Finding the skeletons in complex liquid closets

When bubbles and drops splash, they form complex shapes that are difficult to describe with only the point particle approximation, a widely used technique that follows the centroid of the particle. Chen et al. developed a process to describe complex liquid structure using the minimum amount of information.

The technique works by extending the point particle approximation to handle more complex shapes, representing thin ligaments with 1D lines (or 2D sheets) and spherical drops as points. The team found this “skeleton” accurately describes the basic topology of a complex liquid interface, provides information about more complex structures on top of the basic model, and acts as a reduced-order model, requiring minimal information to perform such calculations.

“This is a robust way to obtain the skeletons that can automatically ignore the small scales on the boundary, and a clean skeleton can be obtained without postprocessing such as pruning,” author Xianyang Chen said.

To develop their method, the authors systematically shrank a surface described by a mathematical function, called an index function, until it collapsed into a thin skeleton structure.

“The original structure is described by an index function that identifies regions containing liquids. The skeletonization process involves diffusing an index function by solving a parabolic partial differential equation, and at the same time moving the interfaces (that separate two fluids) with it, until they ‘collapse’ into each other and form skeletons,” Chen said.

The authors plan to extend the model to predict two phase flows more efficiently and reduce computation time.

Source: “Characterizing interface topology in multiphase flows using skeletons,” by Xianyang Chen, Jiacai Lu, Stéphane Zaleski, and Grétar Tryggvason, Physics of Fluids (2022). The article can be accessed at https://doi.org/10.1063/5.0109333 .