann constant and e is a molecular energy parameter. Values of tabulated as a function of k T/e, have been published (Hirschfelder et al., 1964 Bird et al., 1960). Neufeld et al., (1972) correlated using a simple eight parameter equation that is suitable for computer calculations (see, also, Danner and Daubert, 1983 Reid et al., 1987). Values of a and e/k (which has units of kelvin) can be found in the literature—for only a few species—or estimated from critical properties (Reid et al., 1987 Danner and Daubert, 1983). The mixture a is calculated as the arithmetic average of the pure component values. The mixture e is taken to be the geometric average of the pure component values. 

The parameter k contains the molecular collision number per unit area of adsorbent surface and hence varies as in contrast for site... 

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