An Overview of Current Insights and New Perspectives for Semi-Industrial Applications of Cavitation Reactors

Abstract

This overview is intended to shed light on the current state of knowledge on highly efficient cavitation reactors, which are used in industry yet often remain undisclosed. The development of ultrasound (US) and hydrodynamic cavitation (HC) reactors requires a thorough understanding and precise engineering to ensure the efficacy of cavitation processes in larger industrial settings. Successful scaling-up must maintain a high energy density and ensure a homogeneous distribution of cavitation. Industrial reactor designs for both US and HC are typically optimised for continuous flow operations, though some configurations operate in a loop system. This review provides a concise examination of various reactor setups, with examples of relevant chemical and environmental applications, focusing on energy consumption and scalability challenges. Despite the similarities in the effects of acoustic and hydrodynamic cavitation, US and HC are best regarded as complementary technologies in industrial applications. This work presents our direct experience in designing novel cavitation reactors for specific applications, incorporating recent advances from the literature and insights from industry. Notably, the synergistic effects of hybrid technologies are gaining attention, particularly the integration of HC with cold plasma, which is emerging as one of the most effective techniques for treating polluted water. These technologies play a crucial role in modern process engineering, and continued advancements in their design and understanding will further expand their industrial applications in chemical processing.

1. Introduction

In 2006 the transfer of cavitational chemistry from research labs to large-scale applications was still a work in progress, with few synthetic reports [1]. Even two decades later, the discipline cannot be regarded as mature, because if at one site, ultrasonic activation was clearly generated by cavitational phenomena, the strict relationship to the equipment used strongly affected the reproducibility of the experiments [2].

Proper control of cavitation in larger reactors is critical to maintaining efficiency and preventing undesirable effects such as excessive heating and corrosion. Tailored designs are often required to meet the specific needs of different applications.

In the last few years, relevant reports have highlighted recent advances in sonochemistry, in particular using sonocatalysis to carry out reactions under milder conditions while potentially improving selectivity and efficiency thanks to the positive interaction between solid catalysts and ultrasound [3]. The modelling of the acoustic cavitation field has evolved significantly and the main advances have been discussed by Tiong et al. [4]; however, further investigations are still ongoing to optimise sonochemical reactor designs and applications. New insights into acoustic cavitation modelling will facilitate the design and scalability of sonochemical systems. Analogue studies and surveys have shown the broad applicability of hydrodynamic cavitation in the selection of a suitable HC reactor design [5]. Process temperature, HC inlet pressure, and cavitation number are crucial parameters, especially for the degradation of recalcitrant pollutants and the disinfection of harmful microorganisms. HC is becoming the best alternative technology due to its versatility and large-scale processability. The industrial use of HC was discussed by Meneguzzo and Zabini, who reported the production of almond milk and beer in a single operation with clear advantages [6]. Ciriminna et al. pointed out the need for commercial HC reactors for extraction processes [7]. Industrial sonochemical reactors were first developed in the 1960s by Saracco and Arzano, who described an optimised system for the hydrogenation of unsaturated oils. Their work showed that the reactor geometry has a significant influence on the reaction kinetics [8]. In the 1990s, great progress was made in the industrialisation of sonochemistry with the development of loop reactors (Harwell reactor), cylindrical tubular reactors, and modular, series-connected units (Branson reactor) [9]. Large-scale reactors must be equipped with several ultrasonic transducers [10] designed as multistage systems consisting of several smaller ultrasonic units connected in series [11].

The scaling-up of sonochemical batch reactors suffers from the limited penetration depth of ultrasonic waves into the liquid. For this reason, several industrial applications have been developed in flow-through reactors. Scaling laws are used to establish the relationship between reactor size and the power necessary to achieve and sustain cavitation [12]. Maintaining appropriate power density across larger reactors is vital to achieving the desired cavitation effects [13]. The design and geometry of cavitation reactors must be optimised for larger scales. This includes considerations such as the shape of the reactor chamber, the arrangement of cavitating elements (e.g., ultrasonic horns or transducers), overall flow dynamics [14], and the eventual combination of different frequencies [15].

The primary industrial applications of cavitation technology include water treatment, where it enhances pollutant degradation and microbial inactivation; emulsification, which improves the stability and uniformity of emulsions; heterogeneous catalysis, by effectively cleaning and regenerating catalyst surfaces to maintain efficiency; and sonocrystallisation, which promotes controlled nucleation and crystal growth, leading to improved product quality and yield.

Solid/liquid extraction is typically a batch process, and a new paradigm is a flow-through procedure with a multi-horn or multi-transducer flow reactor [16,17], also for semi-industrial biomass delignification [18]. Scaling up also introduces challenges in selecting reactor materials, which must withstand increased stresses and pressures associated with larger volumes and higher power levels. Material compatibility with the cavitation process, resistance to erosion, and durability become critical factors. Larger reactors may generate more heat due to higher power inputs, necessitating the incorporation of efficient heat dissipation mechanisms to prevent overheating and maintain optimal operating conditions. The successful experience in the extraction of extra-virgin olive oil assisted by ultrasound showed that commercial square-shaped tubular reactors were not suitable because of the irregular wave transmission with consequent heat generation. Differently, a correct reactor design with a round shape drastically minimises heat generation [19]. Energy efficiency at larger scales is another key concern in achieving the goal of process intensification [20]. In terms of energy consumption, HC is generally more favourable than ultrasound. The latter can be based on a horn-type system or a multiple transducer. Acoustic cavitation with horns struggles to efficiently convert acoustic energy throughout a large fluid volume because the intensity of cavitation decreases exponentially with distance from the tip of the horn, becoming negligible at relatively short distances. In contrast, while using multiple transducers results in lower operating intensities for the same power dissipation levels, the new generation of reactors described in Section 5 allows for highly efficient flow-through chemical processes. Recent literature confirms the advantages of flow-through cavitation reactors [21]. Starting from studies on sono-microreactors, the development of mesoscale and pilot-scale systems could be successfully applied in the production of nanoparticles and also the degradation of pollutants in wastewater. Strategies to optimise energy transfer, minimise losses, and enhance overall reactor performance remain active areas of research and development. A notable example of a flow-through industrial application of ultrasound is sonocrystallisation, which ensures faster nucleation kinetics, reduces crystallisation time, and promotes uniform crystal morphologies with controlled particle size distribution. In particular, the crystallization of active pharmaceutical ingredients (APIs) helps prevent undesired polymorphs and ensures consistency in pharmaceutical formulations [22]. The engineering development of new industrial plants incorporating cavitation reactors is often led by manufacturers, who rarely rely on dedicated academic studies for support. Large-scale reactor development is primarily industry-driven, with academic research mainly focused on fundamental aspects. The equipment must be robust enough to withstand long operating hours, minimising corrosion phenomena while ensuring ease of maintenance. In the following sections, we describe various types of cavitation reactors that can be scaled up for pilot- or large-scale applications.

