From: Ultrasonic intensification as a tool for enhanced microbial biofuel yields
S.No. | Parameters | Equations | Definitions | References |
---|---|---|---|---|
1 | Acoustic energy density (AED) | \({\rm AED} = \frac{P}{V}\) \(P = mc_{\rm p}{\left(\frac{{\rm d}T}{{\rm d}t}\right)}^{}_{t=0}\) | 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 | \({\rm UI} = \frac{4P}{{D^{2} }}\) | P absolute ultrasonic power, D diameter of the probe tip | [111] |
3 | Ultrasonic intensity | \({\rm UI} = \frac{P}{A}\) | UI ultrasonic intensity, P ultrasonic power, A surface area of the probe | [112] |
4 | Cell disruption at given acoustic power | \(F_{\rm N} = - {\rm exp}\left[ { - \left( {\frac{t}{\alpha }} \right)^{\beta } } \right]\) | 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 | \(\varepsilon_{{\rm rr}} (r) = - 2 v_{\rm R} R^{2} r^{ - 3}\) \(v_{{\rm R}} = {{\rm d}R}/ {{\rm d}t}\, {\dot{Q}}_{\rm a} {\rm O}_2 Z\) \(= (2P_{\rm h}/ {3\rho})^{0.5} (R_{\rm m}^3/ R^3-1)^{0.5}\) | 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 | \(E_{\rm s} = \frac{P t}{{V\, {\rm TS}_{0} }}\) | 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 | \(Q_{\rm u} = P \times t\) | Q u energy output, P ultrasonic power, t ultrasonic time | [116] |
8 | Ultrasound dose | \({\rm UD}_{0} = \frac{P \times t}{V}\) | UD0 ultrasonic dose, P ultrasonic power, t ultrasonic time | [116] |
9 | Sonochemical effectiveness factor(e us) | \(\varvec{e}_{{{\rm us}}} = f,\eta I,{\mathbb{V}}_{\rm us} ,T\) \({\mathbb{V}}_{\rm us}=V_{\rm us}/V_{\rm tot}\) | f applied frequency, ηI calorimetrically determined power of the transducer, T average temperature in the reactor, \({\mathbb{V}}_{\rm us}\) 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: \(P_{\rm AW}(r, t)=\rho_{\rm L}\frac{R}{r}\left[ 2\left(\frac{{\rm d}R}{{\rm d}t}\right)^2+R \frac{{\rm d}^{2}R}{{\rm d}t^2}\right]\) |