1.3 Hydrodesulfurization (HDS) Process
1.8.1 Cavitation Bubble Dynamics
due to ultrasound propagation. Occurrence of cavitation phenomenon induced by the propagation of the ultrasound wave can be explained as follows: In oscillatory motion during propagation of the wave, the fluid elements in the bulk medium are pulled apart from each other. If the amplitude of the ultrasound wave is strong enough to overcome the Laplace pressure (2σ r) of the liquid medium, the bond between the two fluid elements can break with creation of a void or cavity between them. In the subsequent compression cycle, this cavity is annihilated, giving rise to extreme concentration of energy. Theoretically, for creation of a “cavity”, the acoustic pressure has to overcome the van der Waal’s distance between the two molecules.
This would require enormous pressure amplitude (> 10,000 bar) of the ultrasound wave. However, in practical situation, cavitation occurs at very low pressure amplitude as 1.2 bar. This is due to presence of nuclei or weak spots in the liquid that assist occurrence of cavitation phenomenon. These nuclei or weak spots could be small bubbles or particles already present in the liquid or these could also be gas pockets trapped in the crevices in the solid boundaries of the processor or ultrasound probe. Under the influence of pressure variation due to ultrasound, these gas pockets or bubbles expand in the rarefaction cycle giving rise to cavitation event. The cavitation bubbles in this case are filled with non-condensable gas, usually air. If the temperature of the bulk liquid is sufficiently high, local vaporization of the liquid may also occur resulting in formation of vapor bubble.
occurrence of cavitation in the medium is variation in the bulk pressure of the medium. On the basis of this criterion, various types of cavitation can be categorized as follows:
Acoustic Cavitation: Acoustic cavitation is caused by the pressure variation in the liquid due to passage of an acoustic wave. It generally occurs in the acoustic frequency range of 20 kHz – 1 MHz.
Hydrodynamic Cavitation: Hydrodynamic cavitation occurs due to pressure variation
in the liquid flow velocity generated by the changing flow geometry. This pressure variation generally occurs at low frequencies (100 Hz – 10 kHz).
Optical Cavitation: Optical cavitation is a result of local evaporation of liquid due to
intense local energy dissipation caused due to sources such as high–intensity laser.
Particle Cavitation: Particle cavitation is produced by any elementary particle (such as proton) rupturing the liquid.
The phenomenon of cavitation is influenced by many physical factors related to ultrasound itself and the physical properties of the liquid medium. Given below is a brief description of the effect of each of this factor / property. Fig. 1.10 lists some of these factors and properties that affect the radial motion of cavitation bubbles.
Figure 1.10: Physical factors (or parameters) and properties influencing cavitation
Ultrasound Frequency: The intensity of the transient collapse of the bubble in the compression half period of the ultrasound wave depends on the expansion of the bubble, which occurs in the rarefaction half period. As the frequency of the ultrasound wave increases, the period of the wave and the duration of both rarefaction and compression half cycles decrease. For a given pressure amplitude of the ultrasound wave (higher than transient cavitation threshold), expansion of the bubble reduces with increasing frequency; and hence, the intensity of the subsequent transient collapse as well. Thus, the cavitation effect tends to be lower at higher frequencies.
For power ultrasound used for sonochemical application, frequencies in the range of 20–30 kHz are normally used. In oxidation reactions, however, higher frequencies could be employed so as to enhance the reaction rate due to higher rate of hydroxyl radical formation at these frequencies. The acoustic pressure amplitude (and hence the net power input) required to cause transient cavitation at higher frequencies (in the range of 100-500 kHz) is significantly higher than that for 20 kHz.
Ambient or Static Pressure in the Medium: Ambient or static pressure in the medium is an important factor governing the expansion of the cavitation bubble in the rarefaction half cycle of ultrasound. The bubble expands to size higher than its original (or equilibrium) size, only when the instantaneous pressure in the medium falls below the ambient pressure. This means that higher acoustic pressure amplitude (and hence higher energy) is needed for generating cavitation at higher static pressure, or in other words, transient cavitation for a given acoustic pressure amplitude can be eliminated (and converted to stable, small amplitude oscillatory behavior) by raising the static pressure in the medium. For cavitation bubbles which are significantly smaller than the resonance size, the transient cavitation threshold is essentially equal to the static pressure in the medium.
Acoustic Intensity: Acoustic intensity or acoustic pressure amplitude has a profound effect on the characteristics of cavitation events occurring in the medium. To achieve transient motion of the cavitation bubble which would result in generation of high temperature and pressure peaks in the bubble during collapse would require certain minimum amplitude of the wave, called as “transient cavitation threshold”. This requires expansion of the bubble to at least twice of its initial size. Below this threshold value, the amplitude of the wave would be too small to cause significant bubble growth. In such cases, the bubble undergoes small amplitude, stable, oscillatory motion, which is not energy intensive. As noted in previous sub-section, for cavitation bubbles which are much smaller than the resonance size corresponding to the applied frequency, the transient cavitation threshold is essentially equal to the static pressure in the medium. This for typical frequency range of 20-50 kHz used for power ultrasound used in sonochemical reactions, the transient cavitation threshold for atmospheric static pressure is about 1.2 to 1.5 bar. The size range of initial bubble radii that undergo transient motion and collapse for this range of frequency and pressure amplitude is 2 – 20 microns.
Physical Properties: Viscosity, Surface Tension and Vapor Pressure: Viscosity of
the medium is result of the natural cohesive forces active in the liquid. It acts as a break on the radial motion of bubbles. Moreover, it is also responsible for the attenuation of the acoustic wave, with loss of the energy of the wave into thermal.
Increase in liquid viscosity dampens the radial motion of the bubbles, thus limits the maximum size attained during radial motion. The cavitation intensity, as indicated by the temperature and pressure peak attained during collapse, decreases with increasing viscosity of the liquid.
Surface tension indicates the difficulty in creating cavitation in the liquid. An increase
in surface tension of the liquid increases the cavitation threshold, i.e. the minimum acoustic pressure amplitude for creation of cavitation in liquid. The intensity of the cavitation bubble collapse increases with increasing surface tension of the medium.
The vapor pressure of the bulk liquid medium depends on the temperature of the medium. During ultrasound irradiation, the temperature of the medium increases continuously due to viscous and thermal dissipation of the momentum of the ultrasound waves. Higher vapor pressure of the liquid medium causes evaporation of the solvent vapor in the bubble. This vapor can cushion the collapse of the bubble in the compression half cycle of the wave and reduce the intensity of the collapse. As explained in greater details in the next section, some of the vapor can also get entrapped in the bubble which results in generation of chemical and radical species during the collapse.