2. Hydrodynamic Cavitation

Hydrodynamic cavitation reactors (HCRs) are continuous-flow devices designed to generate cavitation. Unlike acoustic cavitation, which relies on low-frequency ultrasound to create a low-static-pressure region in the medium, in HC, the velocity of the fluid is altered to create low-static-pressure regions. HCRs have been widely used in various applications, including wastewater treatment, biodiesel synthesis, and water disinfection, among others [23]. Based on the operating characteristics of the device, HCRs can be broadly classified into two types: (1) devices with moving parts and (2) devices without moving parts [23]. Besides the geometric parameters, material properties and operating conditions also play significant roles in affecting cavitation in HCRs. The schematics of different devices are shown in Figure 1. Cavitation in HCRs is characterised by a dimensionless parameter known as the cavitation number ($C_v$), which is defined in Equation (1):

$$C_v={\displaystyle \raisebox{1ex}{$P_2-P_v$}\!\left/ \!\raisebox{-1ex}{$0.5\ast \rho \ast v^2$}\right.}$$

(1)

• $P_2$—Pressure downstream of the device
• $P_v$—Vapour pressure of the liquid at the bulk-liquid temperature
• $\rho$—Density of the fluid at the bulk temperature
• $v$—Velocity of the fluid at the device inlet

A $C_v\le 1$ is considered optimal for the generation of cavitation. Lower values of $C_v$ result in increased cavitation intensity.

The design and operational parameters of devices without moving parts, such as orifices, venturi, vortex diodes, and venturi orifices with swirlers, will be discussed in detail.

2.1. Devices Without Moving Parts

2.1.1. Orifice Devices

Orifice devices consist of a plate with dimensions different from those of the inlet flow channel. As fluid flows through the orifice plate, its velocity increases, resulting in a reduction in local static pressure, which subsequently induces cavitation [24]. The performance of these reactors is influenced by their geometrical characteristics, namely size, shape, and number of holes in the orifice (Figure 2). Reducing the size of the holes increases fluid velocity, thereby increasing cavitation intensity. Hole shape, such as being rectangular or elliptical, can also contribute to the cavitation.

In the case of multiple-hole orifices, a large number of small holes is more effective than an orifice with a single hole [23], as shown in textile dye degradation [25]. The orifice reactors have a growing industrial application for wastewater treatment and the degradation of organic pollutants [26].

Relevant factors are α and β (Equations (2) and (3)), which are discussed in detail below.

$$\alpha ={\displaystyle \raisebox{1ex}{$Total perimeter of the holes in orifice$}\!\left/ \!\raisebox{-1ex}{$Total flow area in the orifice$}\right.}$$

(2)

$$\beta ={\displaystyle \raisebox{1ex}{$Throat area of orifice$}\!\left/ \!\raisebox{-1ex}{$Cross sectional area of pipe$}\right.}$$

(3)

As the value of β increases, the higher throat velocity in the fluid leads to an increase in the collapse pressure of cavities, resulting in more intense cavitation.

α is directly proportional to the number of holes in the orifice and inversely proportional to the size of the holes in the multiple-hole orifice plate. The β values influence the diameter of the orifice hole with respect to the cross-sectional area of the pipe [21]. The factors α and β, which depend on the number of holes and the diameter of holes, directly affect the number of cavities generated and the intensity of cavity collapse, respectively. Increasing α increases the number of cavity generation sites, and in contrast, decreasing β increases the velocity and thereby reduces the cavitation number given by (Equation (1)), increasing cavitation.

The cavitation intensity affects the physical and chemical effects of cavitation, which depend on the bubble dynamics of the cavities affected by the geometrical parameters of the reactors. For an orifice reactor, the collapse pressure and temperature, depending on the inlet pressure of the reactor, initial radius of the nuclei, and β, are given by Equations (4)–(6). This is valid for an initial cavity size of 0.01 to 0.1 mm, inlet pressure of 1–8 atm, diameter of orifice of 1–10 mm, and percentage of free area of holes of 1–20% [27].

$$P_{collapse}=C_1\ast R_0^{-1.2402}\ast P_{in}^{2.1949}\ast {({\displaystyle \frac{d_0}{d_p}})}^{-0.4732}$$

(4)

$$T_{collapse}=C_2\ast R_0^{-0.2877}\ast P_{in}^{0.3579}\ast {({\displaystyle \frac{d_0}{d_p}})}^{0.1303}$$

(5)

$$OH=C_3\ast R_0^{0.2428}\ast P_{in}^{-4.6457}\ast {({\displaystyle \frac{d_0}{d_p}})}^{-0.4732}$$

(6)

• R₀—Initial radius of cavity in µm
• P_in—Inlet pressure of the fluid in atm
• d₀/d_p—Orifice-to-pipe-diameter ratio

The single bubble dynamics explained by several equations, such as the Rayleigh–Plesset and Keller–Miksis equations, link the cavitation intensity to the bubble dynamics. The cavitation intensity depends on the collapse pressure and temperature of the cavities, which depend on the ratio of the maximum radius of cavities (R_max) that can be attained to the initial radius of nuclei (R₀) in the system. The expansion of the cavity in the low-pressure region, followed by compression of the bubble during pressure recovery, causes high temperature and pressure inside the cavities [28]. The cavity is assumed to undergo adiabatic compression during the pressure recovery when neglecting heat and mass transfer effects, and the maximum temperature and pressure reached in the cavity during compression are given by Equations (7) and (8).

$$P_{max}=\left[P_v+P_{g0}{ \ast \left({\displaystyle \frac{R_0}{R_{max}}}\right)}^3\right]\ast {\left({\displaystyle \frac{R_{max}}{R_{min}}}\right)}^3$$

(7)

where

• P_v—Vapour pressure of the liquid
• P_g0—Initial gas pressure inside the cavity
• R₀—Initial radius of the cavity
• R_max—Maximum radius of the cavity
• R_min—Minimum radius of the cavity at collapse

The collapse temperature, depending on the maximum radius of the cavity, is given by Equation (8).

$$T_{max}=T_{\infty }\ast {\left({\displaystyle \frac{R_{max}}{R_{min}}}\right)}^{3(\gamma -1)}$$

(8)

• $T_{\infty }$—Temperature of the bulk medium
• R_max—Maximum radius of the cavity
• R_min—Minimum radius of the cavity at collapse

Higher values of R_max/R₀ increase the collapse pressure and temperature and, in turn, the cavitation yield. The increase in pressure and temperature inside the cavity during the collapse of the cavities promotes the dissociation of molecules, leading to the formation of reactive OH^• radicals, which affect the chemical effects of cavitation. The physical effects of cavitation applications, such as emulsification [29], depend on the jet hammer energy of the cavity collapse, which is given by Equation (9).

$$E_J=z_2\ast {\rho }_L\ast R_{max}^3\ast U_J^2$$

(9)

• $E_J$ is the jet hammer energy
• ${\rho }_L$ is the density of the liquid medium
• R_max is the maximum radius of the cavity
• $U_J$ is the jet velocity

The optimal values of α and β must be determined based on the specific application. The selection of α and β values should align with the application’s requirements, whether it demands more intense cavity collapse with fewer cavities or a larger number of cavities with less intense collapse.

