The Correlations Between Surface Tension And Temperature For Normal Saturated Fluids

Surface tension is an interesting and useful property of fluids. The general trend is that surface tension decreases with the increase of temperature and becomes zero at the critical temperature. Recently, to explore the correlations between surface tension and temperature seems to be quite an attractive subject to research. These models are mainly based on the use of:(i) general correlation based on the corresponding states principle;(ii) specific correlation for every fluid;(iii) use of equations of state and the density gradient theory; and(iv) the use of Group Contribution methods and/or Artificial Neural Network method. We merely discussed two methods(i and ii) in this paper.Firstly, corresponding states principle proposed by Van der Waals is that substances behave similarly when they are reduced in the same way. In this paper, we tried to reduce the surface tension and temperatures in a more effective way for saturated normal fluids. After careful calculations in the framework of our method, we find that the reduced surface tensions linearly depend on the reduced temperatures. By comparing to other correlations, the correlation proposed here is clearly the one giving the best overall result in the temperature region studied. In addition to the critical point temperature, it also needs the triple point temperature and triple point surface tension as references, which differs from the other former correlations. But we shall denote that the accuracy holds validly in the temperature region studied, which is a low-intermediate temperature region. The reason why the new correlation is not for the higher temperature region is that the calculating surface tension is negative. Thus, the improvement has been made to this problem in the next work. The new generalized corresponding states correlation is well to represent the experimental surface tension data for each of 38 saturated normal fluids from the triple temperature up to the point near the critical point. The new correlation gives AAD values below 3% for all of these 38 liquids with the only exception being octane with AAD=4.30%. Hence, the new generalized corresponding states correlation gives the better overall results in comparison with other correlations for these 38 normal saturated fluids.Secondly, for the specific correlations, each fluid has different regressed coefficients. Recently, in order to improve the performance and accuracy of the correlations used in the REFPROP program, Mulero et al. summarized and filtered the available data for 117 fluids considered in the program and gave the newest coefficients for REFPROP correlation for every fluid. The new coefficients are sufficiently accurate and trustworthy, so they are presently used by the new version of the REFPROP program to calculate the surface tension. In terms of these 117 fluids, in REFPROP program, two to six adjustable coefficients are used depending of the fluid. By calculating, we observe that the Weibull distribution model with only two adjustable coefficients can well describe the relationship between surface tension and temperature. We show that for 112 out of the 117 fluids the new correlation with two adjustable coefficients deviates less than 2%(absolute average mean deviation AAD) with respect to the correlations used in REFPROP. On the other hand, we found that for 99 fluids the AAD value is below 1%. For 17 out of the 117 fluids the maximum percentage deviations between the correlations are higher than 10.4%, which is due to the fact that near the critical point the surface tension goes to zero and then the percentage deviations increases significantly despite the absolute difference between the values is really very little. In order to obtain more accurate results, we shorten their temperature region. Furthermore, we show that it is possible to consider just one adjustable coefficient for 63 fluids, being the AAD below 1.7% and the maximum deviation below 6%. In this paper we show that the REFPROP correlation can be replaced by a Weibull-type correlation including an exponential term and a maximum of two adjustable coefficients.