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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

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【作者】 周钢兰叶青施燕博刘袁凯

【Author】 Zhou Gang Lan Yeqing Shi Yanbo Liu Yuankai (Science College of Nanjing Agricultural University,Nanjing,210095,Jiangsu,China)

【机构】 南京农业大学理学院南京农业大学理学院 江苏南京210095江苏

【摘要】 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=A1*exp(-x/t1)+y0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。

【Abstract】 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*1n(x+c) andy=A1*exp(-x/t1) +y0,respectively with Origin soft- ware.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.

【基金】 国家教育部“21世纪中国高等学校农林专业化学基础课程的创新与实践”项目(BIA010092-F01);南京农业大学教育教学改革项目(2005Y306)
  • 【文献出处】 计算机与应用化学 ,Computers and Applied Chemistry , 编辑部邮箱 ,2007年08期
  • 【分类号】O647.1
  • 【被引频次】12
  • 【下载频次】528
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