The biodiesel production is compared with four different orifice plates with different numbers of holes, α, and β. The maximum conversion for an inlet pressure of 1.5 bar and 20 min operations shows a conversion of 77% for an orifice plate with an α value of 0.4 mm^−1, whereas for a similar condition with an orifice plate with an α value of 1.33 mm⁻¹, it shows a conversion of 94%. This is attributed to the increasing cavity-generating spots with an increasing number of holes. For this same application, using a plate with a smaller β value of 0.25, a maximum conversion of 96% is obtained. This is due to the formation of a higher number of smaller cavities, resulting in a higher number of cavitation events and better emulsification, leading to higher mass transfer [30]. Chitosan degradation was studied with plates having α values ranging from 0.8 to 2 mm⁻¹ and β values ranging from 0.01 to 0.04 for an inlet pressure of 0.2 MPa and treatment time of 3 h. The degradation of chitosan increased with increasing the value of α; when comparing the plates with similar α values, plates with a larger number of holes and smaller hole diameter showed improved degradation of chitosan. This study also showed that increasing the value of β to 0.04 increased the degradation of chitosan to 33%. This is attributed to the enhancement of the cavitation region due to an increase in flow area, which in turn increased the intensity of cavitation [31]. For the rhodamine B dye degradation, increasing the α value to 4 mm⁻¹ showed an increase in the first-order dye degradation rate constant of 5.33 × 10⁻⁵/s, in comparison to the orifice plate with an α value of 0.8 mm^−1, with a rate constant of 2.67 × 10⁻⁵/s. In this same study, the β value is varied from 0.022–0.139. It can be seen that the first-order rate constant for the degradation of dye is 2.5 × 10⁻⁵/s for a β value of 0.139, and reducing the β to 0.022 gives a rate constant of around 5.5 × 10⁻⁵/s. In this case, the reduction in β leads to the formation of a larger number of cavities experiencing increased turbulence [32]. However, there are no such global values of α and β for the efficient design of orifice devices, and they are chosen based on the specific application.

A higher inlet pressure also raises the recovered downstream pressure, intensifying cavity collapse but reducing the number of cavities generated [33]. Due to the increase in inlet pressure of the fluid in the reactor, the maximum radius obtained by the bubble decreases. This is due to the increase in fluctuating velocity with increases in inlet pressure in the reactor. This is limited by the Weber number criterion, which is proportional to the ratio of inertial force to the surface tension force, which stabilises the cavity [27].

The maximum size of the cavity bubble is controlled by the Weber criterion, and exceeding the critical Weber number leads to the splitting of the cavity. The Weber number is given by Equation (10).

$$We={\displaystyle \frac{\rho \ast v^{\prime 2}\ast d}{\gamma }}$$

(10)

• ρ—Density of the liquid
• $v^{\prime }$—Turbulent fluctuating velocity
• d—Bubble diameter

The critical Weber number for the splitting of the cavity is 4.7, and the maximum bubble size attained is given by Equation (11).

$$d_m={\displaystyle \frac{4.7\ast \gamma }{\rho \ast v^{\prime 2}}}$$

(11)

where

• d_m—Maximum stable bubble diameter
• γ—Surface tension of the liquid
• ρ—Density of the liquid
• $v^{\prime }$—Turbulent fluctuating velocity

To optimise cavitational performance, an appropriate inlet pressure must be maintained to maximise cavity collapse without drastically lowering the number of cavities generated.

2.1.2. Venturi Devices

Venturi devices consist of a convergent section, a throat, and a divergent section. Unlike an orifice device, the velocity and pressure change gradually in a venturi device (Figure 2). This gradual change in velocity and pressure allows the cavities to grow to a significant size and enables the bubbles to remain in the low-pressure region for a longer duration [21]. Similarly to orifice devices, venturi devices are also affected by geometrical factors such as γ (Equation (12)) and the divergence angle of the divergent section, as well as operating parameters like temperature and inlet pressure.

$${\displaystyle \raisebox{1ex}{$\gamma =Throat height/Diameter$}\!\left/ \!\raisebox{-1ex}{$Throat Length$}\right.}$$

(12)

The cavitation number increases with a longer throat length and decreases with a larger throat diameter. The value of γ affects the residence time of the cavities, which determines the maximum size the cavities can reach, and, consequently, influences the cavitation intensity. Numerical studies have shown that an optimal γ value of 1:1 yields the best performance.

The density contour and pressure profile along the length of the venturi show a minimum-pressure region where vaporous cavities in the flowing liquid are higher than 1:1, and even though higher ratios of γ have no effect on the number of cavities generated and their growth rate. In spite of this, increasing the γ beyond 1:1 causes an increase in the permanent pressure drop, restricting the cavities from experiencing the oscillation behaviour of the surrounding pressure field and thus causing these cavities to become inactive and dissolve in the surrounding liquid medium, thereby causing a reduction in the length of the active cavitation zone [34].

If the cross-sectional area is considered constant, a larger throat perimeter increases the number of cavities generated. Throat geometries such as rectangular, slit, and elliptical provide better cavitation performance than circular throats. To understand the influence of γ on the cavitation number of different venturi devices, γ values were varied from 1:1 to 1:3, which led to an increase in cavitation number from 0.137 to 0.153, respectively, for an elliptical venturi at an optimised pressure condition of 6 atm pressure. The cavitation values varied from 0.112 to 0.114 in the case of the slit venturi at an optimised pressure of 10 atm, and the cavitation number values remained constant at 0.112 for a circular venturi at an optimised pressure of 8 atm, which shows a reduction in performance of the venturi device with increasing values of γ [34].

The divergence angle is critical in the recovery of pressure downstream of the venturi device, influencing both the collapse pressure and cavitation yield. Higher divergence angles increase the cavitation number and reduce collapse intensity. Numerical studies have shown that a divergence angle of 5.5° is optimal [35]. Reducing the outlet divergence angle is an effective way to generate more microbubbles and increase cavitation yield by raising the collapse pressure of the bubbles.

Other operational parameters, such as temperature, significantly influence the cavitation yield. An increase in temperature raises the vapour pressure, causing cavitation to initiate earlier. It also reduces gas solubility, affecting the number of nuclei available for cavitation. Higher temperatures, however, lead to a decrease in collapse pressure, thereby reducing cavitation intensity. These reactors have proved to be useful in the removal of API molecules such as Sulfamerazine on a pilot scale, and it is concluded that design parameters play a crucial role in comparing different internal structures [36]. Emulsification of oil-in-water was performed using the slit venturi reactor, which shows a higher size reduction in the oil phase in comparison to the circular venturi per pass [37]. The sterilisation effect of cavitation was studied using a venturi reactor, and geometrical parameters were optimised to increase the killing rate of E. coli [38].

