Sonochemical Effect Induced by Hydrodynamic Cavitation

4 Effect of Gas Type on Adiabatic Bubble Collapse

Dissolved gas determines more than the initial number of nuclei. Gas identity changes the heat capacity ratio, thermal conductivity, diffusivity, solubility, ionization energy, chemical reactivity, and the rate at which the bubble exchanges mass with the liquid. These properties jointly control collapse temperature, luminescence, radical production, and product selectivity. The strongest ideal compression is associated with a large γ, but the highest chemical yield does not necessarily occur for the gas with the largest γ because thermal transport, vapor content, gas chemistry, and bubble stability can dominate [4,25,27-29].

For an ideal mixture with mole fractions $y_i$ and molar heat capacities $c_{p,i}$ and $c_{v,i}$, an effective heat capacity ratio can be estimated by:

where $y_i$ is the gas phase mole fraction of species i.

The effective exponent during a real collapse is frequency and time scale dependent. Slow oscillation permits heat exchange and drives the behavior toward isothermal compression. Rapid terminal compression moves the gas core toward adiabatic behavior while retaining a thermal boundary layer. A gas phase Peclet number expresses the competition:

where ${\alpha }_g$ is gas thermal diffusivity. Large ${\mathrm{Pe}}_g$ indicates interface motion faster than thermal diffusion across the bubble radius.

A second useful descriptor is the initial noncondensable gas fraction relative to total bubble contents:

where $n_g$ is moles of noncondensable gas and $n_v$ is moles of vapor.

A large ${\chi }_g$ increases the gas spring and can prevent complete collapse, while a very small ${\chi }_g$ allows intense compression but may produce an unstable cavity with limited chemical feedstock and weak rebound. In practical reactors, gas concentration also affects nucleation density. Degassing may intensify the collapse of the few remaining bubbles but reduce the number of active events. Gas sparging may create more nuclei and improve oxygen supply, yet excessive gas loading can cushion collapse and produce persistent gas holdup. Optimization therefore requires both per bubble intensity and active bubble population.

Table 4.1. Qualitative influence of common gases on cavitation chemistry

Gas	Key physical properties	Likely collapse effect	Chemical implications
Argon	Monatomic, high γ, relatively low thermal conductivity, chemically inert	Strong compressional heating and stable spectroscopic emitter	Often favors high hot spot temperature and radical yield; widely used reference gas
Xenon	Monatomic, high polarizability, low ionization energy, high molar mass	Can enhance light emission and alter plasma chemistry	Potentially strong excitation but high solubility and cost limit process use
Helium	Monatomic but very high thermal conductivity and diffusivity	Rapid heat loss can offset the high γ	Can reduce hot spot temperature compared with argon under otherwise similar conditions
Nitrogen	Diatomic, γ near 1.4, chemically reactive at high temperature	Lower ideal heating than monatomic gas	Can form NO, NO2-, and NO3-; competes for oxidants at high temperature
Oxygen	Diatomic and reactive	Supports oxygen radical pathways	Promotes HO2•, O2•-, peroxide, and oxidation; may also quench excited states
Air	N2/O2 mixture with water vapor	Practical compromise between nuclei, oxygen supply, and thermal softness	Produces mixed oxygen- and nitrogen derived chemistry
Carbon dioxide	High solubility, polyatomic, lower effective γ, acidifies water	Strong thermal and chemical damping	Often suppresses hot spot temperature; generates carbonate/bicarbonate chemistry
Hydrogen	High diffusivity and thermal conductivity; combustible	Rapid transport and heat loss	Strong reducing radical chemistry but major safety constraints
Steam rich bubble	High polyatomic vapor fraction	Substantial cushioning and endothermic dissociation	Provides H• and •OH precursor but can lower temperature and oxidant survival

Rare gas experiments in acoustic cavitation are especially valuable because they isolate the effect of heat capacity and thermal transport. McNamara and coworkers measured emission temperatures between approximately 2300 and 5100 K as gas vapor composition was varied [25]. Okitsu and coworkers showed that the relationship between rare gas atmosphere and chemical yield is not governed by temperature alone [28]. The transferable lesson for hydrodynamic cavitation is that gas composition must be treated as a process variable, not merely as an uncontrolled liquid property.

Figure 4.1. High speed image sequences showing interaction, deformation, jetting, and collapse of two cavitation bubbles. [36]. The sequence illustrates why neighboring bubbles change collapse symmetry and energy focusing.

Bubble interaction can overwhelm the single bubble gas effect. Neighboring cavities modify the pressure field, exchange shock waves, coalesce, and collapse asymmetrically. The high speed sequences in Figure 4.1 show that spacing and relative size can redirect jets and distribute shock emission over multiple events [36]. In a dense hydrodynamic cloud, increasing inlet pressure may increase vapor volume while decreasing the chemical yield per unit energy because shielding, coalescence, and radical recombination become stronger [11].

Figure 4.2. Representative high speed images of cavitation bubble clusters generated by focused shock waves at different operating conditions. [37].

Fattahi and coworkers quantified chemistry in controlled bubble clusters and found a maximum conversion of focused shock wave energy to chemical energy at an intermediate cluster energy density, rather than at the largest cluster [37]. Their result was obtained with acoustically or laser mediated cluster generation, but it directly informs hydrodynamic cloud design: more bubbles are useful only while each bubble retains sufficient collapse intensity and products can escape the cluster without immediate recombination.

Figure 4.3. Measured conversion of focused shock wave energy to chemical energy as a function of cluster energy density. [37].

Table 4.2. Gas management strategies for hydrodynamic cavitation reactors

Strategy	Potential benefit	Potential penalty	Recommended verification
Operate air saturated	Simple and reproducible in open systems	Gas content changes with temperature and pressure history	Measure dissolved oxygen and temperature before each run
Argon saturation	Can increase per bubble hot spot intensity	Cost, gas consumption, and possible reduction in oxygen chemistry	Compare radical yield per joule and not conversion alone
Oxygen sparging	Raises dissolved oxygen and can support secondary oxidation	Excess gas holdup cushions collapse and changes pump behavior	Measure void fraction, pressure drop, off gas, and oxidant yield
Partial degassing	May reduce cloud shielding and intensify remaining collapses	Reduces nucleation population and can delay inception	Measure inception pressure, bubble count, and chemical yield
CO2 addition	Controls pH and may assist carbonate chemistry	Thermally damps collapse and scavenges •OH through bicarbonate/carbonate	Track inorganic carbon, pH, and product selectivity
Closed loop gas control	Enables repeatable composition and mass balance	Requires gas liquid equilibrium control and safety instrumentation	Use gas analysis, pressure control, and leak testing