The positive value is Winsor Type II. The zero HLD is an optimal condition in Winsor Type III. The negative value is Winsor Type I. The HLD equation is divided into two equations for the ionic and the nonionic surfactants, as follows [28; 33; 34; 35; 36; 37; 38; 39; 40]:  
\[\mathrm{HLD_{ionic}=\;ln(S)-\;K_{i}(EACN)-\;f(A)-\;\alpha_{T}(T-T_{ref})+\;\sigma} \tag{1}\]  
\[\mathrm{HLD_{nonionic}=\;bS-\;K_{n}(EACN)-\varnothing(A)+\;c_{T}(T-T_{ref})+\;\beta} \tag{2}\]  
where S is the salinity (g/100 mL), b is a co-efficiency constant of salinity (g/100 mL)\({}^{-1}\), K\({}_{i}\) and K\({}_{n}\) are the constants for the ionic and nonionic surfactant, respectively, EACN is an equivalent alkane carbon number, f(A) and \(\varnothing(A)\) are the functions of the alcohol or the cosurfactant, \(\alpha_{T}\) and c\({}_{T}\) are the temperature constants (\({}^{\circ}\)C\({}^{-1}\)), T \(-\) T\({}_{ref}\) is the difference between the experiment temperature and the reference temperature (25 \({}^{\circ}\)C), and \(\sigma\) and \(\beta\) are the surfactant characteristic parameter of the ionic and nonionic surfactants, respectively. The HLD for the mixture of the same type of surfactants, such as anionic-anionic, cationic-cationic, or nonionic-nonionic, is assumed as the ideal case. The mixed HLD is a sum of each HLD equation multiplied by the mole fraction of each surfactant. In the case of different type mixtures (e.g., anionic-nonionic, or cationic-nonionic), the excess free energy will be included in the HLD as a non-ideal case, as follows [41; 42]:  
\[\rm{HLD_{mixed~{}ionic-nonionic~{} surfactant}}=\,X_{i}\,HLD_{i}+\,X_{n}\,HLD_{n}+\frac{G_{EX}}{RT} \tag{3}\]  
where \(X_{i}\) and \(X_{n}\) are the mole fractions of ionic surfactant and nonionic surfactant, respectively (in this case: \(X_{n}=1-\,X_{i}\)), \(HLD_{i}\) and \(HLD_{n}\) are the HLD equations of ionic and nonionic surfactant, respectively, \(\frac{G_{EX}}{RT}\) is the term of the excess free energy, \(G_{EX}\) is the excess free energy of the surfactant transference, R is the gas constant (8.31 1/mol\(\cdot\)K), and T is the experiment temperature (Kelvin). Positive values of \(\frac{G_{EX}}{RT}\) indicate the hydrophobicity of the actual mixture relative to the ideal mixture, whereas negative values indicate the hydrophilicity of the actual mixture relative to the ideal mixture. The zero \(\frac{G_{EX}}{RT}\) is the ideal mixture, which is assumed for the same-types-of-surfactant mixture. The \(\frac{G_{EX}}{RT}\) value of the binary mixture can be determined by the thermodynamic method [42; 43]. The Margules expression, which assumes that no entropic parameter is involved in excess free energy, is the simplest one and is shown in Equation (4) [42; 43]:  
\[\rm{\frac{G_{EX}}{RT}}=A_{1}X_{i}X_{n}^{2}+\,A_{2}X_{i}^{2}X_{n} \tag{4}\]  
where \(A_{1}\) and \(A_{2}\) are the constants, \(X_{i}\) is the mole fraction of the ionic surfactant, and \(X_{n}\) is the mole fraction of the nonionic surfactant. The HLD equation has been applied in a large number of studies [27; 42; 44; 45; 46; 47; 48; 49; 50]. The HLD equation is not only used to reduce the time-consuming of the experiment but also to characterize the hydrophobicity of the oil and phase behavior of microemulsions [27]. [PERSON] et al. (2003) applied the nonionic HLD equation to determine the EACN value of pine oil, which was found to be \(-\)12.1 [50]. [PERSON] et al. (2008) used the HLD equation as a method to determine the \(\sigma\) values of anionic surfactants (e.g., sodium dioctyl sulfosuccinate (AOT), sodium dihexyl sulfosuccinate (SDHS or AMA), C\({}_{12,13}\)-(PO)\({}_{8}\)-SO\({}_{4}\)Na, C\({}_{12}\)-SO\({}_{4}\)Na, C\({}_{12,15}\)-(EO)\({}_{2}\)-SO\({}_{4}\)Na,\({}_{\alpha}\)) [27]. The results showed that the anionic surfactants had a wide range of \(\sigma\) values from positive to negative values. For example, the \(\sigma\) of AOT was positive, and the \(\sigma\) of the SDHS was negative.