2.1.3. Vortex Diode

A vortex diode is a disc-shaped device with cylindrical axial and tangential ports (Figure 2). The axial port comprises a diffuser section, an expander, and a straight section. Both the axial and tangential ports have the same divergence angle. When fluid flows in the reverse direction, from the tangential port to the axial port, the tangential velocity in the vortex diode increases from the wall toward the centre, generating a strong swirling motion that forms a well-defined vortex core. This swirl induces centrifugal forces that create a radial pressure gradient, lowering the pressure in the central region of the device and promoting cavity formation at the core. Owing to this strong pressure gradient and the significant density contrast between the liquid and the vapour cavities, large cavities naturally migrate toward the axis of rotation, while smaller cavities largely follow the liquid streamlines and orbit around the vortex core. As a result, vapour structures are redistributed toward the centre of the device, and the formation of wall-bounded cavitation is effectively suppressed [39]. The performance of the vortex diode is evaluated using a parameter known as diodicity (D), given by Equation (13). The design of the vortex diode is affected by several factors, including diode geometry, size, aspect ratio, nozzle configuration, and the Reynolds number. Devices with higher diodicity provide better performance.

$$D={∆P}_r /{∆P}_f$$

(13)

• ${∆P}_r$—Reverse-flow pressure drop
• ${∆P}_f$—Forward-flow pressure drop

Diodicity is affected by the flow rate of the fluid in the vortex diode, which is characterised by the dimensionless Reynolds number (Re), and for a vortex diode, it is given by Equation (14).

$$Re={\displaystyle \raisebox{1ex}{$\rho \ast vn\ast dn$}\!\left/ \!\raisebox{-1ex}{$\mu $}\right.}$$

(14)

• ρ—Density of the fluid
• $vn$—Velocity of the fluid in the nozzle
• $dn$—Diameter of the inlet nozzle
• µ—Dynamic viscosity of the fluid

The aspect ratio (${\alpha }_v$) of the vortex diode is given by Equation (15):

$${\alpha }_v={{\displaystyle \raisebox{1ex}{$d_v$}\!\left/ \!\raisebox{-1ex}{$h$}\right.}}_v$$

(15)

• d_v—Diameter of the chamber
• h_v—Height of the chamber

The aspect ratio affects the strength of the vortex formed in the diode chamber. In the absence of wall friction, increases in the aspect ratio led to higher diodicity. The optimal aspect ratio varies with the Reynolds number [40]; for the highest Reynolds number flow in the diode, the optimum aspect ratio was found to be six. However, the increase in diodicity with respect to Reynolds number seems to plateau after a certain value. The divergence angle of the tangential and axial ports to the diode plays a crucial role in vortex strength. Increasing the divergence angle from 5° to 7° enhances the diodicity of the diode [39]. The divergence angle of the diode affects the flow pattern in both the cases of forward and reverse flow, which affects the overall pressure drop of the fluid in the device. In the case of reverse flow, the path lines show the formation of a vortical structure wherein the fluid in the vortex is brought to the centre after several rotations over the chamber radius. These path lines show that not all fluid travels the same distance before reaching the chamber exit. The path lines for forward flow also show that fluid impinges on the chamber, and depending on the angle of the inlet, it affects the uniformity in the radial flow, which would further lower the values of the pressure drop. Increasing the divergence angle of the diffuser helps in reducing the short path taken by the fluid element, which, in the case of reverse flow, leads to a formation of strong tangential vortex where most of the fluid elements are thrown to the periphery of the chamber, and similarly, in the case of forward flow, helps in inducing uniformity in radial flow which helps in avoiding the shorter path for the fluid elements. These changes to the divergence angle influence the flow pattern in the diode, which in turn affects the pressure drop of the flow in the diode and the diodicity of the vortex diode. Increasing the angle of divergence from 5° to 7° increases the reverse flow pressure drop by 34.67% and forward flow pressure drop by 20.6% in comparison to a diode of divergence angle of 5°, thereby increasing the total diodicity of a 7° divergence angle diode [39].

Nozzles with an inlet diameter equal to the height of the diode, attached to both the tangential and axial portions, result in higher diodicity. Moreover, the radius of curvature of the expander section of the nozzle influences diodicity. A larger radius of curvature increases the pressure drop for forward flow, which in turn reduces the diodicity of the diode [39]. The throat diameter of the device can be adjusted while keeping the device diameter constant. This modification shows that the maximum tangential velocity increases with an increase in throat diameter up to a scaling factor of four, after which it levels off. The frequency of fluctuation decreases with scale, which impacts the cavity dynamics. The strength of the swirl component and reverse-flow core remains a linear function of the inlet’s Reynolds number as the device scale increases. Flow pattern predictions show a little change in general behaviour with increasing Reynolds number. Swirl velocity in the diode increases with increasing Reynolds number and converges to a particular profile with different Reynolds numbers. The inlet Reynolds number of the diode varies in the range of 8600–172,544 for throat diameters ranging from 6 to 48 mm. The predictions exhibit the lowest maximum tangential velocity for a throat diameter of 6 mm and observed a relatively large increase in maximum swirl ratio when doubling the throat diameter to 12 mm, and further increasing in throat diameter to 24 mm showed that the throat velocity reached a constant value of 3.5 m/s with increasing the Reynolds number of the inlet flow [40]. The precessional frequency can be related to the inlet Reynolds number through the Strouhal number given by Equation (16).

$$St={\displaystyle \frac{f\ast L}{V_i}}$$

(16)

• f—Precessional frequency
• L—Diameter of the diode chamber
• V_i—Inlet velocity of the fluid

It was found that the Strouhal number varies in the range of 2.3 to 2.6 when the Reynolds number is varied from 17,085 to 31,346.

Vortex diode devices have the potential for the removal of antibiotics and organic pollutants, and also for the sterilisation of water. The vortex diode is used for disinfecting both Gram-positive and Gram-negative bacteria and shows greater efficacy in comparison to an orifice device. The pilot-scale study for the removal of ciprofloxacin and metformin using the device showed that, along with hydrodynamic cavitation, incorporating oxidising agents such as hydrogen peroxide showed a significant effect on the removal of the contaminants owing to the complex structure of the molecule [41,42]. Vortex diodes show better performance in the degradation of API pollutant Naproxen in comparison to the orifice device [43].

2.1.4. Venturi and Orifice with Swirler

Venturi and orifice devices are equipped with a swirler in the flow path to shift the cavitation zone away from the wall and into the core of the fluid flow. The presence of the swirler influences the cavitation inception, pressure drop, and flow characteristics. The parameters affected by the swirler lead to changes in turbulent fluctuations, which in turn affect cavity dynamics. The performance of the venturi and orifice devices with a swirler is influenced by the swirl ratio and Reynolds number [44]. The swirl ratio is defined by Equation (17):

$$\mathrm{S} = {\displaystyle \raisebox{1ex}{$u\theta max$}\!\left/ \!\raisebox{-1ex}{$\overline{ut}$}\right.}$$

(17)

• u_θmax—Maximum tangential velocity
• $\overline{ut}$—Mass average velocity at throat

The pressure drop increases with velocity. However, the pressure drop for an orifice and venturi device with a swirler is lower than that in the same devices without a swirler. Cavitation inception occurs at a lower pressure drop for orifice and venturi devices with a swirler compared to those without one [44]. The difference in pressure drop at cavitation inception is 10 kPa for the orifice and 5 kPa for the venturi, with and without a swirler, respectively.

The presence of a swirler in orifice and venturi devices significantly affects flow characteristics. In an orifice without a swirler, the cavitation zone remains near the throat, and only after a certain higher pressure drop do cavity clouds break into fine bubbles [37]. However, in an orifice device with a swirler, the cavitating vapour region in the throat collapses and forms cavity clouds downstream of the device. In a venturi device without a swirler, vapour clouds form at the edge of the throat and move along the diffuser, where they break into smaller vapour clouds. These smaller clouds then move back toward the throat, restarting the process. In contrast, in a venturi device with a swirler, the vapour clouds extend along the axis of the diffuser, and the swirl tends to dampen the axial advance and retreat of the cavity bubbles.

