1. Introduction of Micro- /Nano-fluidic Flow J. L. Lin Assistant Professor Department of Mechanical and Automation Engineering 6/23/2015 1

2. Outline 6/23/2015 2 Defenition of a fluid, fluid particle Viscosity Continuity equation Navier – Stokes equation Reynolds number Stokes (creeping) flow

3. Course outline 3 Unit I Physics of Microfluidics Physics at micrometer scale, scaling laws, understanding implications of miniaturization Hydrodynamics at micrometer and nanometer scale Surface tension, wetting and capillarity Diffusion and mixing Electrodynamics at micrometer scale Thermal transfer at micrometer scale Unit II Fabrication Methods of Microfluidics Clean room micro-fabrication process Unit III Applications of Microfluidics Basic components of microfluidic devices, fluidic control and micro “plumbing” Lab-on-a-chip and  TAS, their application to cell, protein, and DNA analysis Optofluidics, Power microfluidics Emerging applications of microfluidics

4. Course objectives Introduction and a broad overview of the basic laws and applications of micro and nano fluidics Hands-on experience in modern microfabrication techniques, design and operation of microfluidic devices The ability to work effectively with the original publications in the area of microfluidics. The ability to effectively present literature data in the area of microfluidics. 22-Jan-08 4

5. Textbooks 5 Introduction to Microfluidics, Patrick Tabeling and Suelin Chen Oxford University Press, 2006 Theoretical Microfluidics, Henrik Bruus, Oxford University Press, 2007 Fundamentals And Applications of Microfluidics Nam-Trung Nguyen, Steven T. Wereley, Artech House Publishers, 2006 Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves Pierre-Gilles de Gennes, Francoise Brochard-Wyart, David Quere, Springer, 2003 Microfluidic Lab-on-a-Chip for Chemical and Biological Analysis and Discovery Paul C.H. Li, CRC, 2005 Fundamentals of BioMEMS and Medical Microdevices Steven S. Saliterman, SPIE, 2006

6. Grade Cumulative score: Attendance 20% Homeworks 30% Final Report 20% Oral Presentation 30% Each student will have an opportunity to present a 15-minute talk based on original publication(s) in the field of micro/nano fluidics. List of recommended topics and papers will be provided. 6

7. Definition of a fluid 6/23/2015 7 When a shear stress is applied: Fluids continuously deform Solids deform or bend

8. Velocity field 6/23/2015 8 y x y x y x y x Lagrangian velocity field Eulerian velocity field material derivative

9. Stress Field 6/23/2015 9 FF AA x y z

10. Viscosity 10 - Newtonian - non-Newtonian Newtonian Fluids Most of the common fluids (water, air, oil, etc.) “Linear” fluids Non-Newtonian Fluids Special fluids (e.g., most biological fluids, toothpaste, some paints, etc.) “Non-linear” fluids viscosity apparent viscosity couette flow

11. Viscosity 6/23/2015 11 The SI physical unit of dynamic viscosity m is the pascal-second (Pa·s), which is identical to 1 kg·m −1 ·s −1. The cgs physical unit for dynamic viscosity m is the poise (P) 1 P = 1 g·cm −1 ·s −1 It is more commonly expressed as centipoise (cP). The centipoise is commonly used because water has a viscosity of 1.0020 cP @ 20 C The relation between poise and pascal-seconds is: 1 cP = 0.001 Pa·s = 1 mPa·s In many situations, we are concerned with the ratio of the viscous force to the inertial force, the latter characterized by the fluid density ρ. This ratio is characterized by the kinematic viscosity, defined as follows: where μ is the dynamic viscosity, and ρ is the density. m 2 ·s −1 Kinematic viscosity n has SI units [m 2 ·s −1 ].

12. Dynamic viscosity 6/23/2015 12 viscosity  [Pa s] [cP] liquid nitrogen1.58 × 10 −4 0.158 acetone3.06 × 10 −4 0.306 methanol5.44 × 10 −4 0.544 water1.00 × 10 −3 1.000 ethanol1.074 × 10 −3 1.074 mercury1.526 × 10 −3 1.526 nitrobenzene1.863 × 10 −3 1.863 propanol1.945 × 10 −3 1.945 ethylene glycol1.61 × 10 −2 16.1 sulfuric acid2.42 × 10 −2 24.2 olive oil.08181 glycerol.934934 corn syrup1.38061380.6 Viscosity  [cP] honey2,000–10,000 molasses5,000–10,000 moltenmolten glassglass10,000–1,000,000 chocolate syrup10,000–25,000 moltenmolten chocolatechocolate45,000–130,000 ketchup50,000–100,000 peanut butter~250,000 shortening~250,000 viscosity  [cP] hydrogen8.4 × 10 −3 air17.4 × 10 −3 xenon2.12 × 10 -2

13. Non-Newtonian: Power law fluids 6/23/2015 13 k = flow consistency index n = flow behavior index

14. Power law fluids 22-Jan-08 14

15. Conservation of mass Rectangular Coordinate System “Continuity Equation” “Del” Operator

16. Conservation of mass Rectangular Coordinate System Incompressible Fluid:

17. Momentum equation Newtonian Fluid: Navier-Stokes Equations - material derivative - Del operator - Laplacian operator

18. Navier-Stokes Equations Rectangular Coordinate System

19. Momentum equation Special Case:   0 (ideal fluid; inviscid) - Euler’s equation - Material derivative - Del operator

20. Momentum equation Special Case: Re << 1, stationary flow - Low Reynolds number flow (creeping flow, Stokes flow)