A finite element based algorithm for determining interfacial tension and contact angle from pendant and sessile drop profiles
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 P&barbelow;endant and S&barbelow;essile D&barbelow;rop Profile A&barbelow;nalysis using the F&barbelow;inite E&barbelow;lement M&barbelow;ethod (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corn oil at 25 and 35°C. The PSDA-FEM detects the stability limit of drop shapes (where the Young-Laplace equation is no longer valid) during dynamic interfacial tension measurements, a feature not possible with traditional arc-length based methods.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. ^
Major Professor: Michael T. Harris, Purdue University.