Clarification of regimes determining sonochemical reactions in solid particle suspensions.

Although there has been extensive research on the factors that influence sonochemical reactions in solid particle suspensions, the role that solid particles play in the process remains unclear. Herein, the effect of monodisperse silica particles (10-100 μm, 0.05-10 vol%) on the sonochemical activity (20 kHz) was investigated using triiodide formation monitoring and luminol tests. The results demonstrate that, in the particle size range considered, the sonochemical yields were enhanced in dilute suspensions (0.05-1 vol%), while further particle addition in semi-dilute suspensions (1-10 vol%) decreased the yields. Two regimes, namely the site-increasing regime and sound-damping regime, are identified in respect of the enhancing and inhibiting effects of the particles, respectively, and their dependence on particle characteristics is analyzed. Both regimes are confirmed based on the cavitation erosion test results or cavitation noise analysis. The clarification of the two regimes provides a better understanding of the dominant factors controlling sonochemistry in the presence of solid particles, as well as a guide for sonochemical efficiency prediction.

Introduction

Since the advent of inexpensive and reliable ultrasonic generators in the 1980s, power ultrasound in the 20–100 kHz range has been extensively used in water and environmental engineering [1], [2], [3]. Instead of interacting directly with molecules to induce a chemical change, the ultrasound causes cavitation, which generates extremely high temperatures (∼5000 K) and pressures (∼1000 atm) at localized hot spots, forming highly oxidizing species (hydroxyl radicals, ·OH) to create sonochemical effects [4]. As an advanced oxidation process (AOP), sonochemistry is a promising tool for the degradation of hazardous chemicals and non-biodegradable materials in wastewater treatment [5], [6]. It fulfills the requirements of “green chemistry” [7]. Research on combining it with other AOPs or biological treatments to reduce the cost has been conducted [8], [9], [10]. However, most of the laboratory experiments on sonodegradation were performed in pure water, which neglected the fact that the sonochemical process could be affected by the suspended solids in wastewater, including sand grains and microplastics [11]. Therefore, it is crucial to investigate the sonochemical activity in aqueous suspensions of solid particles.

The dependence of the sonochemical activity on the characteristics of the suspended solid particles has garnered research interest since the pioneering work of Lu and Weavers [12], Zhang and Hua [13], and Keck et al. [14] in 2002. These particle characteristics include surface properties (roughness and hydrophobicity), geometric properties (size and shape), and most importantly, the concentration of suspended particles (φp). Stoian et al. [15] compared the impacts of sand particles, spherical glass beads, and cation exchange resins (φp = 1 vol% and similar in size), on the sonochemical activity in a stirred horn-type sonoreactor (20 kHz). The researchers discovered that, although all three types of particles were categorized as hydrophilic, sand particles contributed to higher sonochemical yields owing to their higher roughness values and irregular shapes. It was assumed, based on the crevice model [16], that rough surfaces and irregular shapes facilitate the entrapment and stabilization of gas pockets, which function as nucleation sites and initiate the formation of cavitation bubbles.

The solid particles used in the existing studies encompassed particles of different size ranges (ISO), from clay-sized (<2 μm) [12], [13], [14], through silt- and sand-sized (2 μm–2 mm), to gravel-sized (>2 mm) particles [17], [18], [19]. Some researchers also reported using solids in powdered form [20], [21], [22]. However, the effect of particle size is much debated. Some researchers believed that larger particles are less likely to be trapped at pressure antinodes where cavitation primarily takes place [23], while others argued that sufficiently large particles can mimic a solid wall and promote the asymmetric bubble collapse [24]. Tuziuti et al. [25] noticed a rapid increase in sonochemical yields at 42 kHz as the size of alumina particles (20 g/L) increased from 1 to 10 μm, followed by a plateau (no increase) with a further increase in size (10–80 μm). By contrast, Lu et al. [26] suggested that increasing the particle size from 2 to 130 μm could reduce the sonochemical yields at 20 kHz by > 10% in silica particle suspensions at the same mass concentration.

Thomas [27] classified particle suspensions into three types according to particle concentration. They are dilute (<1 vol%), semi-dilute (1–25 vol%), and concentrated (>25 vol%) suspensions based on rheology. The values of φp adopted in previous research cover all three types, but the role of the particles in sonochemical reactions at various φp is still not clear. Katekhaye and Gogate [28] discovered that the sonochemical yields at 20 kHz were higher in dilute suspensions of titania powder (0.2–0.6 vol%) than in water and increased with φp. They attributed this to the increase in the number of active sites for heterogeneous nucleation, and the catalytic activity of titania [29]. Her et al. [19] studied the sonochemical activity in semi-dilute suspensions of 100-μm inert glass beads (3–12 vol%) at 1 MHz, and reported lower sonochemical yields than in water; the yields decreased with increasing φp. This is consistent with the recent findings of Barchouchi et al. [17] suggesting that the scattering-induced attenuation of ultrasound waves can be related to the inhibited production of reactive free radicals. For sonochemical reactions in concentrated suspensions, it is the rapid growth of apparent viscosity with φp that might predominate [15]. Microparticles in large quantities could form a barrier that prevents gas or vapor from diffusing through the bubble surface, making it harder for cavitation bubbles to oscillate or collapse [30]. However, extremely high φp is rarely encountered in the tertiary treatment of wastewater.

