# Cellulose Recovery from Agri-Food Residues by Effective Cavitational Treatments
## 2 Acoustic and Hydrodynamic Cavitation: Highlights
### Hydrodynamic Cavitation  
Cavitation phenomena such as the formation, growth and instantaneous collapse of gas- or vapor-filled bubbles, can also be generated by liquid flow in hydraulic systems (hydrodynamic cavitation, HC). In this case, pressure variations in the flowing liquid are generated by the fluid passing through constrictions (Figure 3).  
The HC can be generated by Venturi tubes, orifice plates, throttling valves or rotating indentations (See Figure 3) [42].  
HC can be explained, according to [PERSON]'s equation, based on the relationship between velocity and pressure of the fluid. Bubbles are generated when pressure falls below the vapor pressure of the liquid in correspondence of the constriction. The cavitation bubble generation is described by the cavitation number Cv (Equation (1)):  
\[C_{v}=\frac{P_{f}-P_{v}}{0.5\rho U^{2}} \tag{1}\]  
Figure 2: General representation of the acoustic cavitation phenomena.  
where \(P_{f}\) is the downstream pressure, \(P_{v}\) is fluid vapor pressure, \(\rho\) is the fluid density and \(U\) is the average velocity nearby the orifice. In theory, cavitation will be formed when \(C_{v}\leq 1\); in practice, it is influenced by other factors than flow velocity, such as the presence of various suspended particles and dissolved gases [43]. A high cavitation number implies that cavitation will not likely take place and vice versa. If cavitation is already in progress, lowering the cavitation number by increasing the flow rate or by decreasing the pressure will boost the cavitation intensity. Increasing the cavitation number may stop cavitation entirely [44].  
The bubbles' collapse occurs downstream from the constrictions, where the flow decreases and the pressure restores. Under appropriate conditions, the bubbles explosion results in release of large magnitudes of energy which helps the cleavage of the complex biomass structure. Moreover, the copious local low-intensity temperature and pressure impulses generated during HC make it suitable for reactions that require relatively mild pressure and temperature conditions, thus preventing, for example, the formation of degradation products [45].  
Bubble dynamics is noteworthy when considering the effects of cavitation. In particular, two main features should be considered: (1) the maximum bubble size and (2) the distance covered by the bubble before downfall, i.e., bubble life. The former defines the cavitation intensity; larger bubbles, formed at high temperature or low pressure [46], collapse with a greater intensity and can produce greater effects on a substrate than smaller ones. For example, they can deeply modify the structure of biomass. Conversely, bubble life is an estimation of the volume where cavitation effects are located, corresponding to the active portion of the system. Commonly, bubble life drops as the region of effective cavitation decreases and vice versa. Many factors affect cavitation, such as the viscosity of the fluids and the vapor pressure. Indeed, to create this phenomenon, highly viscous fluids entail higher energy input, as well as a fluid with a low vapor pressure. Additionally, the geometry and size of the cavitator could deeply influence the process efficiency.  
As HC is easier and more economical to scale-up than AC, it is often applied to biomass as a physical pretreatment method for delignification, in order to enhance the enzymatic digestibility of cellulose [47]. Indeed, the high energy-efficiency of HC-assisted processes is useful for scaling up. Moreover, it also allows the reduction of chemical catalysts, still with high lignin removal and high glucose (Glu) yield.  
Figure 3: Hydrodynamic cavitation phenomenon in a fluid: Venturi effect and rotor-stator system.  
In addition to the physical biomass pretreatment for cellulose recovery, HC can also be exploited as a green process to enhance extraction of bioactive compounds, proteins and lipids from biomass [48; 49; 50].