Читать книгу Biodiesel Production - Группа авторов - Страница 44

Vibrations ranging between 18 kHz and 100 MHz can be classified as ultrasound, and the process of ultrasonication involves the use of sound waves generated from a probe or in a bath for enhancement of chemical conversions such as transesterification [51]. In the bulk liquid, ultrasound generates acoustic pressure (P _a), which adds to the already existing hydrostatic pressure (P _h). P _a depends on exposure time t, amplitude pressure of wave P _A, and acoustic cycle sin 2π as depicted in Eq. (2.4):

(2.4)

The generated sound waves have regions of compression during one half of the acoustic cycle where the liquid is compacted, creating a high pressure (P _a + P _h) along with heat generation, and regions of rarefaction during the other half when the liquid experiences a local vacuity (P _a − P _h), experiencing sudden cooling owing to decreasing local pressure [52]. The wave intensity I is related to P _A as shown in Eq. (2.5), where ρ is liquid density, while c is the speed of sound in the liquid:

(2.5)

The intensity of the wave is distributed as energy (generating heat) and thus gradually decreases over increasing distance as shown in Eq. (2.6), where I ₀ = sound intensity at probe, α = absorption coefficient, and d = distance of molecule from probe:

(2.6)

Regions in the rarefaction region often experience a fall in pressure exceed the critical distance when P _a − P _h is quite large, and this results in molecules being stretched beyond the critical distance R, which causes cavitation bubbles to form, subsequently when the compression wave hits this region. Pressure increase causes temperature and pressure inside the cavitation bubble to increase abnormally (up to 4000 K and 90 MPa) before it implodes, spreading the heat afterward, which greatly enhance chemical conversion such as transesterification. The investment costs in this process are low, and the process itself is very energy efficient; however, exposing the oil to such extreme changes in temperature and pressure at a molecular level may have damaging effects on the glycerides and FFAs, hampering fuel yield. Nevertheless, it is still one of the most sought PI approaches in commercial biodiesel production [46], as seen in Table 2.3.