AN INTRODUCTION TO MICROFLUIDICS : Lecture n°2

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AN INTRODUCTION TO MICROFLUIDICS : Lecture n°2. Patrick TABELING, [email protected] ESPCI, MMN, 75231 Paris 0140795153. Outline of Lecture 1. 1 - History and prospectives of microfluidics 2 - Microsystems and macroscopic approach.

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AN INTRODUCTION TO

MICROFLUIDICS :

Lecture n°2

Patrick TABELING, [email protected]

ESPCI, MMN, 75231 Paris

0140795153

Outline of Lecture 1

1 - History and prospectives of microfluidics

2 - Microsystems and macroscopic approach.

3 - The spectacular changes of the balances of forces as

we go to the small world.

Outline of Lecture 2

- The fluid mechanics of microfluidics

- Digital microfluidics

Fluid mechanics of

microfluidics

Reynolds numbers are small in microsystems

Re = Ul/n ~ l2

One thus may think in the framework of Stokes equations

Microhydrodynamics

Stokes regime : inertial terms are neglected

Acceptable approximation in most case. Exceptions are

Micro-heat pipes and drop dispensers

Let us reverse U

-U

If it is a Stokes solution, arrows must be inverted

everywhere

Because if we reverse U

-U

We obtain a non plausible streamline pattern

Experiment

Performed by

O Stern (2001)

Darcy law governs Hele Shaw cells

In a Hele Shaw cell, flows are potential

An important notion : the hydrodynamic resistance

Increases as the system size decreases

Analogy with electrokinetics

Another important notion : the hydrodynamic capacity

Deformable tube :

dP=k-1 dV/V

Example :

Volume V

Pressure P

Now Qm=rdV/dt

Thus Qm=mkdP/dt and hence C=km

U

uc(t)

up(x,t)

The bottleneck effect

The expression

Response : C=m/E=πD2Lr/4E et R=12nl/b3w

with t=RC

Experiment in a microchannel, 1.4 mm deep

Expérience effectuée au MMN (2001)- Matthieu Cécillon

Because to reach a steady state, it takes a time t equal to

t ≈ RC then t ≈ kmR

One must avoid dead volumes, bubbles, etc..

A PDMS actuator, based on Multi-layer Soft Lithography

Actuation channel

Glass slide

Working channel

PDMS

A. Unger, H-P. Chou, T. Thorsen, A . Scherer et S. R. Quake, Science, 288, 113, (2000).

VC

R

R

From the electrical point of view, pneumatic actuators are

represented by a capacitance/non linear resistance system .

They are not just diodes

Non linear

resistances

R=f(VC)

J.Goulpeau, A. Ajdari

P. Tabeling,J. Appl.Phys.

May 2005

No actuation : Large localized gradient

Actuation : Producing different

by changing the actuaction

parameters

Mechanical actuators dedicated to the generation of concentration gradients

Passive concentration

The same, using mechanical

actuators

(1)Jeon et al, Nature Techn., 20, 826 (2002))

ELECTRICAL REPRESENTATIONS OF ELEMENTARY ACTIVE SYSTEMS

Mixer - Extractor

Microdoser

Mixer

Microdoser

Integrated actuators can be used to make progress in the realization of complex systems : an example is a chip for proteomics

The slip length

z

u

Navier Boundary Conditions

Slip length (or extrapolation length)

Pressure drop with a slip length

DP

Flow rate Q

Depth b

Slip length LS

Two or three things important

to know in microfluidics

Laplace’s law

S

R

V

At mechanical equilibrium : dE=0

Bubble

Capillary phenomena are important in microsystems

Pressure drops

caused by capillarity

are ~ l-1 while

those due to

viscosity behave

like l0

THE PATTERNS WHICH DEVELOP IN “ORDINARY” TWO PHASE FLOWS

…OFTEN PRODUCE COMPLEX MORPHOLOGIES; THIS IS DUE

TO HYDRODYNAMIC TURBULENCE

IN MICROFLUIDIC SYSTEMS, WE OBTAIN MUCH SIMPLER

MORPHOLOGIES : ESSENTIALLY DROPLETS

Laure MENETRIER, 2004

Wetting are exceedingly important in microsytems

3 cases

Complete wetting

Partial wetting

Desorption

S>0 complete wetting

S<0 partial wetting or desorption

When S is non homogeneous, droplets spontaneously

move on the surfaces

qA<qB

Good wetting (S ≈ 0)

Poor wetting (S <0)

Wetting properties of the walls are

important in microfluidic multiphase flows

Oil with or without surfactant (Span 80)

Water

Water

R Dreyfus, P.Tabeling, H Willaime, Phys Rev Lett, 90, 144505 (2003))

NICE DROPS CAN BE PRODUCED

IN MINIATURIZED SYSTEMS IN COMPLETE WETTING CONDITIONS

200mm

When oil fully wets the surface

Oil flow rate

(L/min)

Isolated water drops

Stratified regime

Pear necklace

Large-pearl necklace

Pears

Coalescence

Pearl necklace

Water flow rate (L/min)

WHEN THE FLUIDS PARTIALLY WET THE WALLS

Oil flow-rate (mL/mn)

Water flow-rate (mL/mn)

(R Dreyfus, P.Tabeling, H Willaime, Phys Rev Lett (2003))

Rayleigh instability is the most

important instability to be aware of

Surface energy of a column

d

Surface energy of N spherical droplets

l

UNSTABLE

Applications :Digital microfluidics

- Liquid liquid flows are used in microsystems, in several circumstances.

Producing drops of one liquid into another liquid

so as to generate emulsions, or perform screening

Producing bubbles in a microchannel flow so as

to increase heat exchange, or simply because the

liquid boils.

Digital microfluidics

1 - In air

2 - In a liquid

The drop moves in air over a flat surface

The drop moves in a liquid

in a microchannel

Digital microfluidics is interesting for chemical

analysis, protein cristallization, elaborating novel emulsions,…

Ismagilov et al

(Chicago University)

AN EXAMPLE OF AN INTERESTING PROBLEM : REDUCING THE DROP SIZE OF AN EMULSION BY USING DIGITAL MICROFLUIDICS TECHNOLOGY

10mm

Suppose we are willing to reduce the drop size of an emulsion

One possibility is to cut the drops one by one

in a microfluidic system

Water drop

10mm

U

L0

u

DIFFERENT REGIMES, FOR INCREASING SIDE FLOWS

WHITE = WATER DROP, BLACK (IN THE CHANNEL) = HEXADECANE

To break or not to break

Curve

suggested by

the theory

(Navot, 1999)

BREAKING

VS

(mm/s)

NON

BREAKING

0 1 2 3 4 5 x102

Lf (mm)

Laure MENETRIER, 2004

Side where the contact angle

is smaller

qA<qB

Électrode

+V

qB=qA +1/2CV2

AN IMPORTANT PART OF DIGITAL MICROFLUIDICS

IS BASED ON ELECTROWETTING

Liquid-liquid flows in microsystems may be used to produce

well controlled drops, emulsions,…

… provided the wetting properties of the exposed surfaces,

with respect to the working fluids, are appropriately chosen.