“Foamy flows” of bubble-filled materials occur in a host of industrial processes, including food and cosmetics production as well as drug development and delivery. They are very difficult to model mathematically, however, since the bubbles in these foams can be as tiny as microfluidic crystals or as large as ocean waves. Computer models also need to take into account interactions between the bubbles, which are separated by stable, thin films of liquid.
A team of researchers at Harvard University in the US and ETH Zurich in Switzerland has now overcome these difficulties with a new multilayer volume-of-fluid (multi-VOF) method that handles multiscale, non-coalescing bubbles with ease. The new technique can simulate thousands of bubbles and makes it possible to model the behaviour of foamy flows from the micro- to the macro scales.
Current methods of simulating foamy flows rely on colour-coding individual bubbles in a foam and tracking each of them. These methods are computationally costly, which limits the simulations to just a few tens of bubbles. Real foamy flows, meanwhile, may contain anywhere from thousands to millions of bubbles.
Breaking a foam into a grid
Instead of tracking individual bubbles, the new multi-VOF technique developed by Petros Koumoutsakos and colleagues breaks the foam down into a grid in which each cell of the grid contains parts of a maximum of four bubbles. Each bubble is assigned a unique colour and the colours are used to connect the parts from neighbouring cells. For example, if one part of a bubble is in a particular cell, team member Petr Karnakov explains that the remaining pieces of the bubble must be in neighbouring cells.
Physicists create droplets inside bubbles
The researchers developed an algorithm that finds these remaining pieces by matching the corresponding colours. This approach does away with the need for tracking individual bubbles, thereby allowing the researchers to create predictive simulations across multiple length scales.
The Harvard team backed up its simulations with experiments and complemented them with an open-source software package known as Aphros. After reporting their work in Science Advances, the researchers now plan to apply the computational tools they developed to a variety of science and engineering problems. “These include predicting foam dynamics in food processing, controlling bubbles in microfluidic devices and designing membrane-less electrochemical reactors for hydrogen production,” Koumoutsakos tells Physics World.