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Separation of 300-nm and 100-nm particles in Fabry-Perot acoustofluidic resonators Prateek Sehgal, and Brian J. Kirby Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.7b02858 • Publication Date (Web): 17 Oct 2017 Downloaded from http://pubs.acs.org on October 22, 2017
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Analytical Chemistry
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ӧ
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𝜃𝑓
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Analytical Chemistry Λ = 𝜆/2
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𝜃𝑓 𝑃𝑜∞ (𝑦, 𝑧) = 𝑃𝑜∞ (𝑦 + Λ, 𝑧) ∞ (𝑦, 𝑧 = 0) = 𝐽∞ (𝑦, 𝑧 = ℎ) 𝐽𝑜,𝑧 𝑜,𝑧
∫V 𝑃𝑜∞ (𝑥, 𝑦, 𝑧)𝑑𝑉 = 1 ∞ 𝐽𝑜,𝑧
𝑃𝑜∞ U𝑝𝑥 U𝑝𝑦 𝜃 𝑃𝑜 (𝑟, 𝑡|𝑟𝑜 )
tan 𝜃 = U𝑝𝑥 /U𝑝𝑦 𝑟
𝑡
𝑟𝑜
𝑡=0 𝑃𝑜
𝜕𝑃𝑜 𝜕𝑡
1
+ ∇ ⋅ 𝐽⃗𝑜 = 𝛿(𝑟 − 𝑟𝑜 )𝛿(𝑡) 𝐽⃗𝑜
tan 𝜃 = tan 𝜃𝑓
𝛿
𝑃𝑒 1−𝑒 −𝑃𝑒
𝑦+1
∫ [𝑒 𝑃𝑒𝑦−𝑉𝑎 (𝑦) ∫ 𝑦
0
∇ ⋅ 𝐽⃗𝑜∞ = 0
𝑃𝑒 = 6𝜋𝜂𝑎UFy Λ/𝑘𝐵 𝑇 𝜂 𝑘𝐵 𝑇
∞ 𝑦 ̿ ⋅ ∇𝑉𝑎 𝑃𝑜∞ − 𝐷 ̿ ⋅ ∇𝑃𝑜∞ ) = 0 ∇ ⋅ 𝐽⃗𝑜∞ = ∇ ⋅ (𝑢 ⃗⃗𝑃𝑜∞ − 𝑀
𝑑𝑦 ′ ′ −𝑉 (𝑦 ′ ) ] 𝑑𝑦 𝑃𝑒𝑦 𝑎 𝑒
𝑎 𝑉𝑎 Λ
𝑉𝑎
𝑢 ⃗⃗ ̿ 𝑀
̿ 𝐷
𝑉𝑎
𝜆/8 UF 𝜃
𝜃𝑓 U𝑝
𝑉𝑎 =
𝜋𝑎3 𝑝𝑎2 𝛽𝑓 𝑓1 𝑘𝐵 𝑇
[ cos2 (𝜋𝑦) − 3
𝑓2 2
sin2 (𝜋𝑦)]
𝑓1 = 1 − 𝛽𝑝 /𝛽𝑓 𝑓2 = 2(𝜌𝑝 − 𝜌𝑓 )/(2𝜌𝑝 + 𝜌𝑓 ) 𝑝𝑎 𝜆
𝜆
𝛽
𝜌
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𝜃 𝜃 = 90o
𝜃 = 90o 𝜃 = 𝜃𝑓 = 80o
𝜃𝑓 𝜃𝑓 = 0o & 90o
𝜃> 89.99o 𝜆
𝑙𝑎
𝜃𝑓 = 80o
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Analytical Chemistry
𝜆/2 𝑝𝑎
UF
𝜃 > 89.99o 𝑝𝑎
AUC300,𝑡 𝑦−
UF
UF
𝑆100 (%) = 100AUC100,𝑦 + /AUC100,𝑡 𝑦 < 𝑦𝑠 𝑦 + 𝑦 > 𝑦𝑠
𝑙𝑎 tan(90o − 𝜃𝑠 )
𝜃𝑠
𝑦+
𝜃 = 90o
𝑦 = 𝑦𝑠
𝑆300 (%) = 100AUC300,𝑦 − /
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𝑦𝑠 = 395 𝑢𝑚
𝜆v 𝜃𝑓 = 80o
𝜆v
𝜃𝑓
80o
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Analytical Chemistry
𝑝𝑎
UF
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Analytical Chemistry
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