Micro Process Engineering, Dr.-Ing. Norbert Kockmann, Slide 1

DECHEMA-KolloquiumOrganische Synthesen in

MikrostrukturreaktorenGrundlagen des Wärme- und

Stofftransports in Mikrostrukturreaktoren-

Fundamentals of Heat and Mass Transfer in Microreactors

8th November 2007

Dr.-Ing. Norbert Kockmann

Design of Microsystems, Department of Microsystems Engineering – IMTEK,

Albert-Ludwig University of Freiburg

now at: Lonza AG, CH-3930 Visp, R&D Exclusive Synthesis

Micro Process Engineering, Dr.-Ing. Norbert Kockmann, Slide 2

Contents

Introduction and motivation

Scaling and fluid properties

Fluid dynamics

Pressure loss

Heat transfer in straight channels

Heat transfer in curved channels and networks

Convective mixing in microchannels

Chemical reactions and transport processes

Conclusions

References

Intro

Fluid properties

Fluid dynamics

Heat transfer

Mass transfer

Chemical reactions

Conclusions

Fundamentals of Heat and Mass Transfer

Micro Process Engineering, Dr.-Ing. Norbert Kockmann, Slide 3

University of Freiburg, IMTEK

IMTEK: 18 professor ships

approx. 300 employees

approx. 500 students, diploma, bachelor, master

9300 m2 laboratories and bureaus

600 m2 clean room

Intro

Fluid properties

Fluid dynamics

Heat transfer

Mass transfer

Chemical reactions

Conclusions

Micro Process Engineering, Dr.-Ing. Norbert Kockmann, Slide 4

Microreactors at Lonza, Visp

Area 90 ha

Employees ~2700

Plants- Naphtha cracker- Single product, multi-productand multipurpose facilities

- Fully integrated waste management

Products- Active pharmaceutical ingredients and Biopharmaceuticals)- Vitamines (Vitamin B3 )- Peptides and oligonucleotides- …

Microreactors- pioneering work of D. Roberge- 3 modules for various reactions- GMP production

Intro

Fluid properties

Fluid dynamics

Heat transfer

Mass transfer

Chemical reactions

Conclusions

Micro Process Engineering, Dr.-Ing. Norbert Kockmann, Slide 5

Microfluidics and Micro Process Engineering

Main characteristics

small channels: dh from ca. 10 µm to 1 000 µm

cross sections: rectangular, trapezoidal, semi-circular

often laminar flow: Re < 1000

Analysis of small volumes ⇒ µTAS (micro total analysis systems)

Process design in microstructures ⇒ Lab-on-a-chip

Production of chemicals in small amounts ⇒ µVT, MPE

νhdw

=

© MicroChemTec backbone

Intro

Fluid properties

Fluid dynamics

Heat transfer

Mass transfer

Chemical reactions

Conclusions

Micro Process Engineering, Dr.-Ing. Norbert Kockmann, Slide 6

Microfluidics and Micro Process Engineering

Why micro process engineering?

Defined flow regimes and properties- mainly laminar flow- defined residence time and distribution- small hold-up

Augmented transport processes- rapid mixing- high heat transfer- flame suppression- small inertia and capacities- integrated processes and sensors

Frequently questions to be answered- Why has this device these dimensions and materials?- Why do I operate under these conditions?(temperature, pressure, concentrations, …)

- Why do I need these solvents?- Why do I need this reaction time and constellation?

Schlüter et al. 2004

Intro

Fluid properties

Fluid dynamics

Heat transfer

Mass transfer

Chemical reactions

Conclusions

Micro Process Engineering, Dr.-Ing. Norbert Kockmann, Slide 7

Length scales

typical regimes in conventional and microstructured devices

diffusion in liquids is slow

fast convective mixing

Kockmann 2007

Intro

Fluid properties

Fluid dynamics

Heat transfer

Mass transfer

Chemical reactions

Conclusions

Micro Process Engineering, Dr.-Ing. Norbert Kockmann, Slide 8

Fluid behavior

Fluid properties and control volume

Phase limits- number of gas molecules

- free surfaces- system boundaries

Batchelor, 2000

large thermal fluctuations for onlyfew molecules,

classical properties at N > 106,

fluctuations are also possible in large systems.

Kockmann 2007

Intro

Fluid properties

Fluid dynamics

Heat transfer

Mass transfer

Chemical reactions

Conclusions

Micro Process Engineering, Dr.-Ing. Norbert Kockmann, Slide 9

Properties of gases

Free mean path

Knudsen number Kn

Molecule behavior at the wall

Slip length

S.Nedea et al. 2006

ps

T

psw

Tw

rel22 2

kk

ππ==Λ

L

Λ Kn =

Knudsen number regimesKn < 0.001 continuum (sometimes 0.01 as limit)

