Contents. Microfluidics - Jens Ducrée Physics: Fluidic Networks 1

Transcription

1 Contents 1. Introduction 2. Fluids 3. Physics of Microfluidic Systems 4. Microfabrication Technologies 5. Flow Control 6. Micropumps 7. Sensors 8. Ink-Jet Technology 9. Liquid Handling 10.Microarrays 11.Microreactors 12.Analytical Chips 13.Particle-Laden Fluids a. Measurement Techniques b. Fundamentals of Biotechnology c. High-Throughput Screening Microfluidics - Jens Ducrée Physics: Fluidic Networks 1

2 3. Physics of Microfluidic Systems 3.1. Navier-Stokes Equations 3.2. Laminar and Turbulent Flow 3.3. Fluid Dynamics 3.4. Fluidic Networks 3.5. Energy Transport 3.6. Interfacial Surface Tension 3.7. Electrokinetics Microfluidics - Jens Ducrée Physics: Fluidic Networks 2

3 3.4. Fluidic Networks 1. Analogy to Electric Circuits 2. Example: Simple Electric Circuit 3. Flow Resistance 4. Fluidic Inertance 5. Fluidic Capacitance Microfluidics - Jens Ducrée Physics: Fluidic Networks 3

4 3.4. Fluidic Networks 1. Analogy to Electric Circuits 2. Example: Simple Electric Circuit 3. Flow Resistance 4. Fluidic Inertance 5. Fluidic Capacitance Microfluidics - Jens Ducrée Physics: Fluidic Networks 4

5 Analogy to Electric Circuits Exact approach Navier-Stokes equations Equation of state Boundary conditions Analytical Solution Only cases of high symmetry Numerical Solution Discretization - Tremendous number of lattice points High computational effort - Convergence problems - Etc. Most problems require further simplification! Microfluidics - Jens Ducrée Physics: Fluidic Networks 5

6 Analogy to Electric Circuits Physics of electric circuits Conduction band Some electrons and atoms Hamiltonian Boundary conditions HOPELESS! Electrical engineering One-dimensional current I Discrete set of idealized elements - Resistance R - Inertance L - Capacitance C Elements condensed to discrete point Kirchhoff s laws Microfluidics - Jens Ducrée Physics: Fluidic Networks 6

7 Fluidic Analogs Fluidic analogs fulfilling Kirchhoff s conservation laws Current I Mass flow Potential U Power U I No dissipation - Preserved Two measurements - Pressure - Flow Microfluidics - Jens Ducrée Physics: Fluidic Networks 7

8 Fluidic Potential Rewrite potential Total pressure p tot at heart of U hd Bernoulli p A : pressure drop at element of cross-section A Differential definition d -1 p approximates du hd for small variations R A I m! Microfluidics - Jens Ducrée Physics: Fluidic Networks 8

9 Mechanical power Units of Watt 1 W = 1 N m s Analogy to Electric Circuits Transfer functions Workhorse of electric circuits Relation between - Potential drop - Current Complex number - Amplitude - Phase shift Derivation - Analytical: for rather abstract components (e.g., Ohm s laws) Resistors Capacities Inductivities - Numerical: (CFD) Microfluidics - Jens Ducrée Physics: Fluidic Networks 9

10 Analogy to Electric Circuits Net list of components Alignment Internal coupling DE for entire system Net list Transfer functions Conservation laws Computation of network Numerical procedures (SPICE, SABER) Solution at discrete locations Microfluidics - Jens Ducrée Physics: Fluidic Networks 10

11 3.4. Fluidic Networks 1. Analogy to Electric Circuits 2. Example: Simple Electric Circuit 3. Flow Resistance 4. Fluidic Inertance 5. Fluidic Capacitance Microfluidics - Jens Ducrée Physics: Fluidic Networks 11

12 Example: Simple Electric Circuit Transfer functions Net list Microfluidics - Jens Ducrée Physics: Fluidic Networks 12

13 Example: Simple Electric Circuit Kirchhoff s mesh rule Kirchhoff s node rule DE for system Microfluidics - Jens Ducrée Physics: Fluidic Networks 13

