Numerical simulation of pendant droplet behavior on plain and patterned surfaces using Surface Evolver: Applications to condensation heat transfer

In this work, pendant water droplet behavior on a plain surface was simulated using the Surface Evolver (SE) finite element program to study the three-dimensional shape of the droplet on the surface. The critical droplet volume (CDV) before detachment from the surface was measured and compared against experimental data for different plain surfaces. These computational predictions were shown to agree well with experimental data. Next, patterned surfaces were studied which consisted of a central wetting region 2 mm to 5 mm wide sandwiched between two outer non-wetting superhydrophobic stripes. These superhydrophobic stripes served as “bumpers” to confine the droplet to the wetting region during its simulated growth. For these simulations, the primary inputs to the program were the droplet volume V, stripe width w, and surface static contact angle θ which was varied from 30° to 150°. Water droplet contact angle measurements on the plain surfaces used for initial benchmarking were also reported which included polished aluminum, mill finish aluminum, glass, plastic (acrylic), stainless steel, and copper. The idea of this study was to see if the superhydrophobic borders could be used to effectively “pinch off” a droplet in the wetting region, thereby reducing the critical droplet volume needed for detachment and drainage. The motivation for this work was condensation heat transfer which is common to many HVAC&R applications. In these systems, increasing the droplet shedding frequency is often associated with increased heat transfer and improved system efficiency.

Therefore, the baseline surface adopted in this study was aluminum with and without the use of superhydrophobic stripes. For these simulations, properties of water at 20 °C were used, and the droplet volume was gradually increased until the critical condition was reached and detachment was detected. Typically, more than 1000 iterations were performed before the droplet geometry converged and was ready for measurement. Grid refinement was also performed to make sure that the results were grid independent. According to Surface Evolver, the lowest predicted critical droplet volume on the plain surfaces was <5 μL for θ₁ = 150°, whereas the highest CDV was >295 μL for θ₁ = 30°. For θ₁ = 90° which is typical of aluminum, the CDV on the plain surface was 74 μL for the fine mesh and 83 μL for the rough mesh. When a 3-mm wide θ₁ = 90° wetting region was used, however, bordered by two superhydrophobic stripes with θ₂ = 150°, this CDV was reduced to 71 μL for the rough mesh, and when a 2-mm wide wetting region was used, the CDV was reduced even further to 55 μL. This shows both the promise of the idea and the possibility of using a striped / patterned tube to reduce the critical droplet volume needed for droplet shedding in a condensation environment.