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

Abstract

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.

The Possibility of Changing the Wettability of Material Surface by Adjusting Gravity

“…Figure 5(a) shows a variation of the angle θ of the water drop on DMDCS with the film thickness h under different gravity (θ is calculated by using Equation (10) and assuming h m = 2 × 10 −9 m). It can be seen that the transition region, where the film curvature is negligible, decreases with the increasing gravity.…”

“…Some researchers [8][9][10][11][12][13][14] also derived the same Young's equation based on the thermodynamics of wetting and pointed out that the contact angle depends only on the physical and chemical properties of the solid, liquid, and vapor accordingly and is not affected by gravity. Gravity only affects the shape of the drop [8][9][10][11][12][13][14]. Recently, Bormashenko imposing the transversality conditions on the variational problem of wetting also demonstrates that gravity does not influence equilibrium contact angles [35][36][37].…”

Elucidating the Mechanism of Condensation-Mediated Degradation of Organofunctional Silane Self-Assembled Monolayer Coatings

“…The contact angles were calculated by fitting a vector-parameterized cubic spline over the digitized profile of the droplet. 70 The advancing and receding contact angles were determined based on measurements of four different batches of coated samples and at four different locations on each sample. Leftand right-side contact angles were treated as separate droplets since the advancing (and receding) contact angle did not necessarily occur at the same time for both the left-and right-side contact points.…”

“…Videos of droplet infusion and withdrawal were recorded with the camera at 60 Hz to characterize the advancing and receding contact angles, respectively. The contact angles were calculated by fitting a vector-parameterized cubic spline over the digitized profile of the droplet . The advancing and receding contact angles were determined based on measurements of four different batches of coated samples and at four different locations on each sample.…”

Cloaked Droplets on Lubricant-Infused Surfaces: Union of Constant Mean Curvature Interfaces Dictated by Thin-Film Tension

“…Fundamentally, the droplet shape under the influence of gravity and surface tension forces can be obtained by solving the Young−Laplace (YL) equation. For small droplet volumes (Bo < 1) wherein the effect of gravity can be neglected, the YL equation predicts a constant mean curvature spherical cap shape 30 for droplets on solid surfaces. However, in the case of droplets on LISs, the annular lubricant meniscus gives rise to a rich combination of various other CMC surfaces, namely, nodoid and catenoid.…”