https://doi.org/10.1140/epje/i2014-14065-6
Regular Article
A finite-element method model for droplets moving down a hydrophobic surface
Department of Applied Mathematics and Computer Science, Technical University of Denmark, 2800, Kongens Lyngby, Denmark
* e-mail: oiww@dtu.dk
Received:
31
October
2013
Revised:
25
April
2014
Accepted:
1
July
2014
Published online:
29
July
2014
We set up a 2D computational Finite-Element Method (FEM) model describing the initial descent of a droplet down an inclined hydrophobic substrate. We solve the full Navier-Stokes equations inside the drop domain, and use the arbitrary Lagrangian-Eulerian method to keep track of the droplet surface. The contact angle is included by using the Frennet-Serret equations. We investigate the behaviour of the drop velocity as a function of the slip length and compare with experimental results. Furthermore, we quantify the energy associated with centre-of-mass translation and internal fluid motion, and we also compute the local dissipation of energy inside the drop. The model predicts trajectories for tracer particles deposited inside the drop, and satisfactorily describes the sliding motion of steadily accelerating droplets. The model can be used for determining a characteristic slip parameter, associated with slip lengths and drag reduction for hydrophobic surfaces.
Key words: Soft Matter: Interfacial Phenomena and Nanostructured Surfaces
© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg, 2014