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Nanoparticles and Taylor dispersion as a linear time-invariant system

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Academic year: 2022

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(1)

Nanoparticles and Taylor Dispersion as a Linear Time-Invariant System

a b

(2)

𝐴(𝑡) = 𝑎 + 𝑏 ∙ [ 𝑦 ∙ 𝐴𝑥(𝑡0, 𝜅1/𝑝, 𝛥𝑡, 𝛿𝑡, 𝑡) + (1 − 𝑦) ∙ 𝐴𝑥(𝑡0, 𝜅2/𝑝, 𝛥𝑡, 𝛿𝑡, 𝑡)]

 𝑎 (𝑎𝑢)

 𝑏

 𝑡0 (𝑠)

 𝛥𝑡 (𝑠)

 𝛿𝑡 (𝑠)

 𝜅 = 𝑝 𝑟 (𝑠) 𝑝 = 𝜋 𝜂 𝑌2/2 𝑘𝐵𝑇

𝜎2= 𝜅 𝑡0/2

 𝑦

𝐴(𝑡) = 𝑎 + 𝑏 ∙ [𝑦 ∙ 𝑔(𝑡0, 𝜎1) + (1 − 𝑦) ∙ 𝑔(𝑡0, 𝜎2)]

 𝑎 (𝑎𝑢)

 𝑏

 𝑡0 (𝑠)

 𝜎 (𝑠)

 𝑦

𝑟 =4 𝑘𝐵 𝑇

𝜋 𝜂 𝑌2 𝜎2 𝑡0

𝑦(𝑡) = 𝑦0+ (𝜋 𝜂 𝑌2

4 𝑘𝐵 𝑇) ∙ 𝑟 ∙ 𝑡

(3)

𝑡0

𝑡0

𝑡0

𝑡0

𝑡0

𝑡0

𝑡0

𝑡0

𝑡0

𝑡0

𝑡0

𝑡0

𝑦0= 50.8 𝑠2

𝑦0= 1134.3 𝑠2

(4)

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