Interparticle collisions

Note that flocculation is a purely physical process in which the treated water is gently stirred to increase interparticle collisions and, thus, promote the formation of large particles. After adequate flocculation, most of the aggregates will settle out during the 1 to 2 hours of sedimentation. 

Stokes law is rigorously applicable only for the ideal situation in which uniform and perfectly spherical particles in a very dilute suspension settle without turbulence, interparticle collisions, and without che-mical/physical attraction or affinity for the dispersion medium [79]. Obviously, the equation does not apply precisely to common pharmaceutical suspensions in which the above-mentioned assumptions are most often not completely fulfilled. However, the basic concept of the equation does provide a valid indication of the many important factors controlling the rate of particle sedimentation and, therefore, a guideline for possible adjustments that can be made to a suspension formulation. 

Suslick KS, Doktyez SJ (1989) The sonochemistry of Zn powder. Am Chem Soc 111 2342-2344. Prfozorov T, Prozorov R, Suslick KS (2004) High velocity interparticle collisions driven by ultrasound. J Am Chem Soc 126 13890-13891... 

Doktycz SJ, Suslick KS (1990) Interparticle collisions driven by ultrasound. Science 247 1067-1069... 

The motion of a particle in the flow field can be described in the Lagrangian coordinate with the origin placed at the center of the moving particle. There are two modes of particle motion, translation and rotation. Interparticle collisions result in both the translational and the rotational movement, while the fluid hydrodynamic forces cause particle translation. Assuming that the force acting on a particle can be determined exclusively from its interaction with the surrounding liquid and gas, the motion of a single particle without collision with another particle can be described by Newton s second law as... 

Compressing a gas brings the particles into close proximity, thereby increasing the probability of interparticle collisions, and magnifying the number of interactions. At this point, we need to consider two physicochemical effects that operate in opposing directions. Firstly, interparticle interactions are usually attractive, encouraging the particles to get closer, with the result that the gas has a smaller molar volume than expected. Secondly, since the particles have their own intrinsic volume, the molar volume of a gas is described not only by the separations between particles but also by the particles themselves. We need to account for these two factors when we describe the physical properties of a real gas. 

Note how Equation (2.2) simplifies to become the ideal-gas equation (Equation (1.13)) if the volume V is large. We expect this result, because a large volume not only implies a low pressure, but also yields the best conditions for minimizing all instances of interparticle collisions. 

Rate of interaction-force-controlled interparticle collision... 

Early experience also showed that the induced plasma current in a tokamak generates a magnetic field that loops die minor axis nf Ihe torus. The field lines form helices along the toroidal surface the plasma must cross the lines to escape. It does so through the cumulative action of many random displacements caused by interparticle collisions, tin effect diffusing across the field lines and out of the system). Thermal energy is transported by much the same process. 

Fig. 4. Scanning electron micrograph of 5-Jim diameter Zn powder. Neck formation from localized melting is caused by high-velocity interparticle collisions. Similar micrographs and elemental composition maps (by Auger electron spectroscopy) of mixed metal collisions have also been made.

Fig. 5. The effect of ultrasonic irradiation on the surface morphology and particle size ofNi powder. Initial particle diameters (a) before ultrasound were 160 fim (b) after ultrasound, 80 fan. High velocity interparticle collisions caused by ultrasonic irradiation of slurries are responsible for the smoothing...

Figure 8.4 shows the Trost Jet Mill from Colt Industries. In principle, it is an opposed jet mill and its grinding action is achieved by interparticle collisions in impinging streams. It has a centrifugal classifier, the grinding capacity can be 1 to 2300 kg per hour and the airflow rate varies from 0.2 to 28 m3minf. ... 

Each particle is considered as a center to which other particles diffuse by Browian motion. Thus the rate of flocculation is proportional to the square of the number of particles. The original treatment assumed that all interparticle collisions were effective in causing flocculation. Later modifications (6) assumed that the potential energy barrier between particles resists flocculation and that only those collisions with sufficient energy to overcome this barrier will cause flocculation. The agitation-induced flocculation has also been analyzed theoretically (7). 

Therefore, from Fig. 4.2, the correction factor C is found to be 5. The collisional heat transfer coefficient by interparticle collisions is thus given by Eq. (4.34) as... 

The Eulerian continuum approach, based on a continuum assumption of phases, provides a field description of the dynamics of each phase. The Lagrangian trajectory approach, from the study of motions of individual particles, is able to yield historical trajectories of the particles. The kinetic theory modeling for interparticle collisions, extended from the kinetic theory of gases, can be applied to dense suspension systems where the transport in the particle phase is dominated by interparticle collisions. The Ergun equation provides important flow relationships, which are useful not only for packed bed systems, but also for some situations in fluidized bed systems. 

When the gas-solid flow in a multiphase system is dominated by the interparticle collisions, the stresses and other dynamic properties of the solid phase can be postulated to be analogous to those of gas molecules. Thus, the kinetic theory of gases is adopted in the modeling of dense gas-solid flows. In this model, it is assumed that collision among particles is the only mechanism for the transport of mass, momentum, and energy of the particles. The energy dissipation due to inelastic collisions is included in the model despite the elastic collision condition dictated by the theory. 

When the particle concentration is high, the shear motion of particles leads to interparticle collisions. The transfer of momentum between particles can be described in terms of a pseudoshear stress and the viscosity of particle-particle interactions. Let us first examine the transfer of momentum in an elastic collision between two particles, as shown in Fig. 5.8(a). Particle 1 is fixed in space while particle 2 collides with particle 1 with an initial momentum in the x-direction. Assume that the contact surface is frictionless so that the rebound of the particle is in a form of specular reflection in the r-x-plane. The rate of change of the x-component of the momentum between the two particles is given by... 

Consider a gas-solid suspension which is in a state of steady dilute flow with no interparticle collision or contact. In this situation, the linear particle velocity is practically identical to the superficial particle velocity. The motion of a spherical particle in an oscillating flow field can thus be given by... 

Interactions of the fluctuating part of the particle motion with the mean particle motion through interparticle collisions, which generate pressure and stresses in the particle assembly, consequently yielding apparent viscosity of the particle phase... 

The role of the pressure gradient may be shown in the momentum equation of a gas-solid mixture. Consider a steady pipe flow without mass transfer and with negligible interparticle collisions. From Eq. (5.170), the momentum equations for the gas and particle phases can be given by... 

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