Despite all efforts to understand heterogeneous sonochemistry, the mechanisms underlying the demonstrated enhancing yet inhibiting effects of the solid particles were often poorly addressed or inadequately clarified in literature. It is particularly necessary to analyze the relationship between the influencing regimes and sonochemical activity using multiple disciplines and perspectives, including nucleation kinetics and acoustics in multiphase flows. This assists us by clarifying how the particle characteristics influence these regimes and the sonochemical activity, which facilitates the prediction of sonochemical yields in multiphase sonoreactors.

The objective of this study is to examine and clarify the regimes that underlie the enhancement or inhibition of sonochemical reactions in solid particle suspensions. We investigate the effects of the concentration and size of silica microspheres on sonochemical yields, based on KI dosimetry and luminol techniques, and then analyze the experimental results using the parameters characterizing these regimes.

Materials and methods

Silica particles

Monodisperse silica particles were purchased and used with no further purification (Table 1 includes the supplier details). The particle diameters, which were in the same order of magnitude as the size of acoustically generated cavitation bubbles [31], were confirmed using a particle size analyzer (Malvern Mastersizer 2000). All possible combinations of the four sizes (10, 20, 50, and 100 μm) and eight concentrations (0.05, 0.1, 0.2, 0.5, 1, 2, 5, and 10 vol%) of the silica particles were considered in this work.

Table 1

Physical properties and suppliers of silica particles.

Particle size (μm)	Densitya (103 kg·m−3)	Specific surface areab (m2·kg−1)	Supplier
10	2.55	235	Shanghai Aladdin Bio-Chem, China
20	2.46	122	Sigma-Aldrich, USA
50	2.49	48	Sigma-Aldrich, USA
100	2.36	25	Tokyo Chemical Industry, Japan

Density of silica particles was measured using Archimedes’ principle [32].

Specific surface area of silica particles is calculated as the total surface area of the particles per unit of mass.

Experimental setup

A schematic of the experimental setup is illustrated in Fig. 1. A 20-kHz ultrasonic probe system (VCY−1500, Shanghai Y&Y Sonic) was used to generate ultrasound with an applied power of 250 W. The ultrasonic probe, immersed up to 5.0 cm in the particle suspension, augmented the oscillation displacement amplitude provided by a piezoelectric transducer. An impeller was positioned 2.5 cm from the vessel bottom to ensure that the silica particles were well mixed throughout the cylindrical vessel. The inner radius and height of the vessel were 10.0 and 15.0 cm, respectively. The probe tip and the impeller were positioned symmetrically around the axis of the vessel with eccentricity equal to 0.55. All the tests were performed at minimum impeller speeds required to lift all particles from the vessel bottom; the speeds were determined based on the Zwietering approach [33], [34] and are listed in Table 2. The temperature inside the vessel was maintained using a circulating cooling bath and monitored using a real-time sensor.

Fig. 1

Sketch of the experimental setup. Key: 1: ultrasonic generator, 2: piezoelectric transducer, 3: ultrasonic probe, 4: output tip (emitting surface area: 2.0 cm2), 5: electric motor (maximum speed: 1500 rpm), 6: shaft, 7: pitched blade turbine impeller (diameter: 7.5 cm, pitch angle: 45°), 8: silica particle suspension, 9: glass vessel, 10: cooling bath, 11: readout display, 12: real-time temperature sensor, and 13: supporting rod.

Table 2

Impeller speeds for sonochemical experiments (rpm).

