Table 1 The list of proposed AC and GC models for density, refractive index, heat capacity, speed of sound and surface tension of DESs at atmospheric pressure.
Property | Model | |
|---|---|---|
GC model | ||
Density (g/cm3) | \(\rho_{{_{1} }}^{G} = m_{HBA} \sum\limits_{i = 1}^{p} {k_{i} (\Delta \rho_{{_{1,i} }}^{G} )_{HBA} } + m_{HBD} \sum\limits_{i = 1}^{q} {l_{i} (\Delta \rho_{{_{1,i} }}^{G} )_{HBD} }\) | (1) |
\(\rho_{2}^{G} = m_{HBA} \sum\limits_{i = 1}^{p} {k_{i} (\Delta \rho_{{_{2,i} }}^{G} )_{HBA} } + m_{HBD} \sum\limits_{i = 1}^{q} {l_{i} (\Delta \rho_{{_{2,i} }}^{G} )_{HBD} }\) | (2) | |
\(\rho^{G} = \left( {\frac{{\rho_{1}^{G} }}{Mw}} \right)^{ - 0.2045} + \left( {\frac{{\rho_{2}^{G} }}{Mw}} \right)T^{ - 0.6785} + 0.2818\) | (3) | |
Refractive index | \(n_{{_{1} }}^{G} = m_{HBA} \sum\limits_{i = 1}^{p} {k_{i} (\Delta n_{{_{1,i} }}^{G} )_{HBA} } + m_{HBD} \sum\limits_{i = 1}^{q} {l_{i} (\Delta n_{{_{1,i} }}^{G} )_{HBD} }\) | (4) |
\(n_{2}^{G} = m_{HBA} \sum\limits_{i = 1}^{p} {k_{i} (\Delta n_{{_{2,i} }}^{G} )_{HBA} } + m_{HBD} \sum\limits_{i = 1}^{q} {l_{i} (\Delta n_{{_{2,i} }}^{G} )_{HBD} }\) | (5) | |
\(n^{G} = \left( {n_{1}^{G} } \right)^{ - 0.3597} + \left( {n_{2}^{G} } \right)T^{ - 1.8254} + 1.3695\) | (6) | |
Heat capacity (J/mol K) | \(Cp_{{_{1} }}^{G} = m_{HBA} \sum\limits_{i = 1}^{p} {k_{i} (\Delta Cp_{{_{1,i} }}^{G} )_{HBA} } + m_{HBD} \sum\limits_{i = 1}^{q} {l_{i} (\Delta Cp_{{_{1,i} }}^{G} )_{HBD} }\) | (7) |
\(Cp_{2}^{G} = m_{HBA} \sum\limits_{i = 1}^{p} {k_{i} (\Delta Cp_{{_{2,i} }}^{G} )_{HBA} } + m_{HBD} \sum\limits_{i = 1}^{q} {l_{i} (\Delta Cp_{{_{2,i} }}^{G} )_{HBD} }\) | (8) | |
\(Cp^{G} = \left( {Cp_{1}^{G} } \right)^{0.8653} + \left( {Cp_{2}^{G} } \right)T^{ - 0.4528} + 341.4081\) | (9) | |
Speed of sound (m/s) | \(u_{{_{1} }}^{G} = m_{HBA} \sum\limits_{i = 1}^{p} {k_{i} (\Delta u_{{_{1,i} }}^{G} )_{HBA} } + m_{HBD} \sum\limits_{i = 1}^{q} {l_{i} (\Delta u_{{_{1,i} }}^{G} )_{HBD} }\) | (10) |
\(u_{2}^{G} = m_{HBA} \sum\limits_{i = 1}^{p} {k_{i} (\Delta u_{{_{2,i} }}^{G} )_{HBA} } + m_{HBD} \sum\limits_{i = 1}^{q} {l_{i} (\Delta u_{{_{2,i} }}^{G} )_{HBD} }\) | (11) | |
\(u^{G} = \left( {u_{1}^{G} } \right) - \left( {u_{2}^{G} } \right)T^{0.1851} + 1829.8799\) | (12) | |
Surface tension (mN/m) | \(\sigma_{{_{1} }}^{G} = m_{HBA} \sum\limits_{i = 1}^{p} {k_{i} (\Delta \sigma_{{_{1,i} }}^{G} )_{HBA} } + m_{HBD} \sum\limits_{i = 1}^{q} {l_{i} (\Delta \sigma_{{_{1,i} }}^{G} )_{HBD} }\) | (13) |
\(\sigma_{2}^{G} = m_{HBA} \sum\limits_{i = 1}^{p} {k_{i} (\Delta \sigma_{{_{2,i} }}^{G} )_{HBA} } + m_{HBD} \sum\limits_{i = 1}^{q} {l_{i} (\Delta \sigma_{{_{2,i} }}^{G} )_{HBD} }\) | (14) | |
