Mathematicians develop Brownian theory for the real world – that is, for conditions when the fluid in which the particles move is not static. The work of scientists from Queen Mary University is published in the journal Nature.
Brownian motion describes the random movement of particles in a fluid, but this model only works when the fluid is static or in equilibrium.
In real conditions, fluids often contain particles that move on their own, such as tiny floating microorganisms. They can cause movement in the fluid, which brings it out of balance.
In addition, experiments have shown that motionless “passive” particles can make strange, loop-like movements when interacting with “active” particles. Such motions do not correspond to the usual particle behavior described by the Brownian motion, and until now, scientists have tried to explain how such large-scale chaotic motions arise as a result of microscopic interactions between individual particles.
A new theory put forward by scientists explains this process. The researchers created a model of particle motion in active liquids that takes into account all experimental observations. The calculations showed that the effective particle dynamics follows the so-called “Levy flight”. This concept is widely used to describe “extreme” movements in complex systems that are very far from typical behavior.
Levy flights – a movement consisting of a series of short movements, and in the intervals between them long movements are made. Thus, if we draw the trajectory of such a movement, we get a large figure, consisting of small ones that resemble a large one in shape.
“So far there has been no explanation of how Levy’s flights in microscopic interactions that obey physical laws can actually occur. Our results show that Levy flights can arise as a result of hydrodynamic interactions between active and passive particles in liquids, which is very surprising”.
Kiyoshi Kanazawa, lead author of the study
The researchers found that the density of active particles also influenced the duration of the Levy flight mode. In this regard, they suggested that floating microorganisms could use Levy flights with nutrients to determine the best food search strategies for different environments.