A finite element based algorithm for determining interfacial tension and contact angle from pendant and sessile drop profiles

Nicole M Dingle, Purdue University


Current Axisymmetric Drop Profile Analysis (ADSA) methods numerically integrate the Young-Laplace equation, cast as three arc-length based-1 st order ordinary differential equations, which require one boundary condition to solve for the interfacial tension (γ) and contact angle (&thetas;c). The Pendant and Sessile Drop Profile Analysis using the Finite Element Method (PSDA-FEM) has been developed to determine γ and &thetas;c from pendant and sessile drop profiles. The PSDA-FEM algorithm solves the nonlinear second order-spherical coordinate form of the Young-Laplace equation (requires both physical boundary conditions) to generate the theoretical profiles. PSDA-FEM solves for the parameter estimates by minimizing the difference between the theoretical and experimental surface functions, f(&thetas;). The algorithm simultaneously estimates γ and &thetas;c from sessile drop profiles using a fixed contact angle boundary condition, or solves for γ from pendant drop profiles using a fixed contact line boundary condition. Interfacial tension and contact angle experiments have been performed to validate the use of the PSDA-FEM algorithm, and to support current work in the HOME research group. The error in output γ values from pendant drop profiles is equivalent to or less than the output values by an algorithm based on traditional B-A equations (γ-PD-BA). The accuracy and precision of the output γ values from sessile drop profiles are found to improve with camera resolution and increased volume. The experimental γ values using sessile drops (on four polymer based substrates) have less than 5% error compared to the pendant drop results, and the contact angle estimates are within ±2°. Dynamic interfacial tension measurements of aqueous sodium chloride (NaCl) in Mazola corn oil are performed at 3, 5 and 10 wt% and 25, 35, and 55°C, and 1 M ZrOCl2 aqueous suspensions in corn oil at 25 and 35°C. The PSDA-FEM detects the stability limit of drop shapes (where the Young-Laplace equation is no longer valid) during dynamic interfacial tension measurements, a feature not possible with traditional arc-length based methods. The interfacial tension of aqueous suspensions of tobacco mosaic virus (TMV) particles is also measured and the results are confirmed using ellipsometry.




Harris, Purdue University.

Subject Area

Chemical engineering

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