Cylinrical Couette flow of a vaporgas mixture A ghost effect in 圆柱Couette流动的蒸汽混合气鬼效应.pptVIP

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Cylinrical Couette flow of a vaporgas mixture A ghost effect in 圆柱Couette流动的蒸汽混合气鬼效应.ppt

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Cylinrical Couette flow of a vaporgas mixture A ghost effect in 圆柱Couette流动的蒸汽混合气鬼效应

Randomly distributed moving obstacles Re-emitted Absorbed Evaporating droplets No collision between gas molecules Gas molecule (velocity ) Obstacles: Maxwellian Collisionless gas Toy model 1 Toy model 2 Exponential decay!! Collisionless gas Toy model 1 Toy model 2 Exponential decay!! Collisionless gas Toy model 1 Toy model 2 Exponential decay!! * Decay of an oscillating disk in a gas:Case of a collision-less gas anda special Lorentz gas Kazuo Aoki Dept. of Mech. Eng. and Sci. Kyoto University (in collaboration with Tetsuro Tsuji) Conference on Kinetic Theory and Related Fields (Department of Mathematics, POSTECH June 22-24, 2011) Decay of an oscillating disk If , then Equation of motion of the disk : Exponential decay Collisionless gas (Free-molecular gas, Knudsen gas) Other types of gas External force Drag (Hooke’s law) Gas Decay rate ??? Decay rate Mathematical study Caprino, Cavallaro, Marchioro, M3AS (07) Monotonic decay BC: specular reflection Collisionless gas Collisionless gas Time-independent case parameter Collisionless gas Boltzmann equation Highly rarefied gas Effect of collisions: Neglected Molecular velocity Mean free path Velocity distribution function time position molecular velocity Macroscopic quantities Molecular mass in at time gas const. Equation for : Boltzmann equation collision integral Boltzmann equation Nonlinear integro-differential equation [ : omitted ] Dimensionless form: : Knudsen number Time-independent case parameter Collisionless gas Boltzmann equation Highly rarefied gas Effect of collisions: Neglected Molecular velocity Mean free path Initial-value problem (Infinite domain) Initial condition: Solution: (Steady) boundary-value problem Single convex body given from BC BC : Solved! General boundary BC Integral equation for Diffuse reflection: Maxwell type: Integral equation for Exact solution! Sone, J. Mec. The