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Fluid Mathematics Lab
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The lab solves flows that fluid dynamics alone cannot fully explain by starting from the motion of molecules.
AboutAbout the lab
Approaching the mysteries of flow from the motion of molecules.
The Fluid Mathematics Lab studies fluids in states far from local equilibrium, mainly through theory.
From a mesoscopic standpoint based on kinetic equations, the lab seeks a deep understanding of the various phenomena that occur in fluids.
It aims to open up new areas of application in fluid dynamics and gas dynamics that conventional approaches could not reach.
Key terms
- Kinetic equation
- An equation that treats a gas as the motion of many molecules and describes how the distribution of molecular speeds changes. Examples include the Boltzmann equation
- Boussinesq approximation
- An approximation that simplifies calculations by ignoring changes in fluid density except when considering buoyancy
- Phase change
- A change in the state of matter, such as a liquid becoming a gas (boiling)
ResearchResearch themes
The lab studies mathematical analysis and simulation of nonequilibrium phenomena based on kinetic equations, slip flow (rarefied gas effects), nonequilibrium dynamics of phase change, and microfluidic experiments related to slip flow and phoretic phenomena.
*Illustrative imageRethinking the Approximation for Thermal Convection from the Molecular Level
Using kinetic theory, the lab examined how far the Boussinesq approximation, widely used for buoyancy-driven thermal convection, is valid for an ideal gas. It found that the energy equation should include a pressure work term, which is normally left out.
*Illustrative imageHow Gas Moves at a Corner in a Box
In the flow generated inside a cavity by a moving lid, ordinary fluid dynamics predicts that the force becomes infinite near the corner. By treating the gas near the corner accurately with kinetic theory, the lab showed that the force remains finite.
*Illustrative imageModeling Phase Change such as Boiling from Molecules
The lab modeled gas–liquid phase change involving evaporation and condensation using kinetic theory. It built equations that are easy to use and also have the properties of free energy and entropy, and it also runs two-dimensional simulations.
*Illustrative imageTesting Microscale Flows by Experiment
Focusing on phenomena that stand out at molecular, nano, and micro scales and at the boundary between fluid and solid, the lab aims to understand and apply slip flow and phoretic phenomena by proposing mathematical models and conducting microfluidic experiments.
MembersFaculty
The faculty of the Fluid Mathematics Lab are Professor Shigeru Takata, Associate Professor Tetsuro Tsuji, and Assistant Professor Masanari Hattori.
- ProfessorShigeru Takata
- Associate ProfessorTetsuro Tsuji
- Assistant ProfessorMasanari Hattori
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “Benard cell” Terrence Deacon / CC BY 2.5 (cropped)
- Rethinking the Approximation for Thermal Convection from the Molecular Level: “Rayleigh–Bénard convection pattern in honey wine with cinnamon floating on top after 10 days of fermentation” Ywaz / CC BY-SA 4.0 (cropped)
- How Gas Moves at a Corner in a Box: “Химический факультет ДонНУ 015” Andrey Butko / CC BY-SA 3.0 (cropped)
- Modeling Phase Change such as Boiling from Molecules: “Bubbles inside boiling water” Snehit Jamere / CC BY-SA 4.0 (cropped)
- Testing Microscale Flows by Experiment: “Рождение микрофлюидного чипа 2” Данилюк Валентина / CC BY-SA 4.0 (cropped)
- Related lab (Nano Material Properties Engineering Lab): “Holifield charging chains and high-energy acceleration tubes ( )” Oak Ridge National Laboratory / CC BY 2.0 (cropped)
- Related lab (Thermophysical Engineering Lab): “3D Turbulence Infinitesimal Fluid Element Stretching Orientation Map” Terry Brannigan / CC BY 4.0 (cropped)
- Related lab (Micro Fabrication Systems Lab): “Danos Cristalográficos 5” Hebert Folli / CC BY-SA 4.0 (cropped)
- Related lab (Nano and Micro Systems Engineering Lab): “A MicroVision MEMS mirror” S2upidOnReddit / CC BY-SA 4.0 (cropped)
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