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a dispersion with a particle number density (𝑵) of 0.3 x 106 cm-3 and an extended stability time (𝑨/𝑨𝟎 = 0.5 > 100 days). Cloudy macroemulsions were produced when some functionalising molecules (water, hydrogen peroxide, formic acid) were combined and shaken with 1-MN. This initial lack of solubility was followed by the formation during cavitation of optically transparent, kinetically stable nanoemulsions. Reactions appeared to still take place, producing more polar platelets (Section C, Table S.3 in SI). The ability to react molecules with boiling points that are higher than that of 1-MN (Section D in SI) indicates that the functionalizing chemistry takes place in the hot liquid zone that forms around the collapsing bubbles (secondary sonochemistry) after the partially oxidised platelets are formed in the vapour phase inside the cavitation bubbles (primary sonochemistry) [24]. 3.3 Scale up Scale up is not easily achieved with ultrasound cavitation because the technique typically shows reaction rates that initially increase but then limit and eventually decrease with increasing power input. This is due to the number of cavities becoming so high in the vicinity of the probe tip that the transfer of ultrasound energy into the reaction medium is attenuated [38]. Hydrodynamic cavitation that is produced by the decrease and subsequent increase in local pressure in flowing liquids offers a more attractive means of achieving higher production rates. The pressure drop as the fluid flows around the impact head in the reactor generates cavitation and in hydrodynamic systems this phenomenon is often characterised by a non-dimensional cavitation number (𝑪𝒗) [27] 𝑪𝒗 = (𝑷𝒓 − 𝑷𝒗)⁄(𝟏 𝝆𝒗𝟐) (2) 𝟐 where 𝑷𝒓 is the pressure at a reference point in the flow, 𝑷𝒗 is the vapour pressure of the liquid, 𝒗 is the fluid velocity at the reference point and 𝝆 is the density of the fluid. At large 𝑪𝒗 the flow is single-phase but when the flow is sufficiently fast and 𝑷𝒓 becomes close to 𝑷𝒗 (i.e. when 𝑪𝒗 decreases) cavitation begins to occur. A critical cavitation number (𝑪𝒗(𝒄𝒓)) is used to define this point of incipient cavitation. As 𝑪𝒗 drops below 𝑪𝒗(𝒄𝒓) the number of cavitation events increases. An alternative cavitation number (𝑪𝑵) that has been used for the delivery of hydrocarbon fuels by injectors in diesel and gasoline engines is 𝑪𝑵 = (𝑷𝒖 − 𝑷𝒅)⁄(𝑷𝒅 − 𝑷𝒗) (3) 8PDF Image | graphene platelets with partial oxidation via cavitation
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