Forces on small particles

Small particles with radii smaller than the cavitation bubbles are accelerated in the velocity and pressure gradients around oscillating bubbles. These forces are even greater when particles are subject to shock waves. Particle velocities of up to 500 km/h can be reached. On collision of two such particles, oxide layers are removed and metals are melted together. Such treated metals are used in catalysis, where activity enhancements by a factor of up to 10 are observed. 

Like the Bjerknes forces, solid particles whose acoustic properties differ from those of the liquid are subject to primary and secondary forces. Primary forces drive particles into pressure nodes, where secondary forces between particles are responsible for further aggregation. 

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Water and often fine sand and silt are held in various crude oils in permanent emulsions. Particularly crudes obtained by secondary methods and those from tar sands where water or steam are used contain water and mineral matter emulsified therein by the surface forces on small particles and drops. Azeotropic distillation removes the relatively small amount of water, using the solvent as an entrainer which dilutes the crude. This allows the mineral matter to be separated easily without using centrifuges with their substantial cost and wear, free of organic material, so it may be discarded with-out hazards of fire or odors the bitumen to be recovered for such use or cracked to give volatile fractions and coked to an ash-free coke the water to be obtained as distilled water for reuse. 

Burns J. A., Lamy P. L., and Soter S. (1979) Radiation forces on small particles in the solar system. Icarus 40, 1-48. 

Gould R.K. and Coakley W.T., The effects of acoustic forces on small particles in suspension. In Proceeding of the 1973 Symposium of Finite Amplitude Wave Effects in Fluids, Bjprno L. (Ed.), IPC, Guilford, UK, pp. 252-257. 

Bruus H (2012) Acoustofluidics 7 the acoustic radiation force on small particles. Lab Chip 12 1014-1021... 

Finite difference techniques are used to generate molecular dynamics trajectories with continuous potential models, which we will assume to be pairwise additive. The essential idea is that the integration is broken down into many small stages, each separated in time by a fixed time 6t. The total force on each particle in the configuration at a time t is calculated as the vector sum of its interactions with other particles. From the force we can determine the accelerations of the particles, which are then combined with the positions and velocities at a time t to calculate the positions and velocities at a time t + 6t. The force is assumed to be constant during the time step. The forces on the particles in their new positions are then determined, leading to new positions and velocities at time t - - 2St, and so on. 

If the effect of the external force on the particles during a collision is small in comparison to the interparticle forces, the solution of Eq. (1-129) is ... 

For small displacements molecular vibrations obey Hooke s law for simple harmonic motion of a system that vibrates about an equilibrium configuration. In this case the restoring force on a particle of mass m is proportional to the displacement x of the particle from its equilibrium position, and acts in the opposite direction. In terms of Newton s second law ... 

For small, stationary-state velocities, the viscous force on a particle is directly proportional to the velocity. 

Consider kq to be small enough for a spherical particle to be treated as a point charge in an unperturbed electric field, but let the particle be large enough for Stokes law to apply. Equating the electrical force on the particle with the frictional resistance of the medium,... 

Until fairly recently, the theories described in Secs. II and III for particle-surface interactions could not be verified by direct measurement, although plate-plate interactions could be studied by using the surface forces apparatus (SFA) [61,62]. However, in the past decade two techniques have been developed that specifically allow one to examine particles near surfaces, those being total internal reflection microscopy (TIRM) and an adapted version of atomic force microscopy (AFM). These two methods are, in a sense, complementary. In TIRM, one measures the position of a force-and torque-free, colloidal particle approximately 7-15 fim in dimension as it interacts with a nearby surface. In the AFM method, a small (3.5-10 jam) sphere is attached to the cantilever tip of an atomic force microscope, and when the tip is placed near a surface, the force measured is exactly the particle-surface interaction force. Hence, in TIRM one measures the position of a force-free particle, while in AFM one measures the force on a particle held at a fixed position. 

Electric forces between particles are negligibly small until the particles are almost touching. For comparison, the gravitational force on these particles is almost 6 orders of magnitude larger than this result. Hence interparticle electric forces can generally be neglected in aerosol computations. 

It follows that AGao > AGbo, since rA < rB. Because an adsorption event on smaller crystals decreases the energy of a system more than adsorption on particles in a system composed of larger particles, the driving force for adsorption is larger, thus adsorption should be favored on small particles. 

Figure 5 shows a comparison of van der Waals and the gravitational forces on small ash particles as these approach a collecting surface. Plots A and B indicate that the sub-micron sized particles are readily held on a surface by van der Waals forces. The capture of small particles of ash on boiler tube is further enhanced by surface irregularities of oxidized metal (19). Also, it has been suggested that electrostatic attraction forces enhance the transport and retention of sub-micron sized particles on steel probes inserted in the flue gas of coal fired boilers (7,20). A layer of... 

For applications in Eulerian model formulations the particles are assumed small and the dispersion is sufficiently dilute so that there is no significant particle-particle interactions [64] [65]. The net force on the particles per unit of mixture volume, Fp, is then obtained by multiplying fp by the number density of particles, Np (e.g., Albraten [1]) ... 

The force balance or momentum balance equation describes the spatial motions of small particles or droplets in an unsteady, nonuniform flow. The acceleration of the particle mass increased by the added mass results from action of several forces on the particle. Assuming that there are not any nonlinear interactions between the various forces acting on the particle, one can write (42)... 

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