lomonosov moscow state university€¦ · v. kosyanchuk, moscow (russia) gas flows in structures...
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V. Kosyanchuk, Moscow (Russia) Glasgow, UK July, 25, 2018 1/19Gas flows in structures with oscillating elements
Rarefied gas flows in microstructures with
high-frequency oscillating elements
Vasily Kosyanchuk, Artem Yakunchikov
31st International Symposium on Rarefied Gas Dynamics
Glasgow, UK, July 23-27, 2018
multiscale.ruenmech.ru
Multiscale
Simulation
Laboratory
Institute of
MechanicsLaboratory of
Nanomechanics
Mechanics &
Mathematics FacultyDepartment of
Engineering Mechanics
and Applied Mathematics
Mechanical
Engineering
Research Institute
of the RAS
imash.ru
Lomonosov Moscow State UniversityFaculty of Mechanics and Mathematics
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V. Kosyanchuk, Moscow (Russia) Glasgow, UK July, 25, 2018 2/19Gas flows in structures with oscillating elements
Existing applications of oscillations in MEMS
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V. Kosyanchuk, Moscow (Russia) Glasgow, UK July, 25, 2018 3/19Gas flows in structures with oscillating elements
Two studied problems
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V. Kosyanchuk, Moscow (Russia) Glasgow, UK July, 25, 2018 4/19Gas flows in structures with oscillating elements
Separation effect in microchannels
Free molecular flow(𝐾𝑛 = Τλ 𝐷 > 10)
Natural Knudsen diffusion
Separation factor α ≡𝐽𝐵
𝐽𝐴=
𝑚𝐴
𝑚𝐵
With oscillations
Separation factor α =𝑃𝐵
𝑃𝐴
𝑚𝐴
𝑚𝐵
𝑃( Τ𝑢 𝑐) → 𝑃(𝑐𝐴) ≠ 𝑃(𝑐𝐵) amplification factor γ ≡𝑃𝐵
𝑃𝐴
𝑃 − passing probability
𝑢 − characteristic thermal speed
𝑐 = Τ2𝑘𝐵𝑇 𝑚 − characteristic thermal speed of molecules
Molecular flux 𝐽 between to reservoirs
is related to passing probability 𝑃 as
𝐽 = 𝑃 ∙(𝑝2 − 𝑝1)
2 Τ𝑘𝐵𝑇 𝑚
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V. Kosyanchuk, Moscow (Russia) Glasgow, UK July, 25, 2018 5/19Gas flows in structures with oscillating elements
Molecular trajectory computations
Numerical method
Target characteristic 𝑃 = Τ𝑁 𝑁𝑝𝑎𝑠 − passing probability
𝑁 = 107 − number of probe molecules
𝑁𝑝𝑎𝑠 − number of molecules to pass through the channel
1) Sample molecule at inlet
2) Calculate collision point
3) Calculate reflection from surface based on scattering law
4) Molecule escape though either exit surface
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V. Kosyanchuk, Moscow (Russia) Glasgow, UK July, 25, 2018 6/19Gas flows in structures with oscillating elements
Problem №1. Channel with a series of barriers
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V. Kosyanchuk, Moscow (Russia) Glasgow, UK July, 25, 2018 7/19Gas flows in structures with oscillating elements
Influence of distance between barriers L / D
Separation is observed when ratio of
speeds Τλω 𝑐 reaches values
around unity
Effect vanishes for longer distances
between barriers Τ𝐿 𝐷
Device with only 2 sections is used
here
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V. Kosyanchuk, Moscow (Russia) Glasgow, UK July, 25, 2018 8/19Gas flows in structures with oscillating elements
Influence of wave length λ
By increasing number of sections
and wave length one can achieve
separation for higher values of Τ𝐿 𝐷
Reflection law and surface
accommodation coefficients are
important
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V. Kosyanchuk, Moscow (Russia) Glasgow, UK July, 25, 2018 9/19Gas flows in structures with oscillating elements
Video presented by laboratory of nano- and microsystem
technology of St. Petersburgh polytechnic university
Possible practical implementation
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V. Kosyanchuk, Moscow (Russia) Glasgow, UK July, 25, 2018 10/19Gas flows in structures with oscillating elements
Problem №2. Curving channel
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V. Kosyanchuk, Moscow (Russia) Glasgow, UK July, 25, 2018 11/19Gas flows in structures with oscillating elements
Possible practical implementations
D
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V. Kosyanchuk, Moscow (Russia) Glasgow, UK July, 25, 2018 12/19Gas flows in structures with oscillating elements
Influence of amplitude and wavelength
Separation takes place in only narrow range of amplitudes Τ𝐴 𝐷 (~ 0.25)
Effect is observed when ratio of speeds Τ𝑘 𝑐 reaches values around unity
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V. Kosyanchuk, Moscow (Russia) Glasgow, UK July, 25, 2018 13/19Gas flows in structures with oscillating elements
Amplification factor γ for different wavelengths
Effect gets stronger for higher values of Τλ 𝐴 but requires higher values of
surface wave speeds
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V. Kosyanchuk, Moscow (Russia) Glasgow, UK July, 25, 2018 14/19Gas flows in structures with oscillating elements
Influence of other parameters
Pumping gets stronger with increasing channel length Τ𝐿 𝐷
Separation is observed only for accommodation coefficient close to unity
and when upper and lower surface move in same phase
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V. Kosyanchuk, Moscow (Russia) Glasgow, UK July, 25, 2018 15/19Gas flows in structures with oscillating elements
Extra. Gas pumping
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V. Kosyanchuk, Moscow (Russia) Glasgow, UK July, 25, 2018 16/19Gas flows in structures with oscillating elements
Results for negative wavespeeds 𝑢/𝑐
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V. Kosyanchuk, Moscow (Russia) Glasgow, UK July, 25, 2018 17/19Gas flows in structures with oscillating elements
Effect of pumping is observed in wide range of amplitudes Τ𝐴 𝐷 (from
0.01 to 10)
Pumping gets stronger with increasing channel length Τ𝐿 𝐷
Effect gets weaker for higher values of Τλ 𝐴
Scattering law and values of accommodation coefficient are irrelevant
Phase shift between upper and lower surface is irrelevant
Gas pumping
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V. Kosyanchuk, Moscow (Russia) Glasgow, UK July, 25, 2018 18/19Gas flows in structures with oscillating elements
High-frequency oscillations can significantly influence rarefied gas flow
inside microstructures
Influence is most noticeable when characteristic speed of surface motion
becomes compatible with molecules thermal speed
Presence of separation effect significantly depends on device parameters
(surface conditions, amplitudes and frequencies of oscillations, geometry)
When some characteristic oscillation speed is directed along channel axis
one can get pumping effect
Discussions
Future works:
Computations at moderate Knudsen numbers are required
Conduction physical experiments is also necessary
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V. Kosyanchuk, Moscow (Russia) Glasgow, UK July, 25, 2018 19/19Gas flows in structures with oscillating elements
Thank you
for attention!