Capture inertia

The procedure adopted here is to make use again of RRKM theory to calculate k2/k l as a function of the relative barrier height. In this case, the transition state for the, reaction is taken as the loose ion-molecule complex at the Langevin capture distance. The transition state for the reaction k2 is taken as the tetrahedral intermediate RCOYX ". By a suitable choice of the vibrational frequencies and moments of inertia, this type of calculation shows that E 0-E0 for Cl- + CH3COCl should be around — 7 kcal mol 1 in order to reproduce the experimental efficiency. This amounts to an E 0 of 4 kcal mol-1. 

A large particle will follow a path deviating from the streamline as it approaches the fiber and will impinge on the fiber surface. If the particle follows a path approximately perpendicular to the fiber surface, it is deposited as a result of its inertia. Those particles that do not follow a path directly to the surface of the fiber but that enter the airstream passing within the distance equivalent to the radius of the particle from the fiber will be intercepted. It is only necessary for the surface of the particle to touch the fiber for capture to take place [29]. 

Aerosol particles below the cloud base are captured by precipitation elements due to gravitational coagulation. This type of coagulation is caused by the difference between falling speeds of the aerosol particles and the raindrops or snow crystals. In other words, this means that precipitation elements overtake the particles. The air molecules go around the falling drops (or crystals) while large particles are impacted against the drops due to their inertia. For this reason precipitation elements are considered to be small impactors (see Subsection 4.1.2). 

If we take into account the negative effect of inertia forces on particle capture, it turns out that the grazing trajectory (Fig. 10.13) corresponds to values of b smaller than those in Sutherland s theory and the point of tangency moves from the equator towards the front pole. 

Other mechanisms for particle capture include particle settling, inertia, and hydrodynamics (I). When a particle is captured in a pore, the pore throat diameter is reduced by a factor dependent on particle size and pore throat diameter. The reduced diameter of the pore throat will lead to a lower permeability. Permeability damage due to flow of suspensions increases with particle size and solids concentration. 

Following Spielman and the aims of this book, our discussion is confined to the capture of particles in liquid suspension from low-speed laminar flows, where the particles are generally small compared with the collector. The two principal transport mechanisms are (a) Brownian diffusion for submicrometer-size particles, and (b) interception of micrometer-size, nondiffusing, inertia free particles with the collector as a consequence of geometrical collision due to particles following fluid streamlines. Inertial impaction, which can be important for gas-borne particles, is usually unimportant for particles in liquids, because the particle—fluid density difference is smaller and the higher viscosity of liquids resists movement relative to the fluid (Spielman 1977). In this section we shall... 

A notable feature of inertial deposition of partides on the body is the existence of the Stokes critical number such that at S < So- the capture of particles by the body is impossible in other words, a particle s inertia is not sufficient to overcome particle s entrainment by the flow of carrying liquid [68]. The values of Scr for the cylinder are as follows 0.0625 for potential flow, approximate solution [58] 0.1 for potential flow, numerical solution. If we take into account formation of the boundary layer at the surface, the resulting value will be So- 0.25 [68]. 

On the other hand, very small drops have small inertia, so they follow the streamlines. In this case, the capture efficiency of such drops, which also takes their adhesion into account, is equal to... 

The shear stress sensor for turbulent flow needs to accurately capture the complete turbulent fluctuation spectrum. Therefore, the shear stress sensor should possess a large bandwidth with flat and minimum frequency-phase relationship. For direct measurement, i.e., floating point sensors, the resonant frequency of the floating element and the fluidic damping determines the usable bandwidth. For the thermal sensor, the thermal inertia of the sensor element and the frequency-dependent heat conduction to the substrate influence the usable bandwidth. It is complicated to analytically predict the frequency response of the thermal sensor. Therefore, dynamic calibration is essential to characterize the frequency response of the sensor. 

A sound wave is manifested as one kind of the atmospheric normal modes, known as the acoustic mode, and is caused by the compressibility of air. There are two more kinds One is called the gravity-inertia mode, which is caused by a combinations of the restitutive force of gravity against thermally stable atmospheric stratification and the Coriolis force due to the earth s rotation. The other kind is called the rotational or planetary mode, which is caused by the meridional variation of the Coriolis force. The importance of the latter kind of normal mode as a prototype of upper tropospheric large-scale disturbances was clarified by C. -G. Rossby and his collaborators a little over one decade prior to the dawn of the numerical prediction era (see Section I). In retrospect, the very natrrre of this discovery was hidden in complicated calcnlations for the normal modes of the global atmospheric model. The mathematical analysis was initiated by the French mathematician Marquis de Laplace (1749-1827), and the complete solntions became clear only with the aid of electronic compnters. It is remarkable that Rossby was able to capture the essence of this important type of wave motion, now referred to as the Rossby wave, from a simple hydrodynamic principle of the conservation of the absolute vorticity that is expressed by the sum of the vertical component of the relative vorticity and the planetary vorticify /. 

X 10 cm/sec to 1.2 x 10 cm/sec), the contributions of other mechanisms like Brownian diffusion and particle inertia to total capture can be neglected in comparison to that of the mechanism of direct interception. 

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