Search

Abstract: This paper introduces a robust algorithm to determine the interfacial tension (γ) from pendant drop profiles using the Galerkin finite element method (γ-PD-FEM) to solve the axisymmetric form of the Young–Laplace (YL) equation. In this algorithm, the theoretical profiles are generated by solving the spherical coordinate form of the YL equation. γ-PD-FEM also solves for the parameter estimates by minimizing the difference between the theoretical and experimental surface functions, . This technique is compared to the widely used method of converting the YL equation to the three arc length-based (ALB) first-order ODEs developed by Bashforth and Adams (BA) in 1883, or as denoted in this paper, the γ-PD-BA method. The drop apex is the initial condition for the γ-PD-BA algorithm and the integration is terminated at a specified location along the drop profile. In contrast to techniques based on the BA approach, computation of the theoretical drop profile in γ-PD-FEM is obtained from a second-order ordinary differential equation and requires boundary conditions at the drop apex and at the contact line of the drop to the nozzle. By incorporating both boundary conditions into the problem formulation, the algorithm can also determine if the drop shape is at static equilibrium. Results to be presented include an outline of the computer algorithm, and comparison of γ values obtained from the γ-PD-FEM and the traditional γ-PD-BA method using simulated and experimental drop profile data sets. [Copyright &y& Elsevier]

Abstract: The pendant and sessile drop profile analysis using the finite element method (PSDA-FEM) is an algorithm which allows simultaneous determination of the interfacial tension (γ) and contact angle () from sessile drop profiles. The PSDA-FEM algorithm solves the nonlinear second-order spherical coordinate form of the Young–Laplace equation. Thus, the boundary conditions at the drop apex and contact position of the drop with the substrate are required to solve for the drop profile coordinates. The boundary condition at the position where the drop contacts the substrate may be specified as a fixed contact line or fixed contact angle. This paper will focus on the fixed contact angle boundary condition for sessile drops on a substrate and how this boundary condition is used in the PSDA-FEM curve-fitting algorithm. The PSDA-FEM algorithm has been tested using simulated drop shapes with and without the addition of random error to the drop profile coordinates. The random error is varied to simulate the effect of camera resolution on the estimates of γ and values obtained from the curve-fitting algorithm. The error in the experimental values for γ from sessile drops of water on acrylic and Mazola corn oil on acrylic falls within the predicted range of errors obtained for γ values from simulated sessile drop profiles with randomized errors that are comparable in magnitude to the resolution of the experimental setup. [Copyright &y& Elsevier]