Table 5.

Kinetic expressions derived for ultrasonic parameters

S.No.	Parameters	Equations	Definitions	References
1	Acoustic energy density (AED)	$\mathrm{AED}=\frac{P}{V}$ $P=m{c}_{\mathrm{p}}{\left(\frac{\mathrm{d}T}{\mathrm{d}t}\right)}_{t=0}^{}$	P absolute ultrasonic power, V volume of the medium (cm3 L−1), m mass, c p specific heat capacity, (dT/dt) range of temperature change during sonication	[111]
2	Ultrasonic intensity (UI) with the influence of diameter of the probe tip	$\mathrm{UI}=\frac{4P}{D^2}$	P absolute ultrasonic power, D diameter of the probe tip	[111]
3	Ultrasonic intensity	$\mathrm{UI}=\frac{P}{A}$	UI ultrasonic intensity, P ultrasonic power, A surface area of the probe	[112]
4	Cell disruption at given acoustic power	$F_{\mathrm{N}}=-\exp \left[-{\left(\frac{t}{\mathit{\alpha }}\right)}^{\mathit{\beta }}\right]$	F N cumulative fractions of disrupted cells at given acoustic power, t time of ultrasonication, α and β kinetic constants	[113]
5	Strain rate distribution	${\mathit{\epsilon }}_{\mathrm{rr}}(r)=-2v_{\mathrm{R}}{R}^2{r}^{-3}$ $v_{\mathrm{R}}=\mathrm{d}R/\mathrm{d}t{\dot{Q}}_{\mathrm{a}}{\mathrm{O}}_{2}Z$ $={(2P_{\mathrm{h}}/3\mathit{\rho })}^{0.5}{(R_{\mathrm{m}}^3/R^3-1)}^{0.5}$	ℇ rr strain rate distribution during cavity collapse, v R bubble wall velocity, ρ solvent density, P h external pressure, R m initial radius and R instantaneous radius of imploding cavity	[114]
6	Specific Energy input	$E_{\mathrm{s}}=\frac{Pt}{V{\mathrm{TS}}_0}$	E s specific energy, P ultrasonic power, t ultrasonic time, V volume of the sample, TS0 initial concentration of total solids	[115]
7	Actual energy produced by ultrasonication	$Q_{\mathrm{u}}=P\times t$	Q u energy output, P ultrasonic power, t ultrasonic time	[116]
8	Ultrasound dose	${\mathrm{UD}}_0=\frac{P\times t}{V}$	UD0 ultrasonic dose, P ultrasonic power, t ultrasonic time	[116]
9	Sonochemical effectiveness factor(e us)	${\mathit{e}}_{\mathrm{us}}=f,\mathit{\eta }I,{\mathbb{V}}_{\mathrm{us}},T$ ${\mathbb{V}}_{\mathrm{us}}=V_{\mathrm{us}}/V_{\mathrm{tot}}$	f applied frequency, ηI calorimetrically determined power of the transducer, T average temperature in the reactor, ${\mathbb{V}}_{\mathrm{us}}$ dimensionless cavitationally active volume, V us volume of the reactor space affected by sonication, V tot total working volume	[110]
10	Bubble dynamics model	Micro-convection: ${\text{V}}_{\text{turb}}(\text{r},\text{t})=\frac{{\text{R}}^2}{{\text{r}}^2}\left(\frac{\text{d}R}{\text{d}t}\right)$	V turb velocity of turbulence, P AW pressure amplitude of acoustic wave, R radius of the bubble, dR/dt bubble wall velocity, V b volume of the bubble, ρ L density of the liquid	[31]
		Shock waves: $P_{\mathrm{AW}}(r,t)={\mathit{\rho }}_{\mathrm{L}}\frac{R}{r}\left[2{\left(\frac{\mathrm{d}R}{\mathrm{d}t}\right)}^2+R\frac{{\mathrm{d}}^{2}R}{\mathrm{d}{t}^2}\right]$