Regensburg 2010 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 6: Poster Session I

DY 6.6: Poster

Montag, 22. März 2010, 16:00–18:00, Poster B2

Shape and Pinching-Off of Dew Droplets — •Johannes Blaschke, Tobias Lapp, Björn Hof, and Jürgen Vollmer — MPI for Dynamics & Self-Organization, 37073 Göttingen, Germany

For sessile droplets of a circular cap shape Family and Meakin have shown that the size distribution of dew droplets on flat surfaces is described by a scaling law [1]. In the case of water droplets hanging from a substrate the scaling ansatz has to be augmented to account for shape distortion by gravity and droplets dripping off.

The distorted 3-dimensional profile, h(r), for such stationary hanging droplets is determined by minimizing the total energy functional (for rotationally-symmetric droplets) [2]:

We explore the effect of gravity on the relationship of volume, V(R)=2 π ∫₀^R r h(r) dr, to radius of the wetted area on the substrate, R, and how this is dependent on the contact angle.

An analysis of the energetic stability of these droplet profiles yields the maximum size of the droplets before they are ripped off the substrate by gravity. In order to verify the model, real droplets of a known volume are hung off a substrate and their profiles are compared to the theoretical predictions. Finally, the implications on Family and Meakin’s scaling theory are discussed.
F. Family, P. Meakin, Phys. Rev. A 40, 3836 (1989)
H. C. Wente, Pacific J. Math. 88, 421 (1980)