For venturi and orifice devices with a swirler, the pressure drop is lower than that of the same devices without a swirler, up to a swirl ratio (S) of two. However, for a swirl ratio greater than two, both devices with a swirler show an increase in pressure drop compared to those without a swirler [44]. Devices with a swirler demonstrate a monotonic increase in pressure drop at a swirl ratio of eight or higher, leading to increased turbulent fluctuations, which, in turn, affect cavity dynamics.

2.1.5. Devices with Moving Parts

Rotational hydrodynamic cavitation reactors (RHCRs) are a class of reactors that increase tangential velocity by accelerating the fluid and forcing it to flow through varying cross-sections to create the pressure differentials necessary for cavitation. RHCRs can be classified as rotor–rotor or rotor–stator devices, depending on the mechanics of the device. The key factors affecting the performance of RHCRs include the flow rate, rotational speed, pressure within the device, and the design of the rotor. In RHCRs, increases in rotational speed led to higher tangential fluid velocities, resulting in higher turbulence intensity and increased cavitation intensity. To achieve maximum cavitation intensity, the axial gap between the plates should be minimised [45]. Additionally, increases in temperature enhance cavitation intensity up to a certain point [46]. Serrated-rotary-disc HC generators are rotor–rotor devices in which the design of the disc is crucial for efficient cavity generation. Compared to discs with grooves that are at right angles to each other, discs with grooves inclined at an 8° angle offer better performance [47]. In this design, the groove functions as a venturi, aiding in the distribution of the cavitation cloud. To evaluate the extent and aggressiveness of the cavitation, pressure oscillations were measured using a hydrophone, and cavitation zones were measured using a high-speed camera. For both designs the two facing rotors were separated by 0.8 mm. For a right-angle rotor–stator device, they were separated by 7 mm deep and 10 mm wide grooves. When the rotors are aligned for a right-angled rotor, the cavitation zones are formed in the gap between the rotors, whereas in the case of a modified rotor design with an 8° inclination between the grooves, cavitation zones are formed in the gap between the rotors, along with small cavitation clouds in the gap between the aligned teeth of the rotor. In the case of a right-angled rotor, when the grooves align, a low-pressure region forms between them, whereas the case of inclined grooves causes a larger lower-pressure zone, with the extent of cavitation being much bigger than the former design, causing a more aggressive cavitation. This is validated by measuring pressure oscillation measurements, which show that the amplitude of pressure oscillation in the case of an inclined groove is higher in comparison to a right-angle tooth design [47]. A pinned-disc HC generator is a rotor–stator device where cavitation is generated by a sudden pressure drop and its subsequent recovery downstream of cylindrical pins caused by flow acceleration and separation. Reducing the inlet pressure by adjusting the flow rate increases the cavitation volume fraction but reduces the overall cavitation effect. Advanced rotating HC generators, which are rotor–stator devices, consist of rotating discs with dimples on the disc edges. The pressure amplitude increases as the distance between the plates is reduced. Both vortex cavitation and sheet cavitation have been observed in the system; sheet cavitation occurs in the space between the rotor and stator, while vortex cavitation is predominantly observed in the Cavitation Generation Unit (CGU) [48]. Since both vortex intensity and flow separation occur during the interaction process, the shape, geometrical factors, and arrangement of the CGU should be optimised for improved performance.

Rotor/stator HC units are widely used in industrial applications, particularly for oxidative polymerization and emulsification of oils. These processes benefit from the generator’s low energy consumption, making them highly scalable. The production of fat liquors from waste frying oils is a process with significant industrial impact across various applications [49]. Even more commonly, rotor/stator generators are used in biodiesel production [50] and in the pretreatment of the organic fraction of municipal solid waste to enhance anaerobic digestion [51].

Challenges for the scale-up of hydrodynamic cavitation reactors can be summarised as follows. The geometrical parameters play a crucial role in the scale-up of hydrodynamic cavitation reactors in comparison to the process parameters. Process parameters are system-dependent, and they are affected by several factors, like temperature, inlet pressure, and initial cavity radius. The geometrical and process parameters are optimised for scale-up depending on the application (

Table 1. Reactor types and the effect of parameters on cavitation.

Reactor Type	Parameters	Effect of Parameters on Cavitation
Orifice Plate	1. L/D (Thickness-to-diameter of orifice) 2. β 3.α 4. ID of the pipe	1. Minimum L/D value of 2 is preferred, below which pressure recovery and final collapse conditions are affected. 2. Higher values of β increase the collapse pressure of cavities. Lower values reduce the Cv, improving the effect of cavitation, and are counter-balancing. 3. α values directly affect the shape and number of holes in the orifice reactors, which in turn affect the cavity dynamics. 4. Increasing the ID of the pipe directly affects the velocity of the fluid, which affects the cavitation efficiency.
Venturi Tube	1.γ 2. Convergence and divergence angle of venturi tube	1. γ affects the residence time and growth of cavities in the system 2. The cavitation region within the tube and cavity dynamics depends on the converging and diverging sections of the venturi
Vortex Diode	1. Diodicity 2. Throat diameter 3. Divergence angle of axial and tangential ports 4. Nozzle dimension 5. Radius of curvature	1. Diodicity depends on the Reynolds number of the fluid, improving the efficiency of the device. 2. Increasing throat diameter affects the tangential velocity up to a scaling factor of 4 and levels off. 3. Increasing the divergence angle from 5 to 7° enhances the diodicity of the diode. 4. A nozzle with ID equal to the height of the diode results in a higher diodicity. 5. Increasing the radius of curvature increases forward-flow pressure drop, reducing the diodicity of the device.
Rotational reactors	1. Rotational Speed 2. Distance between the rotor and stator 3. Design of rotor blades	1. The tangential fluid velocity depends on the rotational speed, which determines the flow regime in the device 2. The effectiveness of cavitation directly depends on the distance between the plates 3. The design of the plate acts as a cavitation-generating unit which governs the effectiveness of cavitation

).

In hydrodynamic cavitation reactors, the cavity collapse pressure is strongly influenced by the reactor design parameters [27]. For orifice systems, β plays a critical role, as changing β independently alters other geometrical factors such as the L/D ratio, which in turn affects cavitation inception and flow characteristics [52]. Moreover, β directly impacts the cavitation number, which must be minimised to achieve cavitation effects comparable to those observed in smaller-scale systems [53].

In venturi reactors, the parameter γ plays a crucial role in scale-up, as altering it independently changes the converging and diverging angles of the venturi tube [54]. An increase in γ raises frictional losses, reducing cavitation efficiency, while modifications in the divergence angle directly influence pressure recovery, thereby significantly impacting cavity dynamics [21].

In a vortex diode, variation in the throat diameter significantly influences flow characteristics, with the maximum tangential velocity increasing only up to about twice the smallest throat diameter, beyond which it plateaus [40]. This change in cross-sectional area not only governs the maximum velocity attainable but also impacts the formation and behaviour of the vapour core in the axial port [40]. Furthermore, scaling up alters the eddy frequency within the device, while dimensional modifications directly affect the overall design considerations required to achieve maximum efficiency.

In a rotational cavitation device, the diameter and design of the rotating element govern the maximum tangential velocity and local velocity profile, which in turn influence vapour formation [55]. The blade spacing and rotational speed set the limits on fluid throughput and reactor pressure, thereby controlling both the processable volume and the intensity of cavity collapse.