0.001 < Kn < 0.1 rarefied gases0.1 < Kn < 10 transition regime10 < Kn free molecular regime

x/Λ

( )0

0=

⎟⎠⎞

⎜⎝⎛∂∂

==xx

wxw ζ

Λ−

≈ββζ 2

s

Intro

Fluid properties

Fluid dynamics

Heat transfer

Mass transfer

Chemical reactions

Conclusions

Micro Process Engineering, Dr.-Ing. Norbert Kockmann, Slide 10

Behavior of liquids

Number of molecules N > 106 gives cube with100 molecules on corner length: approx. 10 – 30 nm

continuum in the range of L > 1 µm

Surfaces play major roleStern layerGeneration of electricallycharged layer

electro-kinetic pumps

hydrophilic / hydrophobicWettability and surface tensioncontact angle

( )vlgL

ρρσ−

= Laplace Länge

( )vlh gd ρρσ−

=4

1

Co Confinement number

σ

L. Cheng, D. Mewes, 2006

Intro

Fluid properties

Fluid dynamics

Heat transfer

Mass transfer

Chemical reactions

Conclusions

Micro Process Engineering, Dr.-Ing. Norbert Kockmann, Slide 11

Balance equations

Overview of balance equations

Boltzmann transport equation BTE

balance equations can be derived from BTE

direct solution only possible for few special cases,Cercignani (1988), Sone (2002)

losswin 1

JJx

f F

mx

fw

t

f−=

∂∂

+∂∂⋅+

∂∂

vvv

( ) 1,11

2

dd2

1

xwffffeVw

f F

mx

fw

t

f ωσ∫ −′′⋅=

∂∂

+∂∂⋅+

∂∂ vv

vvv

Fluid dynamics models

molecular continuum

deterministic statistical Euler Navier-Stokes Burnett

MolecularDynamics

Liouville

Direct SimulationMonte Carlo

Lattice Boltzmannmodels

Chapman - Enskog

Gad-el-Hak 2006Intro

Fluid properties

Fluid dynamics

Heat transfer

Mass transfer

Chemical reactions

Conclusions

Micro Process Engineering, Dr.-Ing. Norbert Kockmann, Slide 12

Conservation Equations

continuity equation

momentum equationNavier-Stokes equations

for long straight channels in z-direction

Euler equations for η = 0, τ = 0

1122 AwAw ρρ =

0 div =+ wDt

D vρρ

( )[ ]T grad grad2

1 grad with

div3

2 grad2Div grad-gdiv

ww

wpwwtDt

wD

vvv

vvvvvvv

+=

⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −+=⎟

⎠⎞

⎜⎝⎛ +∂∂

=

w

w δηρρρ

2A

( ) ( )z

Aw

t

A

∂∂

==∂

∂ ρρ0

( ) ( ) ( )gAL

z

Ap

z

Ap

z

wAw

t

wAc ρτρρ−−

∂∂

+∂

∂−

∂∂

−=∂

∂

νhdw

=Re

Reynolds number

Intro

Fluid properties

Fluid dynamics

Heat transfer

Mass transfer

Chemical reactions

Conclusions

Micro Process Engineering, Dr.-Ing. Norbert Kockmann, Slide 13

Energy equations

First law of thermodynamics

energy equation

kinetic ansatz for pressure loss in channels

laminar flow

Vpotkin wqueee dddddd +=++=

2

, 2 iiih

ii wd

Lp

ρζλ∑ ⎟⎟⎠

⎞⎜⎜⎝

⎛+=Δ

Euler number

1212112122

22 g

2g

2ϕρρρρ

−+−+=−+ twypwypw

Intro

Fluid properties

Fluid dynamics

Heat transfer

Mass transfer

Chemical reactions

Conclusions energy dissipation 122112 ppp Δ=−=ϕ

∑ ⎟⎟⎠

⎞⎜⎜⎝

⎛+=

Δ= i

ih

ii d

L

w

p ζλρ ,

2 2

1Eu

L

w

m

V

⋅⋅

=⋅

=ρ

ϕϕε 121212

&

ih

ii d

L

,

λ

iζih

ii d

L

,

λ

ih

ii d

L

,

λ

ih

ii d

L

,

λ

iζ

iζ

iζiζ

iζ

iζ

iζ iζ

iζ

ihi

if

i

ifi dw

CC

,

,,

Re ⋅==

νλ ∑ ⎟

⎟⎠

⎞⎜⎜⎝

⎛+=Δ 2

2, 22

iiiih

if wwd

LCp

ρζηand

Micro Process Engineering, Dr.-Ing. Norbert Kockmann, Slide 14

Pressure loss

Influence on the flow resistance- transition laminar-turbulent- available flow cross section

influence on pressure loss Moody diagram

J.B. Taylor et al., 2005

Intro

Fluid properties

Fluid dynamics

Heat transfer

Mass transfer

Chemical reactions

Conclusions

typical regime

∑ ⎟⎟⎠

⎞⎜⎜⎝

⎛+=Δ 2

2, 22

iiiih

if wwd

LCp

ρζη

Micro Process Engineering, Dr.-Ing. Norbert Kockmann, Slide 15

Surface structure and texture

Fabrication processes, overview from Quinn et al. 2006

micro moldingin capillaries

Kockmann, 2006, Chap. 10, 11, 12

isotropic wet-etching of stainless steel mechanical fabrication of stainless steel Reactiv ion etching of silicon, DRIE, ASE