Particle concentration (vol%)	Particle size (μm)
	10	20	50	100
0.05	136	157	214	236
0.1	210	253	288	325
0.2	313	364	406	442
0.5	386	429	466	510
1	431	463	517	569
2	499	531	589	633
5	603	628	658	686
10	696	723	743	770

Sonochemical experiments

The KI dosimetry was used to provide a quantitative measure of the sonochemical activity. When an aqueous KI solution is sonicated, a fraction of I− can be oxidized by ·OH to give I2. The excess I− then reacts with I2 to form I3− that absorbs spectrophotometrically at 355 nm [35]. To perform KI dosimetry, KI solution (0.1 M) was prepared by dissolving KI (purchased from Tianjin Beilian Fine Chemical Development Co., Ltd.) in degassed distilled water just before each test. The pH value was initially adjusted to 8 ± 0.2 with KOH (0.1 M, purchased from Chengdu Jinshan Chemical Reagent Co., Ltd.). This is because I− in acidic solutions are susceptible to oxidation by oxygen gas, and I3− in strongly alkaline solutions is more likely to react with H2O2 (formed by the recombination of ·OH) to form I− [36], [37]. The silica particles were placed in the vessel, and KI solution was added to a height of 10.0 cm, prior to the sonochemical experiments. Preliminary control tests have revealed that the adsorption of I3− on the glass vessel and silica particles was negligible, and the KI solution did not tend to react with air in the mechanically stirred tanks.

The total sonication time for each test was 25 min, and all tests were performed at room temperature (25 ± 1 °C). An aliquot (6–7 mL) of solution containing minimal particles was taken every 5 min and then centrifuged (2 min at 2500 rpm). Then the supernatant was transferred into quartz cuvettes to determine the concentration of I3−; the I3− concentration was directly proportional to the absorbance measured using a UV–Vis spectrophotometer (UV754N, Shanghai Aucy Scientific Instrument).

The intensity of the sonochemical reactions under heterogeneous conditions was also visualized using the sonochemiluminescence (SCL) method; SCL images were obtained using a solution of luminol (1 mM, purchased from Shanghai Rhawn Chemical Technology Co., Ltd.) and KOH (0.1 M) in complete darkness [38]. To facilitate SCL observation, a 500 mL transparent glass beaker was used as a substitute for the mechanically stirred vessel, and the cooling bath was temporarily removed. Virtually all the silica particles could be lifted from the bottom of the beaker under the environment of ultrasonic agitation. The shutter speed for the digital camera (EOS 200D II, Canon) was set to 30 s, and the lens (EF 50 mm f/1.8 STM) was switched to the manual focus mode.

Results

The measured absorbance was divided by the product of the cuvette width (1.0 cm) and the molar attenuation coefficient (23200 M−1∙cm−1) to determine the concentration of I3− generated. The concentration increased linearly with sonication time in the silica particle suspensions similar to the particle-free scenario (Fig. 2a–c), which is consistent with previous reports [17], [36]. When φp was low (0.05 vol%), slightly more I3− was detected at every point of time compared with the particle-free scenario; smaller particle diameters (dp) led to higher concentrations of I3− (Fig. 2a). When φp = 1 vol%, the 10-μm particles caused less I3− production than the particle-free scenario, while the 100-μm particles still enhanced the formation of I3− (Fig. 2b). Under high φp conditions (10 vol%), adding silica particles of either size reduced the I3− concentration. The concentration at 25 min for the 100-μm particles was over 50% higher than that for the 10-μm particles, which was only half as high as for the particle-free scenario (Fig. 2c). Apparently, the formation of I3− depended largely on both dp and φp.

Fig. 2

I3− production plotted against sonication time for the 10- and 100-μm silica particles at (a) 0.05 vol%, (b) 1 vol%, and (c) 10 vol%; the particle-free scenario is included for comparison. (d) Comparison of the I3− formation rates at various particle sizes and concentrations (the dashed line represents the particle-free scenario). All tests were performed in triplicate, and error bars display the standard deviation.

Given the linear relationship illustrated in Fig. 2(a)–(c), it is reasonable to assume that the formation rate of I3−, denoted by rf(I3−), follows zero-order kinetics (i.e., is independent of sonication time). Consequently, one could estimate rf(I3−) directly from the gradient of the straight line on a concentration versus time graph. With the increase in φp, rf(I3−) exhibited a similar pattern of initial increase and subsequent decrease for all four dp (Fig. 2d). Compared with the particle-free scenario, the addition of silica particles at φp = 0.05–0.5 vol% contributed to higher rf(I3−), while at φp = 1–10 vol% (except for the 1-vol% suspensions of 100-μm particles), less I3− formed. In contrast to the marginal change in rf(I3−) when φp < 1 vol%, the decrease in rf(I3−) was marked at higher φp. For instance, rf(I3−) could decrease by 30% with a tenfold increase in φp (1–10 vol%) for the 100-μm silica particles.

To characterize the enhancing or inhibiting effects of the suspended solid particles on the sonochemical activity and facilitate the comparison of the research findings obtained under different conditions (e.g., different particle types or ultrasound frequencies), we defined the percentage change in the formation rate as Δrf/rfo, in which Δrf is the variation in the formation rate from the homogeneous system (absence of solid particles) to a heterogeneous system (presence of solid particles), and rfo is the formation rate in the absence of solid particles.

