Predictions of the Wettable Parameters of an Axisymmetric Large-Volume Droplet on a Microstructured Surface in Gravity

Abstract

In this study, a numerical model was developed to predict the wettable parameters of an axisymmetric large-volume droplet on a microstructured surface in gravity. We defined a droplet with the Bond number Bo>0.1 as a large-volume droplet. Bo was calculated by using the equation Bo=ρlgγlv3V4π23 where ρl is the density of liquid, γlv is the liquid-vapor interfacial tension, g is the gravity acceleration and V is the droplet volume. The volume of a large-volume water droplet was larger than 2.7 μL. By using the total energy minimization and the arc differential method of the Bashforth–Adams equation, we got the profile, the apparent contact angle and the contact circle diameter of an axisymmetric large-volume droplet in gravity on a microstructured horizontal plane and the external spherical surface. The predictions of our model have a less than 3% error rate when compared to experiments. Our model is much more accurate than previous ellipsoidal models. In addition, our model calculates much more quickly than previous models because of the use of the arc differential method of the Bashforth–Adams equation. It shows promise for use in the design and fabrication of microfluidic devices.

Keywords

• wettable parameters
• axisymmetric large-volume droplet
• gravity
• microstructured horizontal plane
• external spherical surface