14 3.4. Fluidic Networks 1. Analogy to Electric Circuits 2. Example: Simple Electric Circuit 3. Flow Resistance 4. Fluidic Inertance 5. Fluidic Capacitance Microfluidics - Jens Ducrée Physics: Fluidic Networks 14

15 Flow Resistance Fluidic equivalent to ideal resistor Quotient - Potential difference - Current Referring to mass flow I m Alternatively to volume flow I V - Attention: compressibility! Mechanism Viscosity Boundary conditions Character of flow Note No energy dissipation like Ohmic resistor Conversion between - Kinetic energy - Potential energy Microfluidics - Jens Ducrée Physics: Fluidic Networks 15

16 Flow Resistance Analytical solution for tube Hagen-Poiseuille Hydrodynamic resistance Numerical coefficient - Shape of cross-section Microfluidics - Jens Ducrée Physics: Fluidic Networks 16

17 Flow Resistance Inlet resistance Distance to reach fully developed flow profile z devel Inertia - Acceleration from rest to asymptotic velocity Direct current (DC) phenomena Nonlinear term Microfluidics - Jens Ducrée Physics: Fluidic Networks 17

18 Orifice Plate Fluidic constraint Direct current phenomenon Negligible length Vanishing mass resides in aperture - No fluidic inertance Idealized conditions Perfect laminar flow Perfect conversion: potential -> kinetic -> potential energy Real system Energy losses during reconversion Coefficient C d depends on various parameters Microfluidics - Jens Ducrée Physics: Fluidic Networks 18

19 Nozzles Geometrical contraction Cross-section A 1 and A 2 Idle (A 2 = 0) R hd infinite Case A 1 = A 2 R hd vanishes Microfluidics - Jens Ducrée Physics: Fluidic Networks 19

20 3.4. Fluidic Networks 1. Analogy to Electric Circuits 2. Example: Simple Electric Circuit 3. Flow Resistance 4. Fluidic Inertance 5. Fluidic Capacitance Microfluidics - Jens Ducrée Physics: Fluidic Networks 20

21 Fluidic Inertance Setting fluidic mass into motion F=ma AC phenomenon Conversion Pressure - Potential energy Fluid flow - Kinetic energy How tightly can mass flow follow pressure signal? Microfluidics - Jens Ducrée Physics: Fluidic Networks 21

22 Fluidic Inertance Reaction of fluid Speed of sound: 1000 m / s Channel length: 10 mm Time for pressure signal: 10 µs Onset of flow Pressure drops - Viscosity p - Inertia p m Dynamics of system Microfluidics - Jens Ducrée Physics: Fluidic Networks 22

23 Fluidic Inertance Reaction of fluid Speed of sound: 1000 m / s Channel length: 10 mm Time for pressure signal: 10 µs Onset of flow Pressure drops - Viscosity p - Inertia p m Dynamics of system Microfluidics - Jens Ducrée Physics: Fluidic Networks 23

24 Fluidic Inertance Characteristic response time Rewritten - Independent of channel length - Scaling with r 2 0 Example with typical values - = 10-6 m 2 / s - r 0 = 400 µm - Response time of 20 ms 10-2 s - Typical frequencies in µfluidic circuits ~100 Hz Microfluidics - Jens Ducrée Physics: Fluidic Networks 24

25 3.4. Fluidic Networks 1. Analogy to Electric Circuits 2. Example: Simple Electric Circuit 3. Flow Resistance 4. Fluidic Inertance 5. Fluidic Capacitance Microfluidics - Jens Ducrée Physics: Fluidic Networks 25

26 Fluidic Capacitance Elastic components Membranes Compressible fluids AC phenomenon External pressure Intermediate storage of mass flow rate Microfluidics - Jens Ducrée Physics: Fluidic Networks 26

27 Compressible Fluids Finite compressibility Flow by compression of fluid Hydraulic capacitance Microfluidics - Jens Ducrée Physics: Fluidic Networks 27

28 Elastic Membranes Unknown variables Three currents I m,i Pressure p Kirchhoff s mesh rule Flow in side channel Microfluidics - Jens Ducrée Physics: Fluidic Networks 28

29 Elastic Membranes Membrane function Flow by elastic expansion Current in side channel DE for system with one unknown Combination of four equations Microfluidics - Jens Ducrée Physics: Fluidic Networks 29