BME_354_382J_2022_HW2_due on 10_4_22

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BME 354 and 382J Molecular Sensors & Nanodevices of Biomedical Applications Fall, 2022, Homework #2, due on Tuesday 10/4/2022. Total points: 104 First name: ____________ Last Name: ____________ EID: ___________ 1. Microfluidics Fundamentals (18 points): Include references that are relevant and calculations that you make. Feel free to make simple drawings to explain your thoughts. Some answers can be found in the textbook or on internet. (1) What is viscosity (  )? What is the SI unit of viscosity? What is “kinematic” viscosity? What is the viscosity of water at 20  C? (2) What is diffusion coefficient ( D )? What is the SI unit of diffusion coefficient? What is the diffusion coefficient of bovine serum albumin (BSA) in “water” at “room temperature”? (Hint: Use Stokes-Einstein Equation). (3) Name 3 microfluidic devices that take advantage of “laminar flow”. (4) Read the George Whitesides’ 2003 Science paper “Chaotic mixer for microchannels” (Stroock et al., Science , 295, 647-651, 2003) and explain why the mixing length for a traditional microchannel is Pe x l , where l is the hydraulic diameter (called the “typical cross-sectional dimension” in the paper). (5) A circular bar under pure torsion will not break until the maximum shear stress of the bar (  max ) reaches the ultimate strength of the bar material (~1 GPa for silicon). Given the torsion equations below, explain from the scaling law that “a bar that is 10  smaller in radius can be twisted10  more in angle without breaking” (assuming the bar length stays the same). Equations that you will need: τ max = Tr J θ = TL JG  max : maximum shear stress T : twisting moment J : polar moment of inertia, which is 0.5  r 4 for circular cross-section G : Shear modulus (69 GPa for silicon) L : bar length 1

BME 354 and 382J Molecular Sensors & Nanodevices of Biomedical Applications Fall, 2022, Homework #2, due on Tuesday 10/4/2022. Total points: 104 r : bar radius (6) Using the famous Stokes-Einstein equation (Equation 3.34 on page 119, or page 129 for 2 nd edition), calculate the diffusion coefficient of a  20 nm spherical nanoparticle in water at 20  C (the symbol  presents the diameter). 2. Stokes’ law (10 points): For a rigid sphere (radius = a) that is in a low Reynolds’ number flow, the pressure ( p : N/m 2 ) that acts at a given point on the surface of the sphere can be written as: Calculate the overall force (F pressure : N) acting on the sphere as a result of pressure . Need to show the full calculation process. Hint: We all know that the surface area of a sphere is 4  a 2 . Do you know how to get this formula by integration? A = 2 ∫ 0 π πasinθ∙adθ = 4 π a 2 Yes, you need to know how to perform integration in a “spherical coordinate system” in order to answer this question. Also check this document called “Derivation of Stokes Law” in Files\Articles to read. 3. Electrokinetic forces, integrated microfluidic chips, and DNA sequencing (18 points): (1) What is dielectrophoresis (DEP)? What are the key differences between electrophoresis and dielectrophoresis? Why is DEP force not suitable to move nanoscaled objects (e.g., proteins, DNA)? (2) When a particle is experiencing a positive DEP force, does particles move towards cathode (i.e. against the electric field direction)? If not, where are the particle moving to? What strategies (yes, more than one way) can you adopt to turn the positive DEP force to the negative DEP force on “the same” particle? 2

