Table 2 Formulas for calculating tortuosity in packed beds of spherical particles in the literature.
Model Name | Correlation | Applicable void fraction range | Derivation method | Type of tortuosity |
|---|---|---|---|---|
Maxwell (1873) | \(\frac{3}{2} - \frac{1}{2}\varepsilon\) | Not specified | Analytical | Electrical |
Bartell & Osterhof (1928) | \(\frac{\pi }{2}\) | \(\varepsilon =0.4\) | Experimental | Hydraulic |
Carman (1937) | \(\sqrt 2\) | \(\varepsilon =0.4\) | Experimental | Hydraulic |
Weissberg (1963) | \(1 - \frac{{{\text{ln}}\left( \varepsilon \right)}}{2}\) | \(0.36<\varepsilon <1\) | Analytical | Diffusive |
Bear (1972) | \(\frac{1}{{{\varepsilon ^{0.4}}}}\) | Not specified | Experimental | Geometric |
Comiti & Renaud (1989) | \(1 - 0.41{\text{ln}}\left( {\text{\varvec{\upvarepsilon}}} \right)\) | Not specified | Experimental | Geometric |
Du Plessis & Masliyah (1991) | \(\frac{\varepsilon }{{1 - \sqrt[3]{{{{\left( {1 - \varepsilon } \right)}^2}}}}}\) | Not specified | Analytical | Geometric |
Iversen & Jorgensen (1993) | \(\sqrt {1+2\left( {1 - \varepsilon } \right)}\) | \(0.4<\varepsilon <0.9\) | Experimental | Diffusive |
Boudreau (1996) | \(\sqrt {1 - ln({\varepsilon ^2})}\) | Not specified | Analytical | Diffusive |
Ahmadi et al. (2011) | \(\sqrt {\frac{{2\varepsilon }}{{3\left[ {1 - 1.209{{\left( {1 - \varepsilon } \right)}^{\frac{2}{3}}}} \right]}}+\frac{1}{3}}\) | \(\varepsilon >0.4\) | Analytical | Geometric |