There is a clear distinction between the four particle sizes in terms of Δrf/rfo varying with φp (Fig. 3a). Under low φp conditions (0.05–0.2 vol%), I3− formation was enhanced by adding silica particles of either size, and the 10-μm particles had the best enhancing effect. The enhancing effect decreased as silica particles became larger despite a fixed φp. For example, when φp = 0.1 vol%, Δrf/rfo for the 10-μm particles was 57% greater than the Δrf/rfo for the 100-μm particles. However, crucial differences between the large and small particles emerged as φp reached 0.5 vol%. It could be observed that Δrf/rfo was still increasing for the 100-μm particles, while it was decreasing for the 10-μm particles. Thus, the former soon overtook the latter as being most effective in enhancing I3− formation. The intersection point of the curves in Fig. 3(a) indicates that rf(I3−) appeared independent of particle size at φp ≈ 0.3 vol%.

Fig. 3

Percentage change in I3− (or H2O2) formation rate plotted against particle concentration for sonicated suspensions of (a) 10–100-μm silica particles, and (b) solid particles reported in previous work [14], [19], [25], [28]. The dashed line represents no change in the formation rate; the inset in Fig. 3(a) is an expanded view of the curves crossing one another.

When φp = 1 vol%, the addition of the 10–50-μm silica particles generated less I3− compared with the particle-free scenario; by contrast, the 100-μm particles still had an enhancing effect on I3− formation, although Δrf/rfo was already decreasing (Fig. 3a). In this paper, we define the “critical φp” as the particle concentration at which the formation rate of the sonochemical yields in the particle suspensions is the same as that in the particle-free scenario. The critical φp varied among particle sizes, and the larger particles had higher critical φp values (e.g., approximately 0.6 and 1.3 vol% for the 10- and 100-μm particles, respectively). As φp increased (2–10 vol%), adding silica particles of all four sizes inhibited I3− formation. Smaller silica particles had a stronger inhibiting effect at specific φp; for example, the absolute value of Δrf/rfo for the 10-μm particles was 48% greater than the absolute value of Δrf/rfo for the 100-μm particles when φp = 10 vol%.

Fig. 3(b) illustrates the experimental data generated by other researchers. Although it appears impractical to compare their data with those obtained in this study (Fig. 3a), there are still some striking similarities despite the differences in the characteristics of the suspended solid particles and sonochemical reactors. First, their data follow a similar “first increasing then decreasing” pattern of Δrf/rfo against φp. Second, both the φp at which Δrf/rfo starts decreasing and the critical φp for the 10-μm alumina particles (0.7 and 1.8 vol%) in Ref. [25] are lower than those for the 100-μm glass beads (2.0 and 3.4 vol%) in Ref. [19], respectively, which agrees with our results. Third, the range of critical φp values illustrated in Fig. 3(b) is a good approximation to that of the 10–100-μm silica particles used in this study. Although φp of the 3-μm quartz particles in Ref. [14] was not sufficient to reduce the H2O2 formation to the level of Δrf/rfo < 0 at 206 kHz, the critical condition is predictable at a higher φp according to the downward trend. Notably, the highest Δrf/rfo of every work shown in Fig. 3(b) is higher than the value in Fig. 3(a). One possible cause might be the higher frequencies used by these researchers (20–206 kHz), which could contribute to a larger population of cavitation bubbles releasing more radicals [39].

Fig. 4 illustrates the SCL photographs captured with and without silica particles. Luminol molecules reacted with ·OH, producing bursts of blue lights whose intensity was associated with the cavitation intensity. For the homogeneous system (Fig. 4a), the bright areas, otherwise known as the “active zones”, were concentrated near the probe tip. The light intensity reduced with increasing distance from the probe tip due to acoustic pressure dissipation [40]. For the heterogeneous system (Fig. 4b), however, the active zones appeared across almost the entire selected area, and the light intensity was predominantly uniform (except for the periphery of the area).

Fig. 4

SCL images (a) without silica particles, and with (b) 10-μm silica particles (0.1 vol%).

The marked difference in the pattern of SCL emission in Fig. 4 demonstrates the significant role of silica particles in influencing sonochemistry. Additionally, it can be seen from Fig. 3 that large and small values of φp could result in different phenomena related to the sonochemical activity in heterogeneous systems, and the variation in particle size also makes a difference. The critical φp, which is not a specific value but a range of values, depending on the particle characteristics, proves to be a paramount parameter. Two contrasting regimes, one enhancing sonochemical reactions and the other inhibiting, will be proposed, and discussed in detail in the following section.

