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Development of techniques for rapid isolation and separation of particles in digital microfluidics Rezaei Nejad, Hojatollah 2016

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Development of Techniques for Rapid Isolationand Separation of Particles in DigitalMicrofluidicsbyHojatollah Rezaei NejadB.Sc., Shahid Chamran University, Iran, 2007M.Sc., K.N Toosi University of Technology (KNTU), Iran 2010A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinTHE COLLEGE OF GRADUATE STUDIES(Engineering)THE UNIVERSITY OF BRITISH COLUMBIA(Okanagan)April 2016© Hojatollah Rezaei Nejad, 2016        The undersigned certify that they have read, and recommend to the College of Graduate Studies for acceptance, a thesis entitled:    Development of Techniques for Rapid Isolation and Separation of Particles in Digital Microfluidics  Submitted by             Hojatollah Rezaei Nejad           in partial fulfillment of the requirements of   The degree of       Doctor of Philosophy                                                    .  Dr. Mina Hoorfar, School of Engineering, UBCO Supervisor, Professor (please print name and faculty/school above the line)  Dr. Homayoun Najjaran, School of Engineering, UBCO Supervisory Committee Member, Professor (please print name and faculty/school in the line above)  Dr. Vladan Prodanovic, Chemical and Biological Engineering, UBCO Supervisory Committee Member, Professor (please print name