Process parameters like inlet pressure, temperature, initial cavity radius, pH, and additive concentration are system-specific and cannot be generalised, requiring optimisation on a case-by-case basis to achieve optimum results as detailed in the previous sections.

The scale-up of cavitation systems is inherently nonlinear due to the complexity of the multiphase phenomena, and no single parameter can be adjusted independently to ensure success. Comparable efficiency is often achievable only within certain scale-up ratios, beyond which performance declines [40].

To address this, tools such as computational fluid dynamics and simulations are essential for understanding system intricacies, while a hybrid approach combining numbering-up with scale-up offers a practical route to larger scales without compromising efficiency [56].

2.2. Impact of Initial and Boundary Conditions on Cavitation

The impact of initial and boundary conditions for both acoustic and hydrodynamic cavitation is explained below.

2.2.1. Acoustic Cavitation

Acoustic cavitation is affected by several parameters, such as intensity of ultrasound, frequency of ultrasound, initial cavity radius, compressibility of the medium, and temperature of the bulk fluid.

Intensity of ultrasound: For a constant initial cavity radius and frequency of ultrasound, increasing the intensity of ultrasound increases the ratio of $R_{max}/R_0$ attained but reduces the collapse pressure generated [57]. This is attributed to the hindrance of sound penetration into the body of the liquid, such that the radiating surface will be covered in a layer of bubbles.

Frequency of ultrasound: For a constant initial cavity radius and intensity of ultrasound, an increase in the frequency of ultrasound reduces the $R_{max}/R_0$ attained by the cavity, but this also reduces the lifetime of the cavities [57]. The collapse of a cavity is rapid and violent with increasing frequency, which causes an increase in the magnitude of collapse pressure.

Initial cavity radius: For a constant intensity and frequency of ultrasound, the $R_{max}/R_0$ of the cavity decreases with an increase in the initial cavity radius. Small cavities collapse more violently due to their larger growth [57]. The magnitude of the collapse pressure generated decreases with increases in the initial cavity radius.

Temperature of the fluid: Increasing the temperature of the fluid increases the final collapse pressure and temperature for an intermediate value of ultrasound intensity [29].

2.2.2. Hydrodynamic Cavitation

This is affected by several parameters, such as the inlet pressure of the fluid, geometrical parameters of the cavitation reactor, and initial radius of nuclei.

Inlet pressure of the fluid: An increase in pressure in the upstream of the orifice reactor causes a permanent pressure drop and causes an increase in the fluctuating velocity of the fluid [58]. The dynamics of the bubble change with the inlet pressure, as growth is restricted, and show a decrease in $R_{max}/R_0$ with an increasing inlet pressure.

Initial radius of nuclei: The $R_{max}/R_0$ attained by the bubble during the growth phase decreases with an increase in the initial radius of the bubble; the ratio of the maximum radius attained with respect to the initial radius of the bubble is greatly affected by the local turbulence [58].

Geometrical parameters of cavitation reactor: An increase in β increases the power input per unit liquid volume, which in turn affects the fluctuating velocity and frequency of turbulence. A higher frequency of turbulence affects the maximum bubble radius that can be attained, which is explained by the Weber number criteria [58]. This increase in collapse pressure is obtained due to variation in the cavitation inception number, as well as the operating cavitation number, with the diameter of the orifice.

Temperature of the medium: An increase in the temperature of the medium can cause an early onset of cavitation or increase the effects of cavitation, such as collapse pressure and temperature. However, increasing the temperature can also affect the turbulence characteristics in the reactor, which can counteract the above-mentioned positive effects [29]. All the above-mentioned conditions are simulated using the Rayleigh–Plesset equation to understand the effects of cavity dynamics. Simulations of single bubble dynamics are performed using equations such as the Rayleigh–Plesset, Keller–Miksis and Gilmore equations, where the Rayleigh–Plesset equation ignores the effect of heat and mass transfer between the bubble and the bulk fluid, does not capture the effect of compressibility and phase transition, and does not correctly predict the rebound of cavitation bubble after the first collapse. Considering the Keller–Miksis and Gilmore equations, both take into account the effect of compressibility and phase transition and closely predict their effects on the radius of the rebound bubble [59]. The addition of substances that affect the vapour pressure of the fluid causes more phase transition of bulk liquid near the bubble wall, causing an increase in the vapour content of the bubble. An increase in the vapour pressure of the bulk fluid by the addition of aqueous ammonia causes a considerable change in the vapour content of the bubble, affecting the amplitude of the rebound bubble. This is because the compression of vapour in the bubble is restrained by heat and mass transfer [59]. An increase in ammonia vapour content in the bubble decreases bubble deformation and offers large resistance to the compression of bubble content, whereas bubble collapse with pure water reaches a smaller minimum radius of a bubble, giving larger energy density. The energy loss of a bubble shows a steady increase with increasing compressibility and vapour content of the bubble. An increase in the vapour content of the bubble can generate higher peak pressures compared to purely non-condensable gases. In comparing the effects of compressibility and phase transition, the energy loss of the bubble caused by fluid compressibility is 1/5 less than that due to phase transition. With an increasing vapour content of the bubble, the internal pressure of the bubble increases, and during the collapse of the bubble, greater energy is propagated in the form of acoustic radiation in the flow field [60]. The inclusion of mass transfer effects by considering the diffusion of bulk fluid into the bubble affects the cavity collapse conditions. In addition, consideration of heat transfer effects across the bubble takes into account the specific heat capacities of non-condensable gases, along with the diffused material, showing a change in the predictions of collapse conditions [29]. Even though the overall predictions of the cavity bubbles show a similar trend in spite of using different equations, the inclusion of these effects in the simulation gives a better correlation between the simulated results and actual cavity dynamics in the system.

3. Ultrasonic Reactors for Semi-Industrial Applications: Flow-Through Units

Recently, Tiwari and associates reported challenges and strategies for scaling up ultrasonic rectors [61], showing that the ultrasonic energy transferred to the bulk is crucial in most processes. Parameters such as US power (W), US intensity (W/cm²), and acoustic energy density (W/mL) quantify the dissipated ultrasonic energy in the system.

The main concepts and parameters to consider when scaling up ultrasonic reactors are summarised in the

Table 2. Relevant parameters to be considered for scaling up.

Parameters	Definition and Features	Processing Considerations
Power density	Ultrasonic power per unit volume (W/L)	Must be kept constant during scale-up to preserve cavitation intensity and reproducibility of effects
Reactor geometry	Shape and dimensions affect wave propagation, cavitation distribution, and energy dissipation	Dead zones and uneven energy fields increase with reactor size
Frequency	Low frequency (20–40 kHz) favours intense cavitation and physical effects. Higher frequency (>100 kHz) yields milder cavitation, more suited to chemical effects	Single or multi-frequency selection
Transducer arrangement	Scaling up requires multiple transducers or modular/multi-stage reactor design	Positioning and coupling method efficiency are crucial
Acoustic field uniformity	Correct transducer distribution and acoustic impedance of materials	Hotspot and inactive zone elimination/minimisation
Energy efficiency	Not all input power is converted into useful cavitation (over the threshold)	Monitoring calorimetric efficiency and acoustic intensity is necessary
Temperature and pressure	Strongly affect cavitation thresholds	Check optimal cavitation temperature of medium
Physical properties of the medium	Viscosity, surface tension, gas solubility, dissolved gases	All aspects determine bubble dynamics
Flow regime	Flow rate, mixing, and residence time must be optimised to ensure homogeneous exposure	The right pump selection is crucial
Material compatibility	Reactor walls and transducer surfaces must withstand erosion, fatigue, and chemical attack	Selection among titanium, stainless steel, Hastelloy, or PTFE coating
Operation safety	High-power ultrasound may generate heat, vibrations, and noise	Industrial systems require efficient cooling and acoustic shielding

below.

