Table 2 Correlations for mixture physical properties⁴².

Dynamic viscosity

\(\frac{{\mu }_{m}}{{\mu }_{bf}}=0.983{e}^{12.959\varphi }\)

Thermal conductivity

\(\frac{{k}_{m}}{{k}_{bf}}=\frac{{k}_{np}+2{k}_{bf}-2\left({k}_{bf}-{k}_{np}\right)\varphi }{{k}_{np}+2{k}_{bf}+2\left({k}_{bf}-{k}_{np}\right)\varphi }+{B}_{r}\)

\({B}_{r}=3\times {10}^{3}\alpha \varphi {\rho }_{bf}{C}_{pbf}\sqrt{\frac{{k}_{B}T}{{\rho }_{np}{d}_{p}}}f(T,\varphi )\)

\({k}_{B}=1.381\times {10}^{-23} \mathrm{J}/\mathrm{K}\)

\(f\left(T,\varphi \right)=\left(0.028217\varphi +0.00391\right)\frac{T}{{T}_{Ref}}+\left(-0.030669\varphi -0.00391123\right)\)

Volumetric expansion coefficient

\({{\beta }_{m}=(\left(1-\varphi \right){\rho }_{bf}{\beta }_{bf}+\varphi {\rho }_{p}{\beta }_{p})/}_{{\rho }_{m}}\)

Density

\({\rho }_{m}=\left(1-\varphi \right){\rho }_{bf}+\varphi {\rho }_{p}\)

Specific heat capacity

\({C}_{pm}=(\left(1-\varphi \right){\rho }_{bf}{C}_{pbf}+\varphi {{\rho }_{p}C}_{pp})/{\rho }_{m}\)