fluidic networks - dcu

Pr axisbe ispiel: Ausar beitun gsphaAu sarbeit ung de r Stand ard-Ze lle

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

3.1. Navier-Stokes Equations

3.2. Laminar and Turbulent Flow

3.3. Fluid Dynamics3.4. Fluidic Networks3.5. Energy Transport

3.6. Interfacial Surface Tension

3.7. Electrokinetics

3. Physics of Microfluidic Systems

1. Analogy to Electric Circuits

2. Example: Simple Electric Circuit

3. Flow Resistance

4. Fluidic Inertance

5. Fluidic Capacitance

3.4. Fluidic Networks

1. Analogy to Electric Circuits2. Example: Simple Electric Circuit

3. Flow Resistance

„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!

3.4.1. Analogy to Electric Circuits

Physics of electric circuits Conduction band Some 1023 electrons and atoms Hamiltonian Boundary conditions

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

HOPELESS!

Fluidic analogs fulfilling Kirchhoff‘s conservation laws

Current I Mass flow

Potential U Power U I No dissipation

- Preserved Two measurements

- Pressure- Flow

3.4.1. Fluidic Analogs

Rewrite potential Total pressure ptot at heart of Uhd

pA : pressure drop at element of cross-section A

Differential definition

d -1p approximates dUhd for small variations RA Im!

3.4.1. Fluidic Potential

Bernoulli

Mechanical power Units of Watt 1 W = 1 N m s-1

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)

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

2. Example: Simple Electric Circuit3. Flow Resistance

3.4.2. Example: Simple Electric Circuit

Net listTransfer functions

Pr axisbe ispiel: Ausar beitun gsphaAu sarbeit ung de r Stand ard-Ze lle Kirchhoff‘s mesh rule

Kirchhoff‘s node rule

DE for system

3.4.2. Example: Simple Electric Circuit

3. Flow Resistance4. Fluidic Inertance

Fluidic equivalent to ideal resistor Quotient

- „Potential“ difference- „Current“

Referring to mass flow Im Alternatively to volume flow IV

- Attention: compressibility!

Mechanism Viscosity Boundary conditions Character of flow

Note No energy dissipation like Ohmic resistor Conversion between

- Kinetic energy- Potential energy

3.4.3. Flow Resistance

Analytical solution for tube

Hydrodynamic resistance

Numerical coefficient- Shape of cross-section

Hagen-Poiseuille

Inlet resistance Distance to reach fully developed flow profile zdevel

Inertia- Acceleration from rest to asymptotic velocity

„Direct current“ (DC) phenomena

Nonlinear term

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 Cd depends on various parameters

3.4.3. Orifice Plate

Geometrical contraction Cross-section A1 and A2

Idle (A2 = 0) Rhd infinite

Case A1 = A2 Rhd vanishes

3.4.3. Nozzles

3. Flow Resistance

4. Fluidic Inertance5. Fluidic Capacitance

Setting fluidic mass into motion

AC phenomenon

Conversion Pressure

- Potential energy Fluid flow

- Kinetic energy

How tightly can mass flow follow pressure signal?

3.4.4. 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 pm

Dynamics of system

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 pm

Dynamics of system

Characteristic response time

Rewritten

- Independent of channel length- Scaling with r0

Example with typical values- = 10-6 m2 / s- r0 = 400 µm- Response time of 20 ms 10-2 s- Typical frequencies in µfluidic circuits

~100 Hz

3. Flow Resistance

Elastic components Membranes Compressible fluids AC phenomenon

External pressure Intermediate „storage“ of mass

3.3.5. Fluidic Capacitance

flow rate

Finite compressibility Flow by compression of fluid

Hydraulic capacitance

3.3.5. Compressible Fluids

Unknown variables Three currents Im,i

Pressure p

Kirchhoff‘s mesh rule

Flow in side channel

3.3.5. Elastic Membranes

Membrane function Flow by elastic expansion

Current in side channel

DE for system with one unknown Combination of four equations

3.3.5. Elastic Membranes

fluidic networks - dcu

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