Discussion

Effect of increase in nucleation sites

Nucleation in water, the first step in the formation of cavitation bubbles, is heterogeneous in most cases, rather than homogeneous. A typical example of preferential sites for heterogeneous nucleation, the “weak spots”, is the gas-filled micro-crevices on the surfaces of the solid impurities or container walls [41]. Once silica particles are added into water, there will be an increase in the number of nucleation sites, thereby lowering the threshold for cavitation inception [42] and promoting the formation of cavitation bubbles (and thus ·OH). This provides a logical explanation for the enhancement of the sonochemical reactions in the solid particle suspensions based on the kinetics of nucleation.

The most common quantitative model for nucleation kinetics is the classical nucleation theory (CNT) model, which was originally established by Volmer and Weber [43] nearly a century ago and is rooted in Gibbs’s thermodynamics. The CNT model predicts the rate of heterogeneous nucleation, rn, using the following equation (Eq. (1)) [44]:

where rn is the number of nuclei formed in a unit sample volume per unit time; ρs is the number density of sites for heterogeneous nucleation and is expressed in units of (number of sites)/(volume); Z is the Zeldovich factor; j is the rate at which molecules attach to the nuclei; ΔG* is the energy barrier that governs nucleation at a surface, and kBT is the average thermal energy with kB the Boltzmann constant and T the absolute temperature. The main difficulty in applying this theory lies in the lack of knowledge about the surface properties of every single particle, on which the nuclei form. Solid particles vary in size and structure; therefore, we would expect the nucleation sites to be distributed randomly and the nucleation barrier ΔG* to vary between nucleation sites.

In the strictest sense, rn could be determined with a single nucleation site that can be tested using identical conditions many times or with identical sites located in separate sampling units. However, this is seldom achievable in practice [45]. Thus, it seems reasonable to make assumptions about the surface properties with respect to the probability distribution of the “effective” nucleation sites (i.e., sites where the nuclei formed can eventually evolve into active vapor bubbles). Given the monodispersity of the suspended silica particles in this work, we assumed that any part of the particle surface had an equal likelihood of containing an “effective” nucleation site. The site-specific nucleation rate (defined as Js = ρs/SA), consequently, would remain unchanged; SA is the total surface area of the solid particles in a unit volume of the suspension. That is, with a fixed SA, the number of nucleation sites remained constant. In addition, heterogeneous nucleation could be characterized by a single barrier height among the nucleation sites based on our assumption about the particle surface [44].

Upon replacing ρs in Eq. (1) with the product of Js and SA, it can be assumed that the formation rate of the nuclei would be largely dependent on SA:

where SSA is the surface-area-to-volume ratio defined as the total surface area per unit volume of solid particles (distinct from the specific surface area shown in Table 1). This ratio decreases as the particle size increases (without changing shape). SA, which is directly proportional to φp and inversely proportional to dp, appears to be an important indicator of the capability of the total suspended solids in a specified volume to increase nucleation sites. However, although both the 0.5-vol% suspensions of 10-μm particles and the 5-vol% suspensions of 100-μm particles had an identical SA of 3 × 103 m−1, the former enhanced I3− formation while the latter inhibited I3− formation, compared with the particle-free scenario (Fig. 2d). In addition, for φp = 0.5 vol%, smaller silica particles contributed to less I3− formation despite their higher SA (Fig. 3a). Both pieces of evidence necessitate thorough investigation into the circumstances (especially the range of φp) required for enhancing sonochemical reactions by increasing the number of nucleation sites.

Wide discrepancies can be seen between high and low φp for all four dp for the relationship between Δrf/rfo of I3− and SA of the silica particles (Fig. 5a). The relationship exhibits a strong positive correlation for the 0.05–0.2-vol% suspensions of the 10- and 20-μm particles, and the 0.05–0.5-vol% suspensions of the 50- and 100-μm particles. The key factor controlling I3− formation could be the increase in the number of nucleation sites, which might lead to more collapsing bubbles and enhance sonochemical yields. The highest φp for the large particles under this site-increasing regime is greater than that for the small particles. This implies that, with the increase in φp, the enhancing effect of the site-increasing regime on I3− formation is offset and overridden by an inhibitory effect at an earlier stage for the smaller particles whose SA values are higher. When SA = 0.6 × 103 m−1, Δrf/rfo for the 10-, 20-, and 50-μm particles is approximately the same (8.6–9.3 %); however, for the 100-μm particles, it has already dropped to <2.0 %, indicating the important, but not decisive, role the site-increasing regime plays in influencing sonochemical activity. No significant correlations are apparent between Δrf/rfo and SA under higher φp conditions (i.e., φp > 1 vol%), and Δrf/rfo leans toward negative values as the SA becomes larger. This phenomenon signifies the nullification of the enhancing effect produced by the growth of effective sites for heterogeneous nucleation.