BME 354 and 382J Molecular Sensors & Nanodevices of Biomedical Applications Fall, 2022, Homework #2, due on Tuesday 10/4/2022. Total points: 104 (3) The following device ( Nature , 2006, 442, 403-411) uses DEP force to trap individual cells (Hint: This is called dielectrophoretic trapping. You can search for this keyword on line.). Is it using positive DEP force or negative DEP force for trapping? Why? (4) As I said in the Lecture 10, the electric field between two point charges looks like this: Please draw | E | , E 2 (a scalar), and  E 2 (a vector) along the horizontal line and between two electrodes. All I am looking for is the “shape of the curve” and “direction of the vector” (that means you can just make some hand drawings). You can make your own assumption for the charges (same coulomb but different polarity) and the separation distance. Among these three things ( | E | , E 2 , and  E 2 ), which one actually tells you the possible direction of the DEP force? (5) Mark the “control lines”, “valves”, “pumps and “samples lines” for the following microfluidic chips (Left: Anal. Chem ., 2003, 75, 4718-4723; Right: PNAS, 2004, 101, 14431-14436). The pump rate of a typical PDMS peristaltic pump reaches a plateau at about 2-3 3

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BME 354 and 382J Molecular Sensors & Nanodevices of Biomedical Applications Fall, 2022, Homework #2, due on Tuesday 10/4/2022. Total points: 104 nL/s. Why can’t the pump rate go higher? (6) In the paper “Microfluidic digital PCR enables multigene analysis of individual environmental bacteria,” Science , 2006, 314, 1464-1467, find out the volume of each independent PCR reaction chamber. In the paper “High-throughput quantitative polymerase chain reaction in picoliter droplets,” Anal. Chem ., 2008, 80, 8975-8981, find out the volume of each PCR reaction droplet. Recall that the standard PCR reactions in most labs today have the reaction volume of 10-15  l. What is the reduction of reaction volume (i.e., orders of magnitude) for the aforementioned techniques? 4. Electrowetting (10 points): Derive the Lippmann-Young equation from the Lippmann equation and the Young equation: 5. Math (12 points): Briefly explain the following 4 operators (how are they called and what exactly the operations do they perform). The result of each operation is a scalar or a vector? Here F is a vector and f is a scalar. ∇ ∙F ∇ f ∇ 2 f ∇ 2 F ∇ F ∇ ×F 6. Capillary Electrophoresis (12 points): When we talked about CE in Lecture 10, the following schematic was used: This is called the “double-T gated injection”. From the paper “Dorfmanet et al., Beyond Gel Electrophoresis: Microfluidic Separations, Fluorescence Burst Analysis, and DNA Stretching, Chemical Reviews , 113, 2584-2667, 2013”, find out what are: 1. Floating injection 2. Gated injection 3. Double-T injection 4

BME 354 and 382J Molecular Sensors & Nanodevices of Biomedical Applications Fall, 2022, Homework #2, due on Tuesday 10/4/2022. Total points: 104 4. Double-T gated injection 5. Multicross injection What are the differences between these injection methods (simple drawings can well explain the differences)? What are the pros and cons? 7. Glucose sensor (14 points): ( A ) A glucose sensor consists of two electrodes micromachined in a cavity of a silicon wafer. One electrode is made of platinum and the other is the silver/silver chloride electrode. Describe the reactions taking place at the anode and the cathode, respectively, when the potential applied is large enough to drive the redox reactions in this glucose sensor. Hint: Refer to Joseph Wang’s 2008 Chem. Rev. article “Electrochemical glucose biosensors”, 108, 814-825 and use the “first-generation glucose biosensors” as an example. ( B ) From Wang’s paper, find out the reasons of using a “mediator” that shuttles electrons between enzyme and the electrode. But no technology is perfect. What are the problems of using mediator? 5

BME 354 and 382J Molecular Sensors & Nanodevices of Biomedical Applications Fall, 2022, Homework #2, due on Tuesday 10/4/2022. Total points: 104 8. Field effect transistor (10 points): ( A ) In text book page 204 Figure 4.31 (Fig. 4.30 in 2 nd edition, shown below), totally how many photolithography masks are needed for making such a FET? Write down the purpose of each mask (for instance, Mask#1: etch oxide for pMOSFET). ( B ) You probable heard of the term, CMOS, before (e.g., a CMOS camera). What is CMOS? 6

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