AN INTRODUCTION TO MICROFLUIDICS :

Lecture n°1

Patrick TABELING, patrick.tabeling@espci.frESPCI, MMN, 75231 Paris0140795153

1 - Past and present of microfluidics2 - Microfluidics, nanofluidics and macroscopic approach.3 - The changes in the balances of forces that result from miniaturization.

Outline of Lecture 1

SOME REFERENCES

Translation by Suelin CHENOxford University Press To appear, 20 Oct 2005

Oxford Univ Press

MEMS = MICRO ELECTROMECHANICHAL SYTEMS

Systems whose sizes lie in the range 1 -300 microns

A new situation arose in the seventies, further to the tremendous development of microelectronics : it became possible to fabricate all sorts of miniaturized objects : microcondensators, microvalves, micropumps, microresonators, microdispenser...by exploiting an important accumulation of technological knowledge, and taking advantage of the availability of sophisticated equipment.

This generated a substantial economicalactivity

Airbag SensorAirbag Sensor - - Analog DeviceAnalog Device

3 mm

m

Commercial Inkjet using MEMS technologyCommercial Inkjet using MEMS technology

2 mm

There's Plenty of Room at the Bottom

An Invitation to Enter a New Field of Physics

I would like to describe a field, in which little has been done, but inwhich an enormous amount can be done in principle. This field is not quitethe same as the others in that it will not tell us much of fundamentalphysics (in the sense of, ``What are the strange particles?'') but it ismore like solid-state physics in the sense that it might tell us much ofgreat interest about the strange phenomena that occur in complexsituations.Furthermore, a point that is most important is that it would have anenormous number of technical applications.

R Feynman, CALTECH, Dec 1959

Perhaps, everything started with a talk given by R. Feynman….

Micro-Electro-Mechanical -SystemMicro-Electro-Mechanical -System MEMSMEMS

Howe & Muller 1982

First Silicon Beams

1982Fan, Tai & Muller, 1988

Spring

1988

Insect spinning on a micromotor

Fan,Tai and Muller 1989

First micromotor(1989)

QuickTime™ et undécompresseur Cinepak Codec by Radiussont requis pour visionner cette image.

QuickTime™ et undécompresseur Cinepak Codec by Radiussont requis pour visionner cette image.

100 m

Craighead (Cornell)

HOW DO WE FABRICATE A MEMS ?

Microfabrication of a membraneSi

SiOxydation

Si

Depot de resine

SiAttaque par KOHSi

Insolation

masque

Si

Ouverture et strippage

DéveloppementSi

Microfluidics = Realization and study of flows and transfers in (artificial) microsystems

1970 - 1990 : Essentially nothing (apart from the Stanford gas chromatographer)

1990 : First liquid chromatograph (Manz et al)TAS concept (Manz, Graber, Widmer, Sens.Actuator, 1991)

1990 -1998 : First elementary microfluidic systems (micromixers, microréactors, separation systems,..)

1998-2004 : Appearance of soft lithography technology, which fostered the domain. All sorts of microfluidic systems with various levels of complexity are made, using different technologies

A few milestones

First microfluidic system : Terry (1975) (Stanford)

Canal de 1.5 m long

Injection valve

Thermalsensor

Reyes et al, Anal Chem, 74, 2623 (2002)

From Agilent-Caliper

Allow to characterize DNA Fragments with excellent resolution, and in a small time

A microfluidic system for DNA separation

A system which will probably have an impact in biology

(Quake et al, Science 2002)

Chargement, compartimentageMélange, purge.

Les opérations élémentaires

LAB-ON A CHIP

DIAGNOSESHEART ATTACKWITHIN 10 MN

BIOSITE

An elementary Lab-on-a-chip

PERSPECTIVES OF MICROFLUIDICS

Microfluidics is increasingly used in an impressive number of domains

- Food industry- Chemistry- Biotechnology- Oil industry- Drug discovery

In these domains, microfluidic systems of various complexities areneeded, and the challenge is to be able to respond to these needs.Current estimates indicate microfluidic demands will grow at a fast rate over the next 5 years, generating visible economical activity

One day, we’ll perhaps receive this strange watch as a birthday gift

It is not sure however we will be capable soon tomimick a number of natural systems

The spider

The tree

FLUIDS FLOWING IN NANOMETRIC DEVICES- NANOFLUIDICS

1nm 1m100nm m

Nanofluidics

10nm 1m 10m 1mm

MicrofluidicsSinglemolecule

Two admissible definitions of nanofluidics

Definition 1 (engineer definition) :Nanofluidics deals with fluids flowing in systems whose Characteristic sizes range between 10 and 300 nm

Definition 2 (physicist definition) :Nanofluidics deals with fluids flowing in conditions where interactions between micro and macroscopic scales play acrucial role.