and faculty/school in the line above)  Dr. Kenneth Chau, School of Engineering, UBCO University Examiner, Professor (please print name and faculty/school in the line above)  Dr. Pierre Sullivan, Mechanical and Industrial Engineering, University of Toronto External Examiner, Professor (please print name and university in the line above)   April 22, 2016 (Date submitted to Grad Studies)                                                         E   µmμμ μ   μμμμ   μ   ∇                                         Vrms                                               E⃗                         ~100 µ𝑚𝐵𝑜 = √𝑔∆𝜌𝑅2/𝛾𝐿𝐺 ≈10 (𝑚𝑠2) × 103 (𝑘𝑔𝑚3) × 10−8(𝑚2)/0.07 (𝐽𝑚2) = 0.037   𝑅𝑒 =𝜌𝑊𝐷𝜇≈ 103 (𝑘𝑔𝑚3) × 10−3 (𝑚𝑠) × 10−4(𝑚)/10−3 (𝑘𝑔.𝑚𝑠) = 0.1 𝛾𝑆𝐿 = 𝛾𝑆𝐿0 −𝑐2𝑉2𝛾𝑆𝐿𝛾𝑆𝐿0 𝑐𝛾𝑆𝐿 = 𝛾𝑆𝐺 − 𝛾𝐿𝐺cos θcos𝜃 = cos𝜃0 +1𝛾𝐿𝐺12𝐶V2𝛾𝑆𝐺 𝛾𝐿𝐺𝜃0 𝜃   𝑍𝐷 =12𝜋𝐶𝐷𝑓𝐶𝑙 =𝜀0𝜀𝑟𝑙𝐴𝐻𝐶𝐷 =𝜀0𝜀𝑟𝐷𝐴𝑡   𝑅𝑙 = 𝜌𝑙𝐻𝐴𝜀0 𝜀𝑟 ρ𝑙 𝐷  𝑍𝑒𝑞 =  𝑍𝑑 + ( 𝑍𝐿 × 𝑅𝐿)/( 𝑍𝐿 + 𝑅𝐿) 𝑉𝐷 = 𝑉𝑖𝑛𝑝𝑢𝑡(𝑍𝑑 𝑍𝑒𝑞⁄ ) 𝑉𝑙 = 𝑉𝑖𝑛𝑝𝑢𝑡 − 𝑉𝐷    𝜇𝑚𝜇𝑚     +𝑞 −𝑞𝑑?⃑? = −q ?⃗? (r⃑) + q ?⃗? (r⃑ + d⃑⃗)r⃑ −𝑞 ?⃗? +𝑞?⃗? (r⃑ + d⃑⃗) = ?⃗? (r⃑) + (d⃑⃗. ?⃗⃑⃗? )?⃗? (r⃑) + ⋯   ?⃑? = q (d⃑⃗ . ?⃗⃑⃗?) ?⃗? (r⃑)?⃗? =  q d⃑⃗?⃑?𝐷𝐸𝑃 = (?⃑⃗? ∙ ?⃗⃑⃗?)?⃗? ?⃑⃗?    (?⃑⃗?eff)𝜑𝜑(𝑟, 𝜃) =𝑞𝑑 𝑃1(𝑐𝑜𝑠𝜃)4𝜋𝜀𝑚𝑟2+𝑞𝑑3 𝑃3(𝑐𝑜𝑠𝜃)16𝜋𝜀𝑚𝑟4+ ⋯𝜀𝑚 𝑃1 𝑎𝑛𝑑 𝑃3𝜑(𝑟, 𝜃) =𝑝eff (𝑐𝑜𝑠𝜃)4𝜋𝜀𝑚𝑟2𝑟 𝜃?⃗⃑⃗?(𝑡) = 𝑅𝑒(𝐸0 𝑒𝑗𝜔𝑡)?̂?𝑧E0 𝜔 𝑧𝜑1(𝑟, 𝜃) 𝜑2(𝑟, 𝜃)   𝜑1(𝑟, 𝜃) =  −𝐸 𝑟 𝑐𝑜𝑠𝜃 +𝐴 𝑐𝑜𝑠𝜃𝑟2,        𝑟 > 𝑅𝜑2(𝑟, 𝜃) = −𝐵 𝑟 𝑐𝑜𝑠𝜃,        𝑟 < 𝑅.𝐴 𝐵 −𝐸 𝑟 𝑐𝑜𝑠𝜃𝐴 𝑐𝑜𝑠𝜃/𝑟2  𝑟 = 𝑅𝜑1(𝑟 = 𝑅, 𝜃) = 𝜑2(𝑟 = 𝑅, 𝜃).𝐽𝑟1 − 𝐽𝑟2 +𝜕𝜎𝑓𝜕𝑡= 0,    𝑟 = 𝑅 𝐽𝑟1 = 𝜎𝑚𝐸𝑟1  𝐽𝑟2 = 𝜎𝑝𝐸𝑟2𝜎𝑚 𝜎𝑝𝜎𝑓𝜎𝑓 = 𝜀𝑚𝐸𝑟1 − 𝜀𝑝𝐸𝑟2.