Ripples at edges of blooming lilies and torn plastic sheets

Area of Science:

• Physics
• Materials Science
• Botany

Background:

• Ripples form at the edges of flexible sheets due to excess length.
• Blooming lily petals and torn plastic sheets exhibit similar ripple patterns.
• Understanding petal morphology changes during blooming is crucial for botanical studies.

Purpose of the Study:

• To investigate the physical principles governing ripple formation in biological and synthetic materials.
• To establish a quantitative relationship between ripple characteristics and material properties.
• To develop and validate a non-destructive imaging technique for observing dynamic biological processes like flower blooming.

Main Methods:

• Analysis of time-lapse videos of blooming Lilium casablanca and images of torn plastic sheets.
• Application of a scaling relationship a∝w(L-w) to describe ripple amplitude (a), wavelength (w), and arc length (L).
• Evaluation of tomograms of lily buds and proof of principle for X-ray tomography in observing blooming.

Main Results:

• A universal scaling relationship a∝w(L-w) accurately describes ripples in both lilies and plastic.
• Constant buckling stress explains the phenomenological relationship ⟨a⟩∝⟨w⟩.
• Petal thickness does not decrease quadratically along the long axis of lily buds, challenging previous assumptions.
• Non-destructive X-ray tomography successfully produced high-contrast 3D scans of lily buds.

Conclusions:

• Excess edge length is a fundamental driver of ripple formation in diverse sheet-like structures.
• The established scaling law provides a predictive model for ripple behavior.
• X-ray tomography offers a viable, non-destructive method for studying dynamic changes in biological specimens during development, such as flower blooming.