Fig. 5

Percentage change in (a) I3− formation rate and (b) cavitation erosion rate (compared with the particle-free scenario) plotted against particle surface area in a unit volume for sonicated particle suspensions. The dashed line in Fig. 5(a) represents no change in I3− formation rate.

Similar findings were reported by Barchouchi et al. [17], who investigated the role of glass beads (between 8–12 μm and 6 mm) on the I3− production at 575 kHz. The researchers concluded that, with the increase in SA, the sonochemical activity first remained unchanged (i.e., Δrf/rfo ≈ 0) and then markedly decreased after SA exceeded a critical value, irrelevant of the particle size and the frequency. These results are interesting from a comparative point of view. First, the minimum value of the experimental φp used by Barchouchi et al. [17] was 0.0001 vol%, which is much lower than the φp used in the present study (0.05 vol%). Although the addition of glass beads could barely influence the sonochemistry under such low φp conditions, the limited experimental data available in their study might have led to an inadvertent omission of the influence of the site-increasing regime. Second, their critical SA and φp were (0.02–0.06) × 103 m−1 and 0.04 vol%, respectively, both lower than those used in this study (1.0 × 103 m−1 and 0.6–1.3 vol%). This may be attributed to the higher frequencies utilized in their study. Third, their Δrf/rfo did not correlate well with SA above the critical area value, which is similar to the data in Fig. 5(a).

The existence of the site-increasing regime is also sonochemically verifiable by the SCL photographs in Fig. 4. Unlike the concentrated active zones in the particle-free scenario (Fig. 4a), the presence of silica particles induced a uniform light intensity distribution (Fig. 4b), implying that cavitation occurred in a relatively uniform manner throughout the liquid. This SCL pattern resulted from the stirred suspension of silica particles (in violent unsteady-state motion), each having an approximately equal probability of offering sites for nucleation. This is generally consistent with the work of Son et al. [18], who detected peak intensities of SCL in particle-free systems but none upon the addition of 75-μm glass beads.

Apart from sonochemical methods, cavitation erosion (CE) detection is an alternative way of evaluating the intensity of ultrasonic cavitation [46] because the shock waves and micro-jets formed during the asymmetric bubble collapse are responsible for the deterioration of the test surface. Gou et al. [47] and Su et al. [48] conducted CE tests at 20 kHz, in mixtures of 20–40-μm silt particles and tap water, and mixtures of 10–100-μm silica particles and transformer oil, respectively. Both studies found that the CE rate first increased and then decreased with increasing φp. At low φp, positive associations were observed between the CE rate and SA (Fig. 5b), similar to our results obtained using KI dosimetry (Fig. 5a). The critical φp in both studies was approximately 1 vol% as well, which implies that the site-increasing regime might also apply to CE in dilute solids suspensions. The increase in CE rate for Ref. [48] seems less sensitive to the effect caused by higher SA in Fig. 5(b) mainly because the transformer oil was more viscous than municipal water and smaller particle sizes at a fixed φp (0.5 vol%) led to even higher suspension viscosity, mitigating surface erosion [49]. As φp exceeds the critical value, CE alleviation is generally attributed to the attenuation of shock waves and the deceleration of micro-jets caused by solid particles, analogous to the damping effects of entrained air bubbles [50]. However, there are disparities between the abovementioned scenario and the regime that determines sonochemical reactions in semi-dilute suspensions of solid particles. The inhibitory effect of particle addition on sonochemical activity will be analyzed in Section 4.2.

Effect of ultrasound attenuation

When ultrasound waves propagate through a lossy medium, there is always thermal consumption of energy due to viscous attenuation. For heterogeneous media, obstacles in the path such as rigid particles also scatter ultrasound waves in all directions, resulting in further dissipation of energy [51]. Therefore, if silica particles are added into an ultrasonic cavitation field in adequate quantities, there will be a reduction in the amplitude and intensity of ultrasound waves, thereby making it more difficult for cavitation inception to occur and cavitation bubbles (and ·OH) to form. This offers a rational explanation for the inhibition of sonochemical reactions in suspensions of solid particles based on the acoustics of solid–liquid two-phase mixtures.

