Particles masses

Signal of remanent magnetization of small iron particle. Mass is approximately lOmg.Lift off is 4mm. 

The leading order quantum correction to the classical free energy is always positive, is proportional to the sum of mean square forces acting on the particles and decreases with either increasing particle mass or mcreasing temperature. The next tenn in this expansion is of order This feature enables one to independently calculate the leading correction due to quanmm statistics, which is 0(h ). The result calculated in section A2.2.5.5 is... 

Time-of-flight experiments are used to measure particle velocities and particle mass per charge. The typical experiment... 

In many cases the dynamical system consists of fast degrees of freedom, labeled x, and slow degrees of freedom, labeled y. An example is that of a fluid containing polyatomic molecules. The internal vibrations of the molecules are often very fast compared to their translational and orientational motions. Although this and other systems, like proteins, have already been treated using RESPA,[17, 34, 22, 23, 24, 25, 26] another example, and the one we focus on here, is that of a system of very light particles (of mass m) dissolved in a bath of very heavy particles (mass M).[14] The positions of the heavy particles are denoted y and the positions of the light particles rire denoted by X. In this case the total Liouvillian of the system is ... 

Figure 1 shows the particulate loading of a pipe containing gas and particulates where the nonuniformity induced by a disturbance, ie, a 90° bend, is obvious (2). A profile of concentration gradients in a long, straight, horizontal pipe containing suspended soHds is shown in Figure 2. Segregation occurs as a result of particle mass. Certain impurities, eg, metal-rich particulates, however, occur near the bottom of the pipe others, eg, oily flocculates, occur near the top (3). Moreover, the distribution may be affected by Hquid-velocity disturbances and pipe roughness.

On a given metallic particle, the repulsive force, E, is dependent on particle mass, AF electrical conductivity. O density, p and shape, s. 

The particle mass retained by each sieve is determined by weighing after drying when necessary, and each fraction is designated by the sieve size it passed and the size on which it was retained. The sieve diameter of a particle is therefore defined as the size of the sieve aperture through which the particle in question just passes through. Mass fractions of the particles are then presented in tabular or graphical form. 

The origin of the isotope effect is the dependence of coq and co on the reacting particle mass. Classically, this dependence comes about only via the prefactor coq [see (2.14)], and the ratio of the rate constants of transfer of isotopes with masses mj and m2 m2 > mj) is temperature-independent and equal to... 

For any cyclone, regardless of type, the radius of motion (curvature), the particle mass, and the particle velocity are the three factors which determine the centrifugal force exerted on the particle. This centrifugal force may be expressed as... 

Lyachshenko number, dimensionless left hand side, dimensionless particle mass, kg pressure, N/m or force, N mass feed rate, kg/s or volumetric flowrate in mVhr drag or resistance force, N physical properties correction factor for slurries Reynolds number, dimensionless right hand side hydraulic radius, m... 

Panicles entrained in the airstream deposit along the airway as a function of size, density, airstream velocity, and breathing frequency. Sizes of rougjily spherical or irregularly shaped particles arc commonly characterized by relating the settling velociiy of the particle to that of an idealized spherical particle. For example, an irregular particle which settles at the same rate as a 5 pm spherical particle has a mean mass aerodynamic diameter (MMAD) of. 5 pm. Since spherical particle mass, is a function of particle diameter, J... 

Pj = solids density (kg m" ) d = particle mass median diameter (m)... 

Particle Collection Particles in the extracted partial volume flow are retained in the collector filter. Tlie particle mass emitted is determined by the weight difference of the filter before and after the collection. Factors crucial to the measuring precision and the smallest measuring range of particle concentration are ... 

Figure 2.8 Particle mass flux during slurry sedimentation of precipitated calcium carbonate (Coulson and Richardson, 1991)...

Besides the interaction potential, an equation is also needed for describing the dynamics of the system, i.e. how the system evolves in time. In classical mechanics this is Newton s second law (F is the force, a is the acceleration, r is the position vector and m the particle mass). 

Since cyclones rely on centrifugal force to separate particulates from the air or gas stream, particle mass is the dominant factor that controls efficiency. For particulates with high densities (e.g., ferrous oxides), cyclones can achieve 99 per cent or better removal efficiencies, regardless of particle size. Lighter particles (e.g., tow or flake) dramatically reduce cyclone efficiency. 

In this section we show how the fundamental equations of hydrodynamics — namely, the continuity equation (equation 9.3), Euler s equation (equation 9.7) and the Navier-Stokes equation (equation 9.16) - can all be recovered from the Boltzman equation by exploiting the fact that in any microscopic collision there are dynamical quantities that are always conserved namely (for spinless particles), mass, momentum and energy. The derivations in this section follow mostly [huangk63]. 

For the case where there is a mass transfer resistance in the fluid external to the particle (mass transfer coefficient hn), express the mass transfer rate in terms of the bulk concentration C , rather than the concentration Cts at the surface of the particle. 

Film dijfusion With a fast surface reaction on a nonporous particle, mass transfer limitations can arise in the fluid phase. 

Mass Concentration of Fluorescent Particles Mass Concentration of Silicon Dioxide Particles... 

Factors that enhance tunnelling are a small particle mass and a narrow potential energy barrier. In biology, electron transfer is known to occur over large distances (up to about 25 X 10 m). Given the mass of protium is 1840 times that of the electron, the same probability for protium... 

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