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Innovative Hydrodynamic Equations Enhance Understanding of Particle Aggregation
Researchers at Skoltech have introduced groundbreaking mathematical equations that reveal the dynamics of particle aggregation in fluids, a phenomenon integral to both natural and industrial processes. These findings could significantly impact everything from weather patterns to technological applications such as powder transport and aerosol painting.
Published in Physical Review Letters, the new equations streamline the previously necessary combination of two distinct sets of equations, improving accuracy in various contexts where aggregation errors had proven problematic.
The study of fluid aggregation is crucial across numerous domains: in meteorological phenomena like the formation of rain and snow, in astrophysics regarding the creation of planetary rings such as those around Saturn, and in engineering applications where particles flow through pipes and channels.
Historically, the challenge of accurately representing these processes has relied on the work of early 20th-century physicist Marian Smoluchowski, who formulated a set of equations describing aggregation based on the formation of aggregates of varying sizes and their rates of combining. However, Smoluchowski’s approach was limited to idealized, uniform systems, which oversimplifies real-world conditions.
To better reflect the complexities of particle behavior in diverse environments—be it the atmosphere, outer space, or industrial settings—researchers previously had to integrate Smoluchowski’s equations with the Euler or Navier-Stokes equations, which describe fluid motion within variable conditions. This fusion often resulted in a cumbersome mathematical framework that could yield significant errors.
In their recent work, Skoltech Senior Research Scientist Alexander Osinsky and Professor Nikolay Brilliantov have proposed a different route. They have derived new hydrodynamic equations from first principles, introducing coefficients that differ from the traditional reaction-rate and transport coefficients found in Navier-Stokes models.
“These new coefficients reflect a unique combination of characteristics critical to the study of aggregating fluids, similar to how viscosity and thermal conductivity are essential for ordinary fluids,” remarked Brilliantov. The research team utilized extensive computer simulations to validate these novel Smoluchowski-Euler equations, demonstrating their effectiveness in modeling significant aggregating fluids.
The implications of these findings extend to enhancing precision in environmental modelling, particularly in areas such as air pollution assessments, granular flow dynamics, and powder technology. Furthermore, they may influence the design principles for vehicles, potentially leading to advancements in the aerospace and automotive industries.
More information: A. I. Osinsky et al, Hydrodynamic Equations for Space-Inhomogeneous Aggregating Fluids with First-Principle Kinetic Coefficients, Physical Review Letters (2024). DOI: 10.1103/PhysRevLett.133.217201
Citation: Scientists reinvent equations governing formation of snowflakes, raindrops and Saturn’s rings (2024, December 23) retrieved 23 December 2024 from phys.org
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