Particle-Surface Interactions Rebound

When ti2cc = 0, a particle cannot escape the surface force field because all of the rebound energy is required to lift it out of the attractive field of the surface. The critical approach velocity conesponding to V2 = 0 is given by 

Particles of higher velocity bounce, whereas those of lower velocity stick. For d io = dJio = I 0, thus becomes 

The coefficient of restitution depends on the mechanical properties of the particle and surface. For perfectly elastic collisions, e — 1 and the particle energy is conserved after collision. Deviations from unity result from dissipative processes, including internal friction, that lead to the generation of heat and the radiation of compressive waves into the. surface material. 

In his experiment., Dahneke studied the bouncing of polystyrene latex spheres about 1 aem in diameter from polished quartz and other surfaces. Using a laser light source, he measured the velocities of the incident and reflected particles. The velocity of the incident particles was controlled by means of a deceleration chamber. 

A complete model for particle-surface interaction would include both (a) Huid mechanical effects as Lhe particle approaches the surface and b) elastic and surface forces. The Hu id mechanical calculations would take into account free molecule effects as the particle comes to within one mean free path of the surface. The presence of thin films of liquids and surface irregularities further complicate the situation. In practice, the design of cascade impactors (Chapter 6) and other devices in which rebound may be important is carried out empirically, by experimenting with various particle.s, coatings, and collecting surfaces. 

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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... 

Particles will still collide, but the frequency or the impact of the collisions can be minimised. What happens when the particles do come into close contact The encounters may lead to permanent contact of solid particles or to coalescence of liquid droplets. If they are allowed to continue unchecked, the colloidal system destroys itself through growth of the disperse phase and excessive creaming or sedimentation of the large particles. Whether these collisions result in permanent contact or whether the particles rebound and remain free depends on the forces of interaction, both attractive and repulsive, between the particles, and on the nature of the surface of the particles. 

When an aerosol flows over an object in its path, the gas velocity decreases as it approaches the surface. Both tangential and normal components of the gas velocity vanish at the surface of a fixed solid body. The particles, however, are unable to follow the gas motion because of their inertia if they come within one particle radius of the surface, they can adhere depending on the interaction between the attraction and rebound energies discussed in previous sections. An idealized version of the situation is shown in Fig, 4,5. At large... 

Reality is often quite different. When a supercritical fluid mixture expands into pressures as high as ambient conditions, the resultant expansion plume can be a complex mixture it is a high velocity gas stream that entrains precipitated particles of extracted materials and often frozen carbon dioxide. Much adjustment needs to take place in the collection zone in order to achieve something close to 100 % recoveries of solutes with concentration ranges from parts per billion (PCBs) up to 50 % (total fat in a chocolate candy). Besides the flow dynamics of the expansion, several physicochemical parameters cause the deviation from the initial simple model. They include, but are not limited to, volatility of the solute, degree of co-precipitation of solid carbon dioxide (followed almost immediately with uncontrolled subhmation of the solid), aerosol formation, surface tension, occlusion in solid carbon dioxide, rebound from impinging surface, and many other interacting phenomena. 

The ratio between adhesive interaction and elastic properties of the surface, and also the influence of this ratio on adhesion, can be analyzed on the basis of the theoretical concept of adhesion energy. The adhesion of dust particles with a direction of impact normal to the surface of the object has been analyzed by Gillespie and Rideal [239,240]. If the kinetic energy is greater than the energy of adhesion, i.e., the particles will rebound. When ad > k> the par-... 

Fb is negligible for bubbles of diameter smaller than 300 xm. Then, the forces due to T and n counterbalance each other. Hence, at equilibrium, the role of the repulsive disjoining pressure is to keep the film thickness uniform, whereas the role of the attractive transversal tension is to keep the bubble (droplet) attached to the surface. In other words, the particle sticks to the surface at the contact line where the long-range attraction prevails (see Fig. 17a), whereas the repulsion predominates inside the film, where H = P, > 0-Note that this conclusion is valid not only for particle-wall attachment but also for particle-particle interaction. For the zero contact angle, t is also zero [Eq. (152)] and the particle will rebound from the surface (the other particle), imless some additional external force keeps it attached. The deeper understanding of such phenomena has not only fundamental but also practical importance for phenomena like flocculation in emulsions or redeposition of oil droplets on solid surfaces in washing. 

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