Industrial ultrasonic reactors are generally processing flow-through units, equipped with multiple high-power transducers (20–40 kHz) to ensure uniform cavitation in liquid media. The intense shear forces generated by collapsing cavitation bubbles enhance mass transfer, emulsification, and various chemical and physical transformations. The power output can range from 1 kW to over 50 kW, depending on the application, from hundreds to thousands of litres per hour. These reactors are widely used in chemical, pharmaceutical, food, and environmental industries.

One simple strategy to easily scale up ultrasonic processes is to add several tubular units in series. Figure 3 shows four ultrasonic flow reactors (internal volume of 330 mL) working at 22.0 kHz equipped with independent ultrasonic generators (maximum power 1000 W; by SONO Ltd. 29 Leningradsky avenue, Moscow, Russia).

Large-scale ultrasonic reactors are designed for high-throughput applications, offering enhanced process efficiency and scalability. The key features include: high power density across the sonication chamber and modular designs for parallel operation of multiple reactors to increase processing capacity. Modern industrial ultrasonic plants are equipped with real-time monitoring sensors for temperature, pressure, and power input, as well as automated control systems with programmable logic controllers (PLCs) for process stability. The integrated process monitoring and automation also includes data logging capabilities for traceability and quality control.

These reactors can be integrated into production lines and paired with various types of pumps and equipment. When operating under elevated pressures, specific designs ensure compliance with stringent safety standards, ensuring the effective transmission of acoustic oscillations into reactors with relatively thick walls. Increasing the reactor volume can be achieved by extending the length or increasing the diameter. Extending the reactor is simple but increases the processing time, with limited impact on productivity due to the limitations imposed by the speed of cavitation bubble formation. On the other hand, increasing the reactor diameter presents more challenges. As the diameter increases, the natural frequency of radial vibrations decreases, necessitating a shift to bending modes. This transition introduces technical difficulties that must be addressed to ensure successful implementation. In summary, the design of industrial-scale flow-through sonochemical reactors requires a careful balance between enhancing productivity, ensuring safety, and managing the complexities associated with changes in reactor dimensions, particularly in handling cavitation dynamics and mode transitions.

4. High-Pressure Ultrasonic Reactors for Processes Under Supercritical CO₂

Ultrasonic reactors operating under supercritical CO₂ (sc-CO₂) are specialised high-pressure systems designed to couple acoustic cavitation with the unique transport properties of the supercritical phase. Their engineering is challenging, as cavitation behaves very differently in sc-CO₂ compared with conventional liquids.

Ultrasonic components face significant mechanical stress at high pressure, requiring a titanium alloy 6AI-4V, and operate at a frequency of 22 kHz.

As observed, the shape of the tube’s natural vibrations at the standard frequency of 22 kHz becomes significantly more complex for tubes with larger diameters compared to thinner tubes. This complexity necessitates adjustments to the location and method of connecting the transducer to the waveguide. When standard longitudinal or radial placement methods are incompatible with the bending mode, the transducer design must be modified to account for the bending vibrations. Additionally, the speed of sound in the medium being processed must be considered, as waves from opposite walls should not cancel each other out. In cases where submersible emitters cannot be used, for example, when the treated media is sc-CO₂, the oscillations from external ultrasonic emitters must be transmitted into a thick-walled tube. To maximise transmission efficiency, the emitters should be placed at the displacement maxima of the reactor. For this, it is essential to model the displacement distribution in the reactor at the chosen frequency, which should be selected based on the reactor’s natural frequencies. This technology was experimented with on a lab scale, showing the remarkable industrial potential of ultrasound-assisted cold pasteurisation in liquid or supercritical CO₂ [62].

Figure 4 shows the system’s oscillation model. In this case, as presented in the figure, three electroacoustic transducers are placed within a thick-walled tubular reactor. The model was developed using the finite-element method in COMSOL Multiphysics.

The system developed is designed to ensure that the resonant frequency of the emitters matches the natural frequency of the selected tubular reactor. In this case, the system operates at a working frequency of 22.6 kHz. Despite the strong cavitation and mechanical effects on suspended solid matrices in aqueous media, after several hours of sonication at 1.5–2.0 kW, the temperature increase in loop circulation (150 L) was always less than 2–3 °C. Differently, the flow reactor described in Ref. [18], shaped like a parallelepiped with flat surfaces on which the transducers were glued, generated a remarkable heat and an uneven distribution of the ultrasonic wave due to the stresses on the edges of the square structure.

The reactor in Figure 4 can be used both at atmospheric pressure with aqueous solvents and in a closed volume of CO₂ under high pressure, making it highly suitable for applications such as extraction, surface cleaning, and pasteurisation.

5. Magnetostrictive Flow-Through Reactors for High-Temperature Liquid Processing

It is well known that piezoelectric transducers are more efficient than magnetostrictive ones. However, in certain situations, piezoelectric elements are unsuitable, such as in harsh environments where the system must withstand shock loading or operate at high temperatures. The advantages of magnetostrictive transducers are better mechanical properties, the technical simplicity of the cooling system, and higher power. In addition, magnetostrictive transducers have a wider frequency band. With this consideration, a flow-through reactor has been designed for industrial uses. Oscillations are transmitted into the tubular reactor by two magnetostrictive transducers placed on the opposite sides of the reactor, forming a cross configuration. The magnetostrictive transducers are equipped with a water-based cooling system, allowing the device to be integrated into industrial production lines. If necessary, similar systems can be equipped with additional external cooling to meet specific operational requirements. To maximise efficiency, the resonant frequencies of the transducers and the waveguides were matched. We applied units that could achieve an amplitude exceeding 25 µm [63]. The schematic of the device is shown in Figure 5.

