Acceleration, of particles

The previous investigations of hard particle transport processes during laser beam dispersing have shown, that the high speed microfocus radioscopy system is a usable arrangement to observe and analyse the movements, velocities and accelerations of particles inside the molten bath. That possibility was, until now, not given by conventional techniques of process... 

In the molecular dynamics (MD) [1, 2] technique, a system of particles evolves in time according to the equation of motion, E = nijXj, where L, is the net force acting on particle i, and m, and 3q are the mass and acceleration of particle i, respectively. In a molecular system, typical bond lengths are of the order of angstroms while bond vibrations take place at the time scale of 10-13 s. Therefore, the equations of motion for atoms have to be integrated with time steps on the order of 10 15 s. However, many important chemical and biological phenomena in macromolecules take place at much larger time scales, as shown in Table 8-1. 

When the air density is low and particle diameter is small compared with the mean free path, Equation 7 for the velocity must be modified by the drag slip correction. This corrects for the acceleration of particles during the time between collisions with air molecules, which increases the average velocity. The correction factor may be written (4) ... 

On the resistance constitution of the equipment system, the major conclusions that can be drawn from the investigation are (1) Where millets or rapeseeds are the material to be processed, the power for the operation of the impinging stream contactor is mainly (>80%) consumed in the acceleration of particles (2) The pressure loss due to the impingement between the opposing streams is independent of the presence of solid particles. 

Meng, F., Wang, W. and Li, J., A method of measuring velocity and acceleration of particle clusters in two-phase flows. Chinese Patent No. 200910082721.0 (2009). 

For transport of a gas-solid suspension, it is important to be able to evaluate the pressure drop in order to estimate the power consumption. In a pneumatic conveying system, particles are usually fed into the carrying gas and accelerated by the gas flow. The power consumption (or pressure drop per unit pipe length) for the acceleration of particles can be significant compared with that for a fully developed flow condition. Moreover, the pressure... 

Bai, D., Jin, Y., and Yu, Z. Acceleration of particles and momentum exchange between gas and solids in fast fluidized beds, in Fluidization 91—Science and Technology (Kwauk, M., and Hasatani, M., eds.), pp. 46-55. Science Press, Beijing, 1991a. 

After solvent removal the aerosols produced from slurries deliver solid particles, the diameters of which are those of the powder particles. In slurry nebulization used for flame work or plasma spectrometry, they are injected with a velocity that is less than or equal to the nebulizer gas atom velocities, as viscosity drag forces are responsible for their entrainment into the ICP. The velocity of the gas atoms (vG) can be calculated from the gas temperature at the location considered (TG), the injection velocity (vi) and the temperature at the point of injection (T), as vG = Vi x TG/Ti and the acceleration of particles (d2z/dt2) as a result of the viscosity drag forces is ... 

Sedimentation analysis can be successfully used in systems containing particles with radii in the range between 1 and 100 pm. When larger particles settle in a low viscosity medium, such as water, one has to account for the deviations from the Stokes equation due to turbulent flow of medium around the particles, and introduce correction factors accounting for the acceleration of particles at the beginning of sedimentation. Sedimentation of particles with sizes on the order of fractions of a micron and those of smaller sizes is influenced by the diffusion phenomena to a significant extent (see Chapter V,... 

Centrifugal acceleration of particle got into swirling flow is estimated as a = / R and... 

Bradley M.S.A., Famish R.J., Hyder L.M. and Reed A.R., A novel analytical model for the acceleration of particles following bends in pneumatic conveying systems, in Handbook of Conveying and Handling of Particulate Solids, Eds. Levy A. and Kalman H., Elsevier Science B.V. Amsterdam, the Netherlands, 2001. 

Dudukovic et al. [24] introduced an empirical parameter (i//) to take into account the acceleration of particles in the bed, instead of solving Equation (22.10) and Equation (22.11). The average velocity was given as ... 

Unresolved question. The question of the existence of isolated magnetic poles (monopoles) is an active subject of research. Numerous attempts have been made to experimentally isolate magnetic monopoles, without success until now. Theories, notably quantum theories, that predict their existence (in predicting a mass beyond reach by present accelerators of particles) are considered suspiciously while waiting experimental confirmation. 

C. Joshi, T. Katsouleas (eds.) Laser Accelerators of Particles, AIP Conf. Proc. 130 (Am. Inst. Physics, New York 1985)... 

Hinkle, B. L. Acceleration of Particles and Pressure Drops Encountered in Horizontal Pneumatic Conveying, Ph.D. Thesis, Georgia Institute of Technology, Atlanta, GA, 1953. 

Equations (1) and (2) are solved by Euler s explicit scheme using finite difference method. The acceleration of a particle can be obtained from the known contact forces, moments, mass and mass moment of inertia. The acceleration is integrated by time to deld the velocity increment and the velocity is integrated again by time to yield the displacement increment. By repeating these processes for all particles, the motion of all particles and the dynamical behavior of granular material can be obtained entirely. Consequently, the unbalanced forces and moments produce the linear and rotational accelerations of particle in the next calculating step successively. 

A novel analytical model for the acceleration of particles following bends in pneumatic conveying systems... 

A differential equation is an equation that contains one or more derivations of an unknown function. The solution of a differential equation is a function that satisfies the equation. Our first examples of differential equations are classical equations of motion, which involve the position, velocity, and acceleration of particles. The position of a particle is given by the position vector r with Cartesian components X, y, and z ... 

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