Table 5.
Statistical summary of the estimated MLRM coefficients correlating the breakage rate constant k of the nth-order kinetics model with the microhydrodynamic parameters.
| Approach | Best Model | Parameter | Model | |||||
|---|---|---|---|---|---|---|---|---|
| Symbol a | Coefficient b | p-Value | R2 | Adj. R2 | SSR | p-Value | ||
| First-order MLRM | BM 1 | a (mHz) | 5.66×10−3 | 3.91 × 10−5 | 0.922 | 0.911 | 0.253 | 3.91 × 10−5 |
| BM 2 | σbmax (GPa) | 1.52 × 10−1 | 8.45 × 10−3 | 0.978 | 0.970 | 0.073 | 1.12 × 10−5 | |
| a (mHz) | 4.68 × 10−3 | 4.05 × 10−5 | ||||||
| BM 3 | σbmax (GPa) | 1.52 × 10−1 | 1.86 × 10−2 | 0.978 | 0.964 | 0.073 | 1.50 × 10−4 | |
| αb (µm) | 1.86 × 10−3 | 9.24 × 10−1 | ||||||
| a (mHz) | 4.64 × 10−3 | 6.88 × 10−4 | ||||||
| BM 4 | σbmax (GPa) | 1.51 × 10−1 | 1.08 × 10−1 | 0.978 | 0.955 | 0.073 | 1.47 × 10−3 | |
| αb (µm) | 2.07 × 10−3 | 9.41 × 10−1 | ||||||
| a (mHz) | 4.63 × 10−3 | 1.19 × 10−2 | ||||||
| Πσy ( × 10−16 J2/m6s) | 1.06 × 10−4 | 9.90 × 10−1 | ||||||
| Second-order MLRM | BM 1 | a (mHz) | 5.66 × 10−3 | 3.91 × 10−5 | 0.922 | 0.911 | 0.253 | 3.91 × 10−5 |
| BM 2 | σbmax (GPa) | 1.52 × 10−1 | 8.45 × 10−3 | 0.978 | 0.970 | 0.073 | 1.12 × 10−5 | |
| a (mHz) | 4.68 × 10−3 | 4.05 × 10−5 | ||||||
| BM 3 | σbmax (GPa) | 1.40 × 10−1 | 1.90 × 10−2 | 0.982 | 0.971 | 0.060 | 9.14 × 10−5 | |
| a (mHz) | 6.11 × 10−3 | 7.74 × 10−3 | ||||||
| a2 (mHz2) | −7.38 × 10−6 | 3.39 × 10−1 | ||||||
| BM 4 | a (mHz) | 1.22 × 10−2 | 1.27 × 10−3 | 0.994 | 0.988 | 0.020 | 1.14 × 10−4 | |
| Πσy (×10−16 J2/m6s) | 1.19 × 10−2 | 1.81 × 10−2 | ||||||
| αb2 (µm2) | −1.16 × 10−2 | 4.14 × 10−2 | ||||||
| a2 (mHz2) | −3.64 × 10−5 | 4.88 × 10−3 | ||||||
| MLRM with interaction terms | BM 1 | a (mHz) | 5.66 × 10−3 | 3.91 × 10−5 | 0.922 | 0.911 | 0.253 | 3.91 × 10−5 |
| BM 2 | σbmax (GPa) | 1.52 × 10−1 | 8.45 × 10−3 | 0.978 | 0.970 | 0.073 | 1.12 × 10−5 | |
| a (mHz) | 4.68 × 10−3 | 4.05 × 10−5 | ||||||
| BM 3 | a (mHz) | 1.87 × 10−2 | 2.74 × 10−4 | 0.992 | 0.988 | 0.024 | 9.98 × 10−6 | |
| αba (µm.mHz) | −3.25 × 10−3 | 1.20 × 10−3 | ||||||
| aΠσy (×10−16 mHz J2/m6s) | −9.77 × 10−5 | 6.67 × 10−3 | ||||||
| BM 4 | a (mHz) | 1.53 × 10−2 | 3.20 × 10−4 | 0.998 | 0.997 | 0.005 | 6.50 × 10−6 | |
| Πσy (×10−16 J2/m6s) | 1.86 × 10−2 | 1.54 × 10−2 | ||||||
| αba (µm.mHz) | −2.48 × 10−3 | 1.31 × 10−3 | ||||||
| aΠσy (×10−16 mHz J2/m6s2) | −1.51 × 10−4 | 8.96 × 10−4 | ||||||
a: Statistically insignificant (p-value > 0.01) parameters are shown in bold. Πσy is treated as a single parameter, as σy is a constant. b: The coefficients have the units that make the MLRM equation dimensionally homogeneous.