Some notions on the ranges of influence of Intermolecular microscopic forces

MOSY OF WHAT MOSY OF WHAT WE KNOW ON WE KNOW ON THE BEHAVIOURTHE BEHAVIOUROF SIMPLE OF SIMPLE LIQUIDS AT THE LIQUIDS AT THE NANOSCALE NANOSCALE COMES FROM COMES FROM THIS MACHINETHIS MACHINE(Tabor, (Tabor, Israelachvilii Israelachvilii ~1980) ~1980)

This is not the case for the Van der Waals forces between surfaces in the vacuum, whose extent lies in the nm range

FORCES LINKED TO THE PRESENCE OF ADSORBED LAYERS

Debye layers may have sizes comparable toSubmicrometric channels.

In the presence of an electrolyte, Debye layers develop

DEBYE-HUCKEL layers - typically 100 nmup to 1m thick in pure water

1nm 10m100nm km

Nanofluidics

10nm 1m 100m

MicrofluidicsSingleMoleculestudies

VdW force range

Fluctuation forces range

Debye layer thickness

Bubble nucleation barrier

Mean free path in gases

Thermal capillarity length Nanofluidics is a host of Many novel phenomena,Involving interactions betweenMicroscopic and macroscopic scales

BREAKUP OF A NANOJET ( NUMERICAL EXPERIMENTS)

M. Moseler, U. LandmanScience, 289, 5482, 1165 - 1169 (2000)

Microjet Nanojet

Nanojets do not behave like ordinary jets

The reason is that capillary thermal scale matters : l=(kT/)1/2

Working with negative pressures becomes feasible

Macroscopic approach generally assumes that the interfacesare infinitely thin

Laplace law

Boundary conditions

Speculating about possible effects in nanochannels

Laminar flow are not parabolic; they probe the natureof the surfaces exposed to the fluidFree interfaces behave in a strange way in nanochannelsHydrodynamic instabilities behave differentlyFabricate superfluid hydrogen.

500 nm

Nanofluidics is not just an exotic subject : we alreadyuse nanofabricated nanochannels in a number of applications

Separation of long strands of DNS by usine nanopillars (Baba et al, Univ. Tokyo)

A broad prospective on nanofluidics (from A. Van den Berg)

Physical aspects of microfluidics

1nm 10m100nm km

Nanofluidics

10nm 1m 100m

MicrofluidicsSingleMoleculestudies

VdW force range

Fluctuation forces range

Debye layer thickness

Bubble nucleation barrier

Mean free path in gases

Thermal capillarity length There exists interactions betweenmicroscopic and macroscopic scalesin microfluidic systems

Experiment by S. Chu et al (1994)

The cell and a number of its components have sizes comparable to microsystems

Cells can be manipulated individually in microfluidic systems.

PLAYING WITH CELLS ANDCONCENTRATIONGRADIENTS

Cell sorting (Quake et al, 2000)

There exist microscopic scales which are comparable to microsystem sizes

The mean free path in gases may reach micrometers

The notion of fluid particle in hydrodynamics

(According to Batchelor)

should be much smaller than the system size for ordinaryHydrodynamics to apply :

Kn=λL

<<1

Gas flow regimes

Kn0.1 0.6 20« Ordinary »hydrodynamicregime

Slip flow regime

Transitionnalregime

Rarefied gasregime

MICROFLUIDICS

Pressure sensor I

Pressure sensor O

PI

vacuum pump

Mercury column

PO

Pressurized gas tank

Variableresistance

(4)

(3)(2)

(1)

J.Maurer et al (2002)

1

2

3

4

5

6

7

8

9

0 0,2 0,4 0,6 0,8 1Kn

Théory with~ 0.9

S=12μRTLQmΔPPmwb

3

1+6Kn

S=1“Ordinary” hydrod.