Two groups of theories have been principally developed to determine the relationship between acoustic properties (e.g., ultrasound speed and attenuation) and the characteristics of the heterogeneous system (e.g., particle size distribution and concentration). One is the scattering theory, including the model proposed by Epstein and Carhart [52] and Allegra and Hawley [53], in which only a simple superposition of the contribution of each particle was considered, and some “multiple scattering” revisions [54], [55]. The other is the coupled phase theory (CPT) based on two-phase hydrodynamic equations, which inherently integrates “multiple scattering” [56]. The popular CPT model established by Atkinson and Kytömaa [57], which applies when wavelengths (72.5 mm herein) ≫ dp, is adopted in this study. The model defines the imaginary part of a complex-valued wavenumber as the attenuation coefficient (α), measured in reciprocal length. The authors rewrote this parameter in a more concise form elsewhere (Eq. (3)) [58]:

where ω is the angular frequency; κ and ρ denote the bulk modulus and density of either the solid particles (subscript p) or the liquid (subscript l), respectively; the quantities , , and ρ* are given by −1 = φpκp−1 + (1 − φp)κl−1,  = φpρp + (1 − φp)ρl, and ρ* = (1 − φp)ρp + φpρl, respectively; and the dimensionless parameters A and B are defined as (Eqs. (4), (5)):

where ζ = (1 − φp)/2 is the simplified added mass coefficient, and δ = (2μl/ρlω)1/2 is the thickness of the viscous boundary layer with μl being the liquid viscosity. In this study (silica particles in water), the following values of the physical properties (at 25 °C) are used in calculation: κp = 42.5 GPa, κl = 2.2 GPa, ρp = 2500 kg·m−3, ρl = 1000 kg·m−3, and μl = 0.89 mPa·s. Notably, application of the model requires no overlapping of boundary layers surrounding adjacent particles, that is, δ is far less than half the average interparticle spacing h = [(φp/φm)−1/3 – 1]dp/2, where φm is the maximum packing fraction and is ∼64 vol% for monodisperse spheres (random close pack) [59]. Since δ ≈ 0.1 μm and h/2 ranges from 2–101 μm in this work, the requirement for no viscous interactions between particles is already satisfied.

For the specific conditions under examination here (dp = 10–100 μm, φp < 10 vol%, and 20 kHz), it is evident from Eqs. (3)−(5) that α depends on both dp and φp. However, the relationship between the acoustic attenuation and either of the particle characteristics is not immediately apparent from these equations. The calculated α is plotted in a filled contour map as a function of dp and φp (Fig. 6a), exhibiting the waterfall-like dependence of attenuation with φp (log scale). When φp < 1 vol%, there are no substantial changes in the removal of ultrasound energy with the variation in dp or φp. This implies that, at such low φp, the damping of ultrasound by scattering would not be a decisive regime that influences sonochemistry.

Fig. 6

(a) 3D color map of the attenuation coefficient (α) covering the entire range of particle size and concentration (φp) herein; and (b) its absolute value (|α|) as a function of φp for various particle sizes (φp < 10 vol%). The inset in Fig. 6(b) depicts |α| as a function of φp for the 10-μm particles (φp < φm ≈ 64 vol%).

By contrast, at higher φp (1–10 vol%), the absolute change in α values is marked. For all cases, α attains its highest absolute value in the most concentrated suspensions of the smallest particles (10 vol%, 10 μm), reaching 0.75 m−1. At relatively high φp, the sound-damping regime would likely assume a significant part in inhibiting sonochemical reactions. Interestingly, the onset of the steep drop of the attenuation surface occurs at φp ≈ 1 vol% (Fig. 6a), similar to the critical φp in Fig. 3(a), which also corresponds to the critical SA in Fig. 5(a). The critical φp, therefore, functions as a vital parameter that separates the site-increasing and sound-damping regimes (Fig. 6a).

Further scrutiny of the dependence of the ultrasound attenuation on φp reveals a non-monotonic relationship (inset in Fig. 6b). The absolute value of α (|α|) rises initially upon adding more solid particles, reaches a maximum value at φp ≈ 30 vol%, and then decreases with any further increase in φp. This concurs with the observed values of attenuation in the study of kaolinite particles in water obtained by Urick [60] and Hampton [61]. The authors also reported good linearity at low φp where the interaction between particles was insignificant, i.e., φp < 10–15 vol%, covering the entire range of our experimental φp. Similar relationships between our calculated |α| and φp (linear scale) were noted for the four dp (Fig. 6b). In addition, the attenuation of ultrasound scales inversely with dp at a constant φp, implying that smaller particles might contribute more to scattering. This might explain the lower light intensity for the 10-μm particles than for the 100-μm particles at φp = 5 vol% (Fig. 4b). The sizable separation between the curves in Fig. 6(b) makes it feasible to use ultrasound in particle sizing for slurry systems [51].

