Dresden 2011 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 16: Statistical Physics II

DY 16.3: Talk

Wednesday, March 16, 2011, 11:00–11:15, HÜL 186

Apollonian Breath Figures — •Johannes Blaschke, Tobias Lapp, and Jürgen Vollmer — Max Planck Institute for Dynamics and Self-Organization, 37073 Göttingen

The formation of dew droplets on planar surfaces is often referred to as Breath Figures. A scaling theory by Family and Meakin [1] predicts that the size distribution of the small droplets takes the form of a power law with exponent − 5/3. Simulations show a clear deviation from this exponent by δ ≃ 0.1(0). This deviation had not been explained so far.

Taking insight from fractal packings [2], we have developed an extension to Family and Meakin’s theory, which determines the correction to the size distribution for the small droplets. Knowing the fractal dimension of breath figures, d_f, we demonstrate how the correction, δ, is related to d_f: δ = 1/3 (2−d_f). This fractal dimension was subsequently measured from simulations to be d_f=1.6(9). Resulting in: δ = 0.103

The case of breath figures forming on the underside of a horizontal surface constitutes another interesting, and previously unexplored, scenario: When droplets reach a critical size, they are distorted by gravity and eventually fall off the substrate. The previously published theories cannot be applied to this case. We report the results from our simulations and compare these to a kinetic theory.
[1] Family and Meakin. Phys. Rev. Lett. 61 (1988) 428-431
[2] Herrmann et al. Phys. Rev. Lett. 65 (1990) 3223-3226