第二类物质溶液表面张力与浓度关系的数学模型

Establishment of mathematics model on the relationship between solution surface tension and its concentration for the second type matters

利用科学计算绘图软件Origin,将"最大气泡法测定乙醇溶液的表面张力"的实验数据,通过多项式:y=A+B*x+C* X^2和y=A+B*x+C*x^2+D*x^3;对数式:y=a-b*ln(x+c);指数式:y=A_1*exp(-x/t_1)+y_0等数学模型进行拟合。对拟合方程分别求导后,代入吉布斯(J.W.Gibbs)吸附等温式。再利用Origin进一步处理,作第二类物质溶液表面吸附等温线(溶液浓度从无限小至无限大)。然后,将所获得的图形参数进行综合对比分析和论证,最终确立第二类物质溶液表面张力σ与浓度c之间的理想方程,建立起相应的数学模型:即σ=b*exp(-c/a)+d。

The data of surface tension of alcohol solution obtained by the largest gas bubbles were simulated by the formulae of y = A ＋ B＊x＋C＊x^2, y=A＋B＊x＋C＊x^2＋D＊x^3, y=a-b＊ln（x＋c） andy=A1 ＊exp（-x/t1） ＋y0, respectively with Origin software. The simulated equations were differentiated each and the results were introduced to the Gibbs adsorption isothermal equation. The isotherm of surface adsorption for the second type matters with a concentration range from a minimum to a maximum was drawn with Origin software. Then, these obtained curves were analyzed and discussed. Finally, the ideal mathematics model on the relationship between solution surface tension and its concentration for second type matters was established： σ = b ＊ exp（-c/a） ＋ d.