For silica particle suspensions with φp ranging from 1 to 10 vol%, a positive linear relationship exists between the percentage decrease in rf(I3−) and |α| (Fig. 7). This demonstrates that the chief regime here should be the damping of ultrasound due to acoustic scattering, which may lead to fewer cavitation bubbles, and thus less ·OH being produced. We also find evidence of a high correlation between I3− formation and ultrasound attenuation based on experimental data from Refs. [17], [25]. One clear distinction, however, is the slope; for example, the slope obtained based on the data from Tuziuti et al. [25] is the steepest, possibly suggesting stronger inhibiting effects that the attenuation has on sonochemical reactions. This may be attributed to their higher frequency (42 kHz) and, more importantly, the entirely distinct characteristics of the alumina particles. Despite the differences in the slopes, all three sets of data reflect the decisive role the sound-damping regime assumes in influencing the sonochemistry at φp above the critical value.

Fig. 7

Percentage decrease in the I3− formation rate plotted against the absolute value of the calculated attenuation coefficient (|α|) in sonicated particle suspensions. Bulk modulus (κp) and density (ρp) of the solid particles (at 25 °C) used in the calculation: κp = 162 GPa and ρp = 3980 kg·m−3 for alumina particles; κp = 42.5 GPa and ρp = 2500 kg·m−3 for glass beads.

Another efficient approach to verifying the existence of the sound-damping regime is the spectral analysis of the cavitation noise in solid particle suspensions because cavitation noise contains key information concerning collapsing bubbles [62]. Wu et al. [63] investigated the influence of particle addition on the frequency spectrum of the noise and discovered that cavitation noise became less intense when 1-μm alumina particles were added to tap water (φp = 1.1–2.3 vol%). They predicted, based on off-line steady-state detection algorithms, that the acoustic attenuation would overwhelm the influence of nuclei addition when φp > 1.1 vol%, which is similar to the critical φp that we obtained sonochemically. This is more than just a coincidence because of the link between the triggering of sonochemical reactivity and the emergence of white noise in cavitation noise spectra [64]. Ge et al. [30] discovered that, at a fixed φp, 10–100-μm silica particles decreased the cavitation noise, while 500–700-μm particles increased the noise levels. The authors explained that such large particles could barely remain suspended consistently to interact with cavitation bubbles but could increase the total number of nucleation sites. This implies that altering the particle size might also lead to a regime shift, which was not observed in this investigation. It is, therefore, necessary to characterize the two regimes with a wider range of dp and φp in future work.

Notably, the three outlier points above the dashed line in Fig. 5(a) were not discussed when addressing the two regimes because neither appears to have a decisive influence. These three cases signify the gradual transition from one regime into the other, i.e., the process of one regime offsetting or overriding the other, with the variation in φp. The two regimes are fundamental to elucidating the contradictory effects of the suspended solid particles on sonochemical activity.

Conclusions

Based on the sonochemical analysis conducted in silica microparticle suspensions, we proposed and examined two contrasting regimes, namely the site-increasing regime and the sound-damping regime, which are likely to control sonochemical reactions in heterogeneous systems. The summary of the key findings is as follows:

(a) With the increase in φp from 0.05 to 10 vol%, the sonochemical yields initially increased gradually and then decreased suddenly. The overall effect of adding solid particles on the sonochemistry changed from being enhancing to inhibiting as φp exceeded a critical value (∼1 vol%). At a specific φp, the extent of the effect also differed between various dp (10–100 μm). Smaller particles had stronger enhancing effects at low φp or stronger inhibiting effects at high φp.

(b) The sonochemical yields in dilute suspensions were higher than those in the particle-free solutions due to the increase in the number of nucleation sites. Smaller particles in larger quantities contributed to even higher yields due to higher nucleation rates. According to the CNT model, the nucleation rate is directly proportional to the total particle surface area, to which the sonochemical yields correlated strongly. The uniform distribution of the light intensity in SCL images validates this site-increasing regime.

(c) Further addition of solid particles in the semi-dilute suspensions led to lower sonochemical yields than in the particle-free solutions because of the greater damping of the ultrasound by the scattering effect. The sonochemical yields correlated well with the attenuation, which increases with an increase in φp and a decrease in dp within our experimental range, according to the CPT model. This sound-damping regime can also be validated by analysis of the cavitation noise signals in heterogeneous media.

The results presented here describe the important roles that solid particles enact in sonochemical reactions and provide appropriate clarification regarding the influencing regimes. The new insights into these regimes and their transitions could prove useful in predicting sonochemical yields in solid–liquid two-phase flow systems, such as the sonochemical degradation of pollutants in solids-containing wastewater. Future work should focus on the validation of these regimes with a wider range of particle sizes, concentrations, and surface properties.

CRediT authorship contribution statement

Kunpeng Su: Conceptualization, Investigation, Formal analysis, Writing – original draft. Jianhua Wu: Funding acquisition, Supervision. Dingkang Xia: Visualization, Methodology, Data curation, Formal analysis, Writing – review & editing. Xinming Zhang: Methodology, Investigation.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.