𝐴𝐴 =𝜀𝑝∗ −𝜀𝑚∗𝜀𝑝∗ +2𝜀𝑚∗ 𝑅3𝐸0.   𝜀𝑝∗ 𝜀𝑚∗𝜀𝑝,𝑚∗ = 𝜀0𝜀𝑝,𝑚 − 𝑗𝜎𝑝,𝑚2𝜋𝑓 ,            𝜔 = 2𝜋𝑓𝜀0 𝜀0 𝑓𝑝 𝑚𝑝eff = 4𝜋𝜀𝑚𝐴. ?⃗⃑? = 𝑅𝑒[?̃? 𝑒−𝑗𝜔𝑡]?̃?  𝜔?̃?   ?⃑⃗?eff = 4𝜋𝜀𝑚𝑅3𝑅𝑒[𝑓𝐶𝑀] ?⃗⃑?𝑓𝐶𝑀 𝑓𝐶𝑀 =𝜀𝑝∗ (𝜔)−𝜀𝑚∗ (𝜔)𝜀𝑝∗ (𝜔)+2𝜀𝑚∗ (𝜔) 〈?⃑?𝐷𝐸𝑃〉 = (?⃑⃗?eff ∙ ?⃗⃑⃗? )?̃? = (4𝜋𝜀𝑚𝑅3𝑅𝑒[𝑓𝐶𝑀] ?̃? ∙ ?⃗⃑⃗? ) ?̃?. ?⃑⃗?(?⃗⃑?. ?⃗⃑?) = (?⃗⃑?. ?⃑⃗?)?⃗⃑? + (?⃗⃑?. ?⃑⃗?)?⃗⃑? + ?⃗⃑? × (?⃗⃑? × ?⃗⃑?) + ?⃗⃑? ×(?⃑⃗? × ?⃗⃑?) ?⃗⃑⃗? × ?⃗⃑? = 0 ?⃗⃑?〈?⃑?𝐷𝐸𝑃〉 = 2𝜋𝑅3𝜀𝑚𝑅𝑒(𝑓𝐶𝑀)?⃗⃑⃗?(?̃? ∙ ?̃?)𝑅 ?⃗? ?⃑?𝐷𝐸𝑃 = 2𝜋𝑅3𝜀𝑚𝑅𝑒(𝑓𝐶𝑀)?⃗⃑⃗? (|?⃗⃑?|2)   𝜀𝑚 |?⃗⃑?|𝑅𝑒(𝑓𝐶𝑀)𝑓𝐶𝑀 ≤𝑓𝐶𝑀 ≤𝑓𝐶𝑀𝑓𝐶𝑀 𝑚𝑝𝑑𝒖𝑝𝑑𝑡= 𝐅𝑠 + 𝐅𝑏𝑚p 𝐮p 𝐅𝐬𝐅b   𝐅D 𝐅L𝐅𝑠 = 𝐅𝐷 + 𝐅𝐿𝐅g 𝐅bbgLDpp FFFFudtdmfff  LuRe 𝜌f 𝜇f 𝑢f𝐿 ~ 𝑅𝑒 >1   zFFFdtdwm Dbgpp 𝑤p 𝐹Dz𝑅𝑒 =𝜌𝑤𝐷𝜇=1000×10−3×10−510−3=0.01 < 1𝐹𝐷𝑧 = 3𝜋𝜇𝑓𝑑𝑝(𝑤𝑝 − 𝑤𝑓)𝑑p 𝑤f𝑤f𝐹𝑔 = 𝜌𝑝𝑉𝑔𝐹𝑏 = 𝜌𝑓𝑉𝑔𝑉    /p 1)( tewtw   f2pfp18 dgwf2pp18d𝑤∞𝜏                     ˗   60 𝑛𝑚 0.1 𝑛𝑚/𝑠𝑒𝑐 2 mtorr25 𝑚𝑚 × 75 𝑚𝑚20 𝑛𝑚 60 𝑛𝑚 25 𝑚𝑚 × 75 𝑚𝑚       110℃   10 𝜇𝑚           95℃0.01 𝑛𝑚/𝑠𝑒𝑐  300 𝜇𝑚   𝜇𝑚    118° ± 1°  60° ± 5°120℃                                                                    1 Parts of Chapter 4 have been published in CSME conference.            µ𝑙 𝑚𝑀 µ𝑙 𝑚𝑔/𝑚𝑙 𝑚𝑙𝑚𝑙𝑚𝑙   µ𝑙 µ𝑙µ𝑙 𝑠𝑒𝑐 µ𝑙𝑠𝑒𝑐                     µµ µ µ                                                          2 Parts of Chapter 4 have been published in Journal of RSC Advances. Reprinted with permission from [56]    µµg ml⁄ 𝑚𝑝𝑑𝑤𝑝𝑑𝑡= 𝑉𝑔(𝜌𝑝 − 𝜌𝑓) − 𝐹𝐷𝑧𝑉𝑤p 𝐹Dz𝑅𝑒 =𝜌𝑤𝐷𝜇=1000×10−3×10−510−3= 0.01 < 1𝐹𝐷𝑧 = 3𝜋𝜇𝑓𝑑𝑝(𝑤𝑝 − 𝑤𝑓)   𝑑p 𝑤f𝑤f /p 1)( tewtw   f2pfp18 dgwf2pp18d𝑤∞𝜏    