6. Hybrid Flow-Through Reactor for Initiating a Discharge Inside a Cavitation Zone

Technological advancements, particularly in environmental protection, are increasingly focused on integrating traditional methods to achieve synergistic effects. For example, promising new technologies for treating contaminated water combine oxidation-based physical and chemical processes. These include methods utilising the simultaneous action of UV radiation and oxidizers, such as ozone and hydrogen peroxide, as well as various combinations of ozonation and cavitation. Among the techniques for purifying aqueous solutions of organic pollutants, plasma-catalytic processes are particularly noteworthy. The HC-plasma reactor gives a combination of cavitation bubbles and highly reactive conditions during glow plasma discharge, producing a synergistic effect for organic pollutant degradation. The electron has low mobility in the bulk solution, without the presence of a cavitation bubble in the bulk medium, which offers higher resistance to the conduction of charges. The cavitation bubbles are generated in the bulk solution when the liquid passes the constriction of the cavitating device. During the discharge of the glow plasma in combination with the presence of cavitation bubbles in the bulk solution, the conduction of charges happens through the surface of the cavitation bubble, causing the internal gas content of the bubble to be ionised. Because of this, the combination of HC and plasma causes violent bubble collapse, which causes ultra-high temperature generation inside the bubble. This ionisation of bubbles forms highly reactive oxygen species, UV-light emission, and ozone formation, leading to the degradation of the more robust organic pollutants [64]. It has been observed that when a discharge is generated within a cavitation zone, it exhibits characteristics similar to those of a discharge in a gas [65]. Paschen’s law for voltage breakdown in gases is given by the following equation:

$$U_b={\displaystyle \frac{B\ast p\ast d}{\raisebox{1ex}{$ln[A\ast p\ast d$}\!\left/ \!\raisebox{-1ex}{$ln(1+\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\omega $}\right.)]$}\right.}}$$

(18)

where

• A, B—Coefficients determined from experiments
• $p$—Gas pressure
• $d$—Distance between the electrodes
• ω—Coefficient of secondary emission—the number of electrons leaving the cathode per incident positive ion

An external sound field is applied to the fluid medium in the reactor. The bubble dynamics due to the application of external sound in the reactor is simulated with the Noltingk–Neppiars equation which is mentioned below

$$R{\displaystyle \frac{d^{2}R}{{dt}^2}}+{\displaystyle \frac{3}{2}}{\displaystyle \frac{dR}{dt}}={\displaystyle \frac{1}{{\rho }_0}}[\left(P_0+{\displaystyle \frac{2\sigma }{R_0}}\right){\ast \left({\displaystyle \frac{R_0}{R}}\right)}^{3\gamma }-{\displaystyle \frac{2\sigma }{R}}-\left(P_0-P_{a}sin\omega t\right)$$

(19)

where

• $P_0$—Initial pressure in the cavity
• $P_a$—Acoustic pressure amplitude
• ω—Frequency of acoustic radiation
• $R_0$—Initial radius of cavity
• ${\rho }_0$—Density of the liquid
• σ—Surface tension of the liquid

Assuming an ideal gas inside the bubble and neglecting heat and mass transfer, the pressure inside the cavity is given by

$$P_T\left(R\right)=\left(P_0+{\displaystyle \frac{2\sigma }{R_0}}\right){\left({\displaystyle \frac{R_0}{R}}\right)}^{3\gamma }$$

(20)

According to Paschen’s equation given as Equation (18), to treat the whole liquid flow with low energy consumption, there is a need to create a uniform cloud of pulsating bubbles that fills the entire space between the electrodes with the help of ultrasonic cavitation. For the experimental results performed with a plasma reactor coupled with hydrodynamic emitters to generate cavitation bubbles in the reactor length, it was found that both the breakdown voltage and stable discharge voltage decreased with decreasing pressure at the outlet of the hydrodynamic emitter. A reactor length of 150 mm was considered, for this reactor’s optimal pressure drop of 5.98 MPa at the hydrodynamic emitter, which corresponds to an acoustic pressure of 0.7 MPa in the cavitation zone, predicts the gas pressure inside the bubble to be between 6 and 14 Pa, with a breakdown voltage of 33 kV, for gas bubble size with respect to initial bubble size $(R/R_0)$ varying in the range of 5 to 100 [66]. Increasing the pressure behind the hydrodynamic emitter from 0.01 MPa to 0.045 MPa shows an increase in breakdown voltage from 33 kV to 50 kV.

The dimensions and characteristics of this cavitation zone can be controlled by adjusting the design of the emitters as well as the inlet and outlet pressures. By strategically placing electrodes within this zone, a dynamic volumetric discharge can be initiated, resulting in several effects on the treated liquid, including mechanical turbulence, cavitation hot spots, intense UV radiation, radical generation, and plasma-catalytic effects (Figure 6). This type of reactor has been successfully used in the degradation of recalcitrant organic pollutants [67,68].

The comparison with other cavitation technologies demonstrates the much higher efficiency of the HC–Plasma reactor in the degradation of organic pollutants [69]. The industrial interest in exploiting the tremendous oxidative power of this hybrid technology prompted us to scale up the reactor from 15 L/min to 50–60 L/min (Figure 7). The cross-sectional area of the big reactor tube is 230 mm² (vs. the 50 mm² of the small reactor).

7. Ultrasonic Reactors for Nanoparticle Coating of Textiles

Another relevant example of industrial application is the ultrasonic reactors designed for coating fibres and textiles with nanoparticles suspended in a liquid, which must minimise the volume, and the textile must be uniformly treated on both sides. The textile is guided around cylindrical emitters in such a way that both sides of the textile pass over two emitters. These emitters generate an ultrasonic field in the liquid, a model of which is shown in Figure 4.

As shown in Figure 8, there are several nodes in the acoustic field. To address this, the horizontal position of the emitters on one side of the fabric was adjusted so that the pressure maxima of one emitter aligned with the pressure node generated by the other emitter.

This reactor was used for the production of textiles with antibacterial properties [70]. They were tested in a tropical climate and showed significant advantages compared to their non-coated counterparts [71].

8. Conclusions and Perspectives

The present overview of the recent literature, combined with our experience with various semi-industrial applications of cavitation reactors, is intended to highlight the features required and opportunities for the design of large-scale cavitation processes.

Hydrodynamic cavitation is advancing towards industrialisation in wastewater treatment, food processing, and fuels. Rotational and vortex-type devices are often noted for their scale-up potential, energy efficiency, and suitability for continuous operation [72]. Hybrid advanced oxidation processes are the main approach for wastewater treatment. HC is combined with H₂O₂, O₃, Fenton, and photocatalysis with several pilot and semi-industrial demonstrations [73].

Developments in acoustic cavitation reactors focus on emulsification, crystallisation, and food processing [74], with emphasis on the reactor metrics and scale-up criteria appropriate for industrial adoption. For years US has been exploited in cleaning, material testing, enhancing chemical reactions and extractions, and nanoparticles dispersion in functional fabrics.

Continuous biodiesel production using hydrodynamic cavitation reactors has been reported, achieving specification-compliant FAME yields and reduced specific energy consumption, demonstrating practical industrial relevance [75]. In a complementary way, HC rotor/stator units have been exploited for biomass pretreatments in biogas production [51,76].

All these technologies play an essential role in process intensification, contributing to improved efficiency, product quality, and sustainability in several industrial sectors [77]. Given current trends, a broader adoption of cavitation technologies in manufacturing processes appears highly promising. An excellent comparison of acoustic and hydrodynamic cavitation for crystallisation was recently discussed by Flores and associates [78]. Excellent energy distribution throughout the reactor, along with high processing capacity, was observed in flow reactors with several transducers (i.e., Prosonitron reactor). Meanwhile, for HC-assisted crystallisation, there is a possibility of exploring different reactor types, such as rotational HC reactors. The scale-up was supported by computational simulations and laboratory-scale experiments.

Based on our experience, the hybridisation of cavitation reactors will lift performance. The combination with other energy sources, such as microwaves or plasma, will skyrocket the potential of continuous-flow cavitational processes. The main potential industrial applications of continuous flow cavitation reactors are the extraction of primary and secondary metabolites from plant and microbial biomass, advanced oxidation in wastewater treatment, and microbial inactivation.