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Introduction of Micro-/Nano-fluidic Flow

Introduction of Micro-/Nano-fluidic Flow. J. L. Lin Assistant Professor Department of Mechanical and Automation Engineering. Outline. Defenition of a fluid, fluid particle Viscosity Continuity equation Navier – Stokes equation Reynolds number Stokes (creeping) flow. Course outline.

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Introduction of Micro-/Nano-fluidic Flow

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

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

  3. Course outline • 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.

  5. Textbooks • 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.

  7. Definition of a fluid When a shear stress is applied: • Fluids continuously deform • Solids deform or bend 11/7/2014 7

  8. Velocity field Eulerian velocity field y y material derivative x x Lagrangian velocity field y y x x 11/7/2014 8

  9. Stress Field DA DF y x z 11/7/2014 9

  10. Viscosity couette flow viscosity - Newtonian apparent viscosity - 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 10

  11. Viscosity 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. Kinematic viscosity n has SI units [m2·s−1]. 11/7/2014 11

  12. Dynamic viscosity 11/7/2014 12

  13. Non-Newtonian: Power law fluids • k = flow consistency index • n = flow behavior index

  14. Power law fluids

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

  16. Conservation of mass Incompressible Fluid: Rectangular Coordinate System

  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)

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