An improved regression analysis for automatic surface tension measurements

✍ Scribed by V.G. Doví; O. Paladino; E.P. Arato; L. Maga; A. Passerone

• Publisher: Elsevier Science
• Year: 1986
• Tongue: English
• Weight: 400 KB
• Volume: 28
• Category: Article
• ISSN: 0378-4754
• DOI: 10.1016/0378-4754(86)90056-x

✦ Synopsis

Estimates of surface tension are generally based on the information provided by the surface contour of sessile and pendant drops.We have developped a new procedure for data reduction by taking advantage of the particular features of the mathematical model that describes the complex functional form relating contour and surface tension, when the apex coordinates and the corresponding radius of curvature are also only partially known. This procedure results in a two level optimization algorithm. The first step implies the optimization of a general dynamic model and to this purpose both objective function and sensitivity equations are set up. The second step is a local minimization, in that each datum point is assigned a particular position on the curve generated with certain values of the four parameters with respect to which the outer optimization loop is carried out. We have coded this method into an algorithm that uses the Gauss-Newton approximation to the hessian matrix and constrains the parameters to lie within specified bounds. It has been checked extensively for efficiency and robustness and both are quite satisfactory.