\(\sigma^{G} = \left( {\sigma_{1}^{G} } \right) - \left( {\sigma_{2}^{G} } \right)T^{0.0115} + 40.8235\) | (15) | |
AC model | ||
Density (g/cm3) | \(\rho_{{_{1} }}^{A} = m_{HBA} \sum\limits_{i = 1}^{p} {k_{i} (\Delta \rho_{{_{1,i} }}^{A} )_{HBA} } + m_{HBD} \sum\limits_{i = 1}^{q} {l_{i} (\Delta \rho_{{_{1,i} }}^{A} )_{HBD} }\) | (16) |
\(\rho_{2}^{A} = m_{HBA} \sum\limits_{i = 1}^{p} {k_{i} (\Delta \rho_{{_{2,i} }}^{A} )_{HBA} } + m_{HBD} \sum\limits_{i = 1}^{q} {l_{i} (\Delta \rho_{{_{2,i} }}^{A} )_{HBD} }\) | (17) | |
\(\rho^{A} = \left( {\frac{{\rho_{1}^{A} }}{Mw}} \right)^{ - 0.4093} + \left( {\frac{{\rho_{2}^{A} }}{Mw}} \right)T^{ - 0.7434} + 0.5139\) | (18) | |
Refractive index | \(n_{{_{1} }}^{A} = m_{HBA} \sum\limits_{i = 1}^{p} {k_{i} (\Delta n_{{_{1,i} }}^{A} )_{HBA} } + m_{HBD} \sum\limits_{i = 1}^{q} {l_{i} (\Delta n_{{_{1,i} }}^{A} )_{HBD} }\) | (19) |
\(n_{2}^{A} = m_{HBA} \sum\limits_{i = 1}^{p} {k_{i} (\Delta n_{{_{2,i} }}^{A} )_{HBA} } + m_{HBD} \sum\limits_{i = 1}^{q} {l_{i} (\Delta n_{{_{2,i} }}^{A} )_{HBD} }\) | (20) | |
\(n^{A} = \left( {n_{1}^{A} Mw} \right)^{ - 0.2975} + \left( {n_{2}^{A} Mw} \right)T^{ - 2.9213} + 1.4335\) | (21) | |
Heat capacity (J/mol K) | \(Cp_{{_{1} }}^{A} = m_{HBA} \sum\limits_{i = 1}^{p} {k_{i} (\Delta Cp_{{_{1,i} }}^{A} )_{HBA} } + m_{HBD} \sum\limits_{i = 1}^{q} {l_{i} (\Delta Cp_{{_{1,i} }}^{A} )_{HBD} }\) | (22) |
\(Cp_{2}^{A} = m_{HBA} \sum\limits_{i = 1}^{p} {k_{i} (\Delta Cp_{{_{2,i} }}^{A} )_{HBA} } + m_{HBD} \sum\limits_{i = 1}^{q} {l_{i} (\Delta Cp_{{_{2,i} }}^{A} )_{HBD} }\) | (23) | |
\(Cp^{A} = \left( {Cp_{1}^{A} } \right)^{0.5592} + \left( {Cp_{2}^{A} } \right)T^{0.7325} + 31.7092\) | (24) | |
Speed of sound (m/s) | \(u_{{_{1} }}^{A} = m_{HBA} \sum\limits_{i = 1}^{p} {k_{i} (\Delta u_{{_{1,i} }}^{A} )_{HBA} } + m_{HBD} \sum\limits_{i = 1}^{q} {l_{i} (\Delta u_{{_{1,i} }}^{A} )_{HBD} }\) | (25) |
\(u_{2}^{A} = m_{HBA} \sum\limits_{i = 1}^{p} {k_{i} (\Delta u_{{_{2,i} }}^{A} )_{HBA} } + m_{HBD} \sum\limits_{i = 1}^{q} {l_{i} (\Delta u_{{_{2,i} }}^{A} )_{HBD} }\) | (26) | |
\(u^{A} = u_{1}^{A} - u_{2}^{A} T^{0.0258} + 1607.4690\) | (27) | |
Surface tension (mN/m) | \(\sigma_{{_{1} }}^{A} = m_{HBA} \sum\limits_{i = 1}^{p} {k_{i} (\Delta \sigma_{{_{1,i} }}^{A} )_{HBA} } + m_{HBD} \sum\limits_{i = 1}^{q} {l_{i} (\Delta \sigma_{{_{1,i} }}^{A} )_{HBD} }\) | (28) |
\(\sigma_{2}^{A} = m_{HBA} \sum\limits_{i = 1}^{p} {k_{i} (\Delta \sigma_{{_{2,i} }}^{A} )_{HBA} } + m_{HBD} \sum\limits_{i = 1}^{q} {l_{i} (\Delta \sigma_{{_{2,i} }}^{A} )_{HBD} }\) | (29) | |
\(\sigma^{A} = \sigma_{1}^{A} - \sigma_{2}^{A} T^{0.0099} + 40.4052\) | (30) | |