Channel1.14±0.02 min heigth200 m wide

RECENT NUMERICAL SIMULATIONSINDICATE THAT ORDINARY HYDRODYNAMICS IS RECOVERED IN THE SUBMICRON RANGE

THE PHYSICS OF MINIATURIZATION

The spectacular changes of the balances of forces aswe go to small scales.

Scaling laws

Remarks

- Animal maximum speeds do not depend on the scale

- But the fluid velocity, at low Reynolds numbers, varies as the scale.

All animals run at the same speed

Lower members oscillate with a periodT ~ l

Velocity is V~l/T ~l0, size independent

A mechanical example of a scaling law

Vibration frequency of a Cantilever beam

f ≈hc

2πL2

f ~l−1

hL

At what speed does the Thyrannosaurus run ?

20 m/s ?11 m/s

J.R. Hutchintson, M. Garcia, Nature, 415, 1018 (2002)

An apparently controversial issue

Méthod 1 : Compare the exponents of the scaling laws. The smallest “wins”.

Example : Insects are easily caught by water drops

Fmusc~ l2, Fcap ~ l Fmusc << Fcap

Reasonings on the physics of miniaturization

Méthod 2 : More accurate : using theorem

Consider a physical quantity function of n other quantities a = f(a1,a2,…..an)In a system with k dimensions.We are thus dealing with n+1 quantities

The physical law reduces to a simpler expression :

=g(1, 2,…. n+k-1)

Involving n-k+1 variables instead of n+1

Example :

Hydrodynamic flows, characterized by a single scale, have a velocity field which satisfies :

u = U g(x/l,Re)Reynolds number = Ul/

As we miniaturize, the Reynolds number goes to zero, and thus one may conclude that in microfluidic systems, flows are laminar and stable.

Argument :

u(x) = f(x,U,,,l)

n+1=6k=3

On peut donc définir 6-3 nombres sans dimensions

uU

=gxl,Re

⎛ ⎝ ⎜

⎞ ⎠ ⎟

Avec Re=Ul/, le nombre de Reynolds

100 m

Analysis of a microjet

Re=Uaν

≈10 ; Ca=μUγ

≈10−2 ; Bo=ρa2gγ

≈10−3

Conclusion : le jet est laminaire (donc facilement controlable), les gouttes sont sphériques et la gravité est négligeable

Scaling laws in nature

Reasonings on scaling laws are often used to explain a number of apparently strange phenomena in nature

Thermal power lossed by conduction with the environnement, for a fixed T ~ T l

Power extracted from the digestion of the food ~ N l3

To reach a steady temperature, loss and gain must balance :l ~ (T/N)1/2

Since one cannot take an infinite number of meals per day, one cannot miniaturize mammifers at will

Smallest mammifer is ~2 cm

The smallest size of the mammifers

The shred

Smallest mammifer : The pygmee shred

2cm

Advantages being miniaturized : jump high (H~ l0),

walk on water

Disadvantage : being easily caught by a water drop

Scaling laws for the electrostatic micromotor

Small torque, small power(unless we rotate fast)

TorqueC~Fl ~l3

P=CΩ ~Ωl3

EScheme of the electrostatic micromotor

Réalisation d’un micro moteurRéalisation d’un micro moteur

Sacrificial Etching

Sacrificial Layer Structure Layer

MIT micro-turbine project

- Diameter-heigth : 12 mm/3mm- Air flow-rate : 0.15 g/s- Outlet temperature : 1600 K-Rotation speed: 2.4 106 tr/mn- Power : 16W- Weight : 1g- Fuel consumption : 7g/h

Some words….

Limits of the scaling arguments

1)- The detailed factors coming with the scaling lawsTheir analysis allows to determine the range of validity of the reasoning.

2) The spatial structure of the forces at hand.

CONCLUSIONS OF LECTURE 1

1 - Microfluidics is an interdisciplinary domain, driven by applications (existing or potential), in which interesting physics can be done

2 - Most of the phenomena taking place in microsystems can be described in a macroscopic framework; however, for a number of systems (gases, macromolecules,..) the microscopic scales interfere directly with the microsystem size.

3 - Balances of forces are deeply modified as we go from the ordinary to the micro world. Reasoning on scaling laws is a powerful approach to anticipate the changes one may expect from miniaturizing a given system.