ANÁLISIS DE FALLAS EN PROCESO DE VULCANIZACIÓN

In the absence of vibration, a heap of particles is stable at any slope smaller than the maximum angle of repose of static heap (or maximum angle of stability). This angle reduces in the presence of superimposed vibration (Jaeger and Nagel 1992). When a horizontal assembly of particles is subjected to vibration, the surface of the bed becomes unstable. If the vibration acceleration exceeds a critical value, the free surface forms a mound.

This is followed by the flow falling of the surface known as 'avalanches'. The effect will be compensated by an upward convection motion of particles through the central core of the heap. This in turn results in the permanent formation of a heap. Vibration frequency and amplitude play key rolls in dictating the magnitude of this effect (Thompson 1992 , Evesque and Rajchenbach 1989)

The earliest work on vibrofluidization was reported by Faraday (1837) who studied powder circulation patterns and the effect of the air gap beneath the vibrated piles of powders.

Since the above study, vibrofluidization has received considerable attention in heat transfer (Gutman 1976) and drying of granules (Pakowski et al. 1984) and more recently, in mixing and demixing processes (Fan et al. 1990).

Vibration of a particulate bed at sufficiently large amplitude results in what is termed unstable bed behaviour, de Gennes (1992) described a mechanism for this instability which is based on two relevant states

Chapter 3 Literature survey on particle size measurement

termed as passive and active regimes which occur during each oscillation cycle. In passive regime, in response to the upward motion of the containing cavity, particles become compacted and the heap behaves as a solid mass. The angle of repose can not exceed a maximum value. During active regime, the cell moves downward with acceleration greater than that of gravity. The bed becomes fluidised and an excess of granules are raised up to the unstable bed surface. In the consecutive passive lapse, the excess of particles start avalanching down the solid surface of the bed. The heap formation pattern is related to particle interactive forces (Clement et al. 1992). In general, particles with low friction demonstrate fluidization in the top layers of the bed. Whereas, high inter-particle friction forces bring about avalanches and hence change the macroscopic behaviour of the vibrofluidized bed. When surface fluidization is hindered by internal dissipation, the convective motion results in heap formation. This proposed theory that convection is the main mechanism responsible for heaping is in agreement with the work reported by Taguchi (1992) who considered visco-elastic interactions between particles which in turn induce convective motion near the surface. The depth of this localized region increases as vibration becomes more aggressive.

Gallas et al. (1992) studied the effect of shear friction in beds of powders when subjected to vibration and undergoing convective motion. They simply referred to this as a convection cell. The authors found that various types of convection cells are due to either the effect of walls or due to changes in the amplitude of vibration. The direction of convection however, is solely a consequence of shear friction.

Laroche et al. (1989) have pointed out that the convective flow is affected by two types of parameters termed as 'geometric' and 'external'. The former, is expressed as the ratio of the height of the unstable layer to the particle diameter. The latter, is directly related to the acceleration of vibration and frequency of excitation. As acceleration increases, the horizontal free surface of the bed becomes unstable and results in formation of a heap in the centre of the vibrating cell. Further increases in acceleration generates several small mounds with the most stable one close to the lateral boundary of the convective motion inside the cell. This is in contrast with the results given by Al-Khoory (1992) who considers size of the vibrating particles as the only responsible parameter in dictating the geometry of heap formation in beds during vibrofluidization.

Taguchi (1992) studied the onset of turbulent flow during vibrofluidization. He observed that as the vibration acceleration is increased, the depth of fluidised bed gradually increases. There are some local points in rigid parts of the bed which first become fluidised, then change into turbulent motion whilst other layers of the rigid bed are still solid and non-convecting. Aggressive vibration eventually brings about complete fluidization of the bed thereby, giving rise to convective motion. Taguchi argued that vibration in laminar flow is insufficient to bring about convective motion. Therefore, the motion of particles are turbulent even at the onset of vibration.

3.5 Conclusion

The precise behaviour of vibrofluidized beds has not been extensively studied. However, three different regimes have been identified when a

Chapter 3 Literature survey on particle size measurement

bed of granules experiences vibration with an acceleration greater than a critical value. These are known as convective motion of particles towards the free surface of bed, heap formation, and avalanching.

CHAPTER 4

Particle size measurement using vibrofluidization

4.1 Introduction

In the previous chapter, the basic design features together with the relative merits and disadvantages of a number of techniques for particle sizing were reviewed. The majority require either special sample preparation, are expensive or are non-robust. A common problem is associated with their inability to handle relatively large samples (>10 g ) rapidly on-line thus failing to address a major growing need in the powder manufacturing industries.

In the manufacture, for example, of industrial powders as diverse as paint pigments, cement and photocopier toner, there is a requirement to control tightly the particle size distribution. An on-line particle size measurement capability allows immediate re-adjustment of the process parameters which control the particle size if and when required. Presently, this involves taking samples to the laboratory for analysis and feeding the results to the process engineer sometime later.

This chapter describes the basic design features of the vibrating reed technique first developed by Mahgerefteh and Al-Khoory (1991) in order to address the above limitations. It also reviews some of the important preliminary results reported by the authors using the apparatus. These results form the basis of a number of investigations in the present study which attempt to identify the fundamental factors affecting the system's response.