µmms𝑉𝑟𝑚𝑠  kHz       µS/cmgr/cm3µS/cmµS/cm μ   rad/s     μ   μ μ   µ𝑚μ   μμ    𝜇𝑚   𝜏 µ𝑠µ𝑠μ μ   μ μ             𝑛c/𝑛t) 𝑛c𝑛t𝑛c/𝑛t   𝑛c/𝑛t   μμ𝑛c/𝑛t   μ   μ μ μμ𝐷o𝐷i 𝐷oμ   μ𝐷o𝐷i 𝐷o𝐷o − 𝐷i𝐶m𝐶0   μ μ𝐶m 𝐶0 ≈4.5𝐶m) µl𝐶m) 𝑛c/𝑛tμ μμ μ                  μ       μμμμμμ    μ μ       𝐾                                                          3 Parts of Chapter 4 have been published in Journal of Lab-on-a-chip and µTAS conference proceedings. Reprinted with permission from [84]     ?⃑?𝐷𝐸𝑃 = (?⃗? eff ∙ ?⃗⃑⃗?)?⃗? ?⃗? eff ?⃗? ?⃗? ?⃗? eff = 𝟒𝜋𝑎3𝜀𝑚𝑅𝑒(𝑓𝐶𝑀) ?⃗⃑??⃑?𝐷𝐸𝑃 = 2𝜋𝑎3𝜀𝑚𝑅𝑒(𝑓𝐶𝑀)?⃗⃑⃗? (|?⃑⃗?|2)   𝜀𝑚 |?⃑⃗?|𝑅𝑒(𝑓𝐶𝑀)𝑓𝐶𝑀 =𝜀𝑝∗−𝜀𝑚∗𝜀𝑝∗+2𝜀𝑚∗𝜀𝑝∗ 𝜀𝑚∗𝜀𝑝∗ = 𝜀𝑝 −𝑖𝜎𝑝𝜔𝜀𝑚∗ = 𝜀𝑚 −𝑖𝜎𝑚𝜔𝜀0 𝜀0 𝜔(𝜎𝑝𝑏)  (𝐾𝑠)𝜎𝑝 = 𝜎𝑏 + 2 ×𝐾𝑠𝑎 ;  𝜎𝑚 = medium conductivity𝑓𝐶𝑀 ≤𝑓𝐶𝑀 ≤𝑓𝐶𝑀   𝑓𝐶𝑀μ 𝜎𝑝𝑏 = 10−15 𝑆/𝑚 𝜅𝑝 = 10−9 𝑆 𝜀𝑝 = 2.4𝜎𝑝 = 𝜎𝑝𝑏 + 2𝜅𝑝/𝑎 = 10−15 𝑆/𝑚 + (2 × 10−9 𝑆)/(2.5 ×10−6 𝑚) = 8 µ𝑆/𝑐𝑚μ   σε𝑓𝐶𝑀𝑓𝐶𝑀    𝜇𝑚𝜕2Φ(𝑥,𝑦,𝑧)𝜕𝑥2+𝜕2Φ(𝑥,𝑦,𝑧)𝜕𝑦2+𝜕2Φ(𝑥,𝑦,𝑧)𝜕𝑧2= 0Φ   𝑍   𝑌     μ   μμ               Sμ μ𝑆𝑊   Y   μμμ   𝐾 = 𝐷/𝑊𝐷 𝑊𝐾𝐾 ≈𝐾        μ′   𝑠𝑒𝑐𝑚𝑖𝑛   µ𝑙𝑚𝑖𝑛       𝐾                                                                 4 Parts of Chapter 4 have been published in Journal of . Reprinted with permission from [85]     𝑓𝐶𝑀 µ𝑚           μ   μ      𝑥/𝐿 = 0.2 𝑥/𝐿 = 0.8   𝑥/𝐿 < 0.2 𝑥/𝐿 > 0.8∇|𝐸|2∇|𝐸|2   𝑥/𝐿 = 0.5𝑥/𝐿 = 0.8   ∇   (𝑥 𝐿⁄ = 0.5)   μμ                 18 ng/µL              CO2                                        ‐‐ ‐ ‐            ‐          𝑚𝑖𝑛𝑚𝑚2µ𝑚   𝑚𝑚2   𝑚𝑚2

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