Two Binary Liquid Critical Mixtures Belong to Class of Universality

The dynamic shear viscosity of a binary liquid mixture phenol–water has been measured at different temperatures (50.0°C ≤ T ≤ 75.0°C) and different concentrations (0.00% up to 100.00% by weight of phenol). The critical temperature Tc and critical concentration xc are found to be 67.0°C and 33.90% by weight of phenol respectively, the critical mass density ρc is measured to be 0.8952 g/cm 3. The critical and background amplitudes of specific heat at constant pressure are calculated to be 78.12 J/kg.K and 85.29 J/kg.K respectively. The pressure derivative of the critical temperature along the critical line ' c T T is calculated to be 9.722 ×10-6 K/Pa. In addition, dynamic shear viscosity of binary liquid mixture phenol–cyclohexane has been measured at different temperatures (14.0°C ≤ T ≤ 30.0°C) and different concentrations (2.00% up to 39.70% by weight of phenol). The critical temperature Tc and critical concentration xc are found to be 17.0°C and 2.70% by weight of phenol respectively; the critical mass density ρc is measured to be 0.7627 g/cm 3. The critical and background amplitudes of isobaric thermal expansion coefficient αpc and αpb are calculated to be 8×10 -6 K-1, 6×10-4 K-1 respectively. The pressure derivative of the critical temperature ' c T for the binary is calculated to be 2.8572 × 10-8 K/Pa. The universal quantity Rξ for the binary liquid critical mixture phenol–water is calculated to be 0.2716 ± 0.0005. In addition, the universal quantity Rξ for the binary liquid critical mixture phenol–cyclohexane is calculated to be 0.2699 ± 0.0001. The calculated values of the universal quantity Rξ are in a good agreement with the theoretical value of R + ζ which is equal 0.2710. The two binary liquid critical mixture belong to the class of universality "Two–Scale–Factor Universality". *Corresponding author: Abdelraziq IR, Physics Department, An-Najah Ntional University, Nablus Weast Bank, Israel, Tel: 092345113; E-mail: [email protected] Received October 17, 2015; Accepted November 10, 2015; Published November 20, 2015 Citation: Ata BN, Abderaziq IR (2015) Two Binary Liquid Critical Mixtures Belong to Class of Universality. J Material Sci Eng 5: 211. doi:10.4172/2169-0022.1000211 Copyright: © 2015 Ata BN, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. of critical phenomena has elucidated the mathematical mechanism for scaling and universality, and has provided a number of calculational tools for estimating universal properties [5]. Theory Viscosity The viscosity of a fluid is a measure of its resistance to gradual deformation by shear stress or tensile stress [6]. Viscosity is affected by different factors such as temperature, shear rate, catalyst, pressure, molecular weight concentration and storage age [7]. Mode coupling theory and shear viscosity of binary mixtures The mode coupling theory explains the behavior of the binary mixtures at the critical temperature and concentration. The mode coupling approach of Kawasaki and Perl and Ferrell predicts a critical anomaly of the dynamic shear viscosity coefficient according to the law [8,9]. D 0 ln Aln q ζ η η η− η ∆ η = = + A (2.1) Where η0 the noncritical part of the measured shear viscosity. A is a constant which was calculated by D’Arrigo and given by A ~ 0.054 [10], and D q is Debye momentum cutoff. The dynamic shear viscosity is temperature dependent at the critical concentration which Citation: Ata BN, Abderaziq IR (2015) Two Binary Liquid Critical Mixtures Belong to Class of Universality. J Material Sci Eng 5: 211. doi:10.4172/21690022.1000211