Sticking and Rebound

Jordan [214] analyzed the conditions for sticking and rebound of vertically impinging particles. According to Bradley [25], the force of interaction of two quartz macroparticles with diameter c/ at a distance H between them is given by... 

Jordan [128] considered the conditions for the sticking and rebounding of vertically-incident particles (Fig. V.3). According to Bradley [43], the interaction between two macroscopic quartz particles of diameter dp at a distance of H from each other equals... 

M. BOUDART Let us take a simple case that of a gas on a liquid surface the principle is the same for a solid surface. Consider now a molecule impinging on the liquid surface, will it stick or rebound Knudsen would say that it would stick. For a simple molecule condensing on a simple liquid, we postulate that in the transition state between the gas and the surface layer the molecule has two-dimensional translational freedom and is still free to rotate. Then the sticking probability would be unity. If, however, the activated complex has no rotational freedom, the sticking coefficient is much less than unity in accordance with measurements. Various values of the activation entropy will be obtained for other systems depending on the number of translational, rotational, and vibrational degrees of freedom involved. 

Besides, it is necessary to be able to predict which regime occurs at droplet impact. Threshold criteria are then defined which establish the boundaries between the four basic outcomes (stick, spread, rebound and disintegration). Particular emphasis is given here to the transition from spread to disintegration, due to its relevance to model the secondary spray generated at spray impact (e.g., [17]). Most criteria make use of the Weber number (e.g., [18]). However, care must be taken to assure that viscous effects are negligible (e.g., [2]), otherwise the Weber number alone does not describe the phenomenon. Prompt splash is then predicted to occur when inertial forces overcome capillary effects, i.e., when ... 

An alternative and at least in principle much simpler and easier electrochemical approach to that of the previous section, in which nanoparticles are sequentially isolated, immobilised on an electrode and then analysed via stripping voltammetry, is the direct study of the nanoparticles suspended in a solution phase into which an electrode under potentiostatic control is introduced. The movement of the nanoparticles in the solution is expected to approximate to Brownian which from time to time will bring the nanoparticles close to or in physical contact with the electrode to which they can either stick or rebound, unless the electrode is held at a potential corresponding to the oxidation or reduction of the nanoparticles or at least the surface of the nanoparticles. In the latter case, the nanoparticle impacts on the electrode are revealed by a pulse of current, as shown schematically in Fig. 8.4. These spikes can be used to identify ( fingerprint ) the nanoparticles (by virtue of their onset potentials ), measure their concentrations and to size them as discussed in more detail below. This type of measurement is currently subject to significant levels of interest (see reference (32) for an early review). 

Finally, the parameter R> represents the fraction of particles, once in contact, that stick to the surface. Generally, small particles do not possess sufficient inertia to bounce off a surface, and Rt is simply unity. We noted this earlier in arguing that the surface resistance rc for particles is usually taken to be zero. Whether a particle possesses sufficient inertia to rebound from a surface depends on its Stokes number. Zhang et al. (2001) use the following form for R suggested by Slinn (1982) ... 

Article 6 passes through inductor 7 of an HFC generator where it is heated above the polymer melting point and then passes through the spraying zone. Powder particles stick to the article or rebound from its surface, get to the rarefaction zone and are drawn into the channel of pipeline 1. The installation is loaded with the powder from bin 8. The ready coating is post-fused in the second inductor 9. 

Comment by D. J. Santeler, Aero Vac Corporation The interesting analysis of the molecular rebound from a tube causing an increase in sticking coefficient from 0.90 to 0.997 is equally applicable to the thermal adsorption problem of honeycomb structures. Experimental tests on flat panel vs, honeycomb have given the following improvements 0.70 to 0.91, 0.90 to 0.98, and 0.95 to 0.99, all in good agreement with the molecular equations presented. 

When a solid surface is exposed to a gas, the molecules of the gas strike the surface of the solid. Some of the striking molecules stick to the solid surface and become adsorbed while the others rebound. Initially the rate of adsorption is large as the whole surface is bare but as more and more of the surface becomes covered by the molecules of the gas, the available bare surface decreases and so does the rate of adsorption. However, the rate of desorption, which is the rate at which adsorbed molecules rebound from the surface, increases because desorption takes place from the covered surface. As time passes, the rate of adsorption continues to decrease while the rate of desorption increases until an equilibrium is reached between the rate of adsorption and the rate of desorption. At this stage the solid is in adsorption equilibrium with the gas, and the rate of adsorption is equal to the rate of desorption. It is a dynamic equilibrium because the number of molecules sticking to the surface is equal to the number of molecules rebounding from the surface. 

From the advanced fuel analysis the ash forming elements of the fuel are identified, their melting behaviour is calculated under furnace conditions and a stickiness criterion as function of ash particle temperature is defined for each individual fuel. In the CFD calculations this stickiness criterion is utilised by checking the particle temperature at its impaction on a wall or superheater surface. If the particle temperature is above the stickiness criterion, the ash particle sticks at the wall and the location is recorded as location for possible deposition. On the other hand, if the particle temperature is below the criterion, the particle rebounds back to the furnace and continues its flight. Figure 1 shows a deposition map for the back wall of a bubbling fluidised bed freeboard. The coloured dots show the locations for particle hits at the specified temperature on the wall and clearly indicate the areas of possible deposition in this furnace. The picture on the left of the figure shows the deposit situation in the real furnace and serves as validation for the applicability of the tool. 

Regarding the properties of the sprayed solution, it is observed in Fig. 7.65 that faster agglomeration is obtained as the binder mass fraction and, therefore, the viscosity of the liquid increases. This is due to the higher ability of deposited liquid layers to dissipate the kinetic energy of collisions, so that the particles involved tend to stick together rather than to rebound. 

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. 

In the three-dimensional dependency between restitution coefficient, impact velocity and fiquid viscosity is illustrated. From obtained results it can be seen that during coUisions with small impact velocities the restitution coefficient equals to zero and this indicates that particles stick to each other. Increasing of the fiquid viscosity leads to an increased amount of energy dissipated in contact and as a consequence to the larger values of the minimal rebound velocity (Fig. 30). 

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