ESPCI web site
Please dowload the Article
Here are additional movies from the article: Movie1 Movie2 Movie3 Movie4 (They are illustrative, but are not necessary for the exam)
Question1: Can you explain the order of magnitude for the frequency of natural oscillations of liquid droplets? What is the phenomenon involved? Same questions for the gel beads.
Question2: Explain why the presence of nanometric pores in the substrate (assume semi-spherical shape) prevents adhesion. (i.e. show that it induces dewetting in both liquids and soft solids)
Question3: Can you make sense of the main result (figure 3) of the paper with scaling arguments ?
3a) Give an argument for the ejection speed in the case of an infinitely stiff bead. Compute alpha in this case.
3b) Considering the bead/drop as a single mass plus a spring, give a scaling argument for the speed of ejection (speed of the mass+spring first when it first detaches from the catapult) for the opposite case of ultra-soft spring (fo << f).
One can consider that the final speed of the mass is much smaller than the speed of the catapult (and that the mass almost does not move during ejection) . Use figure 5 to check (check this after with your predicted alpha). Does your prediction of alpha as a function of fo/f agree with the author’s finding?
3c) Bonus question: Can you provide a qualitative argument for the superpropulsion happening when the two frequencies f0 and f have the same order of magnitude?