Related Experiment Video
Updated: Jun 8, 2026

Film Control to Study Contributions of Waves to Droplet Impact Dynamics on Thin Flowing Liquid Films
Published on: August 18, 2018
Superexponential droplet fractalization as a hierarchical formation of dissipative compactons
Sergey Shklyaev1, Arthur V Straube, Arkady Pikovsky
1Department of Chemical Engineering, California Institute of Technology, Pasadena, 91125, USA.
Abstract:
We study the dynamics of a thin film over a substrate heated from below in a framework of a strongly nonlinear one-dimensional Cahn-Hilliard equation. The evolution leads to a fractalization into smaller and smaller scales. We demonstrate that a primitive element in the appearing hierarchical structure is a dissipative compacton. Both direct simulations and the analysis of a self-similar solution show that the compactons appear at superexponentially decreasing scales, which means vanishing dimension of the fractal.
Related Concept Videos
Theories of Dissolution: The Danckwerts' Model and Interfacial Barrier Model
Theories of Dissolution: Diffusion Layer Model
This process starts with a thin layer, saturated with the drug, forming at the interface between the solid and liquid. The solute then diffuses from this layer into the main solution. The Noyes-Whitney equation suggests that the rate of dissolution relies on the diffusion...
Phase Transitions: Vaporization and Condensation
Precipitate Formation and Particle Size Control
The obtained precipitate should be either a pure substance of known composition or easily converted to one by a simple process, such as ignition or drying. In addition, the precipitate should be insoluble and easily filterable. In general, filterability...
Excess Pressure Inside a Drop and a Bubble
The Colloidal State

