Spline Based Shape Prediction and Analysis of Uniformly Rotating Sessile and Pendant Droplets

Prediction and analysis of the shapes of liquid-vapor interface of droplets under the influence of external forces is critical for various applications. In this regard, a geometric model that can capture the macroscopic shape of the liquid-vapor interface in tandem with the subtleties near the contact line, particularly in the regime where the droplet shape deviates significantly from the idealized spherical cap geometry, is desirable. Such deviations may occur when external forces such as gravity or centrifugal dominate over the surface tension force. Here we use vector parametrized cubic spline representation for axisymmetric fluid-fluid interfaces along with a novel thermodynamic free energy minimization based heuristic to determine the shape of liquid-vapor interface of droplets. We show that the current scheme can easily predict the shapes of sessile and pendant droplets under the action of centrifugal force over a broad range of surface contact angle values and droplet sizes encountered in practical applications. Finally, we show that the cubic spline based modeling approach makes it convenient to perform the inverse analysis as well, i.e., predict interfacial properties from the shape of a droplet under the action of various types of external forces including gravity and centrifugal. We believe that this versatile modeling approach can be extended to model droplet shapes under various other external forces including electric and acoustic. In addition, the simple shape analysis approach is also promising for the development of inexpensive interfacial analysis tools such as surface tensiometers.