micro replicamolding

Intro

Fluid properties

Fluid dynamics

Heat transfer

Mass transfer

Chemical reactions

Conclusions

Micro Process Engineering, Dr.-Ing. Norbert Kockmann, Slide 16

Surface roughness or texture

Fabrication technologies- silicon etching- isotropic etching- mechanical fabrication

feasible surface roughness

J.B. Taylor et al., 2005

ε2−= hcf dD

ε

or

21 εε −−= hcf dD

Intro

Fluid properties

Fluid dynamics

Heat transfer

Mass transfer

Chemical reactions

Conclusions

Micro Process Engineering, Dr.-Ing. Norbert Kockmann, Slide 17

Transition regime

turbulent flow regimetransition depends on- surface roughness- inlet conditions

critical Reynolds number

in microchannels- high flow velocities- high pressure loss- dissipative heating

flow in bends and curves- first vortices at Re ≈ 10- secondary vortices at higher Re numbers- transient fluctuations at Re ≈ 200 - 400

W. Albring, 1988

2300 Re kritkrit ≈=

νhdw

Streak lines in tubular flow in transition regime laminar-turbulent

Micro Process Engineering, Dr.-Ing. Norbert Kockmann, Slide 18

Analytical solutions

Hagen- Poiseuille, capillary flow

flow in rectangular channelFourier series or Prandtl‘s membrane analogy

entrance flow

VdL

p

h

&4

128

πη

=ΔΔ

⎥⎥⎦

⎤

⎢⎢⎣

⎡−⎟

⎠⎞

⎜⎝⎛

ΔΔ

=4

1

4)(

22

D

rD

L

prw

η

( ) ⎟⎠⎞

⎜⎝⎛

⎟⎠⎞

⎜⎝⎛

+Δ

= ∑ yh

nx

b

m

hmbnnm

hb

L

pyxw

nm

πππη

sinsin16

),(,

22224

22

numerical (CFDRC)

analytical

0.00

0.01

0.02

0.03

0.04

0.05

velo

city

[m/s

]

0.00 0.02 0.04 0.06 0.08 0.1

channel width [mm]

Baehr/Stephan, Wärme- und Stoffübertragung, 2004

orRe056.0=h

in

d

L

164.089.0:channel

224.02.1:tubeReRe/1

21

212

1

CC

CCC

C

d

L

h

in ++

=

Intro

Fluid properties

Fluid dynamics

Heat transfer

Mass transfer

Chemical reactions

Conclusions

Micro Process Engineering, Dr.-Ing. Norbert Kockmann, Slide 19

Laminar flow in straight channels

pressure loss

channel cross section

21

,21 2

wd

Lppp

i ih

ii

ρλ ⋅⎟⎟⎠

⎞⎜⎜⎝

⎛=−=Δ ∑

96

92.56

64Re

===

=

f

fi

C

Cλ

ReifC λ=

Intro

Fluid properties

Fluid dynamics

Heat transfer

Mass transfer

Chemical reactions

Conclusions

Micro Process Engineering, Dr.-Ing. Norbert Kockmann, Slide 20

Numerical solvers

Finite Difference FD

FEM; z.B: COMSOL

Multiphysics Simulation

Polynomial function in theelement as solution function

flow and residence time in a reactor with baffles

Capillary fillingof a microchannel

Intro

Fluid properties

Fluid dynamics

Heat transfer

Mass transfer

Chemical reactions

Conclusions

Micro Process Engineering, Dr.-Ing. Norbert Kockmann, Slide 21

Numerical solvers

Lattice Boltzmann methods LBMCellular Automata

approximation of the continuousBoltzmann equation on grid points

formulation of collision term

Multiphysics simulation- turbulent flow and mixing- heat transfer- diffusion and chemical reactions

www.latticeboltzmann.com/

D3Q19: 3 dimensions, 19 points

( ) 1,11

2

dd2

1

xwffffeVw

f F

mx

fw

t

f ωσ∫ −′′⋅=

∂∂

+∂∂⋅+

∂∂ vv

vvv

summation overin- and outlet flows

www.imtek.de/simulationChen, Doolen, 1998

D3Q27: 3 dimensions, 27 points

Intro

Fluid properties

Fluid dynamics

Heat transfer

Mass transfer

Chemical reactions

Conclusions

Micro Process Engineering, Dr.-Ing. Norbert Kockmann, Slide 22

Numerical solvers

Finite Volume VOF: CFD-ACE+, Fluent, CFX, a.o.

Pro‘s and Con‘s of numerical solutions:FD, “exact“ approximation, rectangular lattice,

VOF, “exact“ approximation, various elements,

LBM, rapid method with arbitrary geometries,

FEM, multiphysics, solution depends on applied polynom.

www-ifkm.mach.uni-karlsruhe.de

Intro

Fluid properties

Fluid dynamics

Heat transfer

Mass transfer

Chemical reactions

Conclusions

Micro Process Engineering, Dr.-Ing. Norbert Kockmann, Slide 23

Channel structures, bends

laminar flow in curves and bendsDean flowgeneration of vortex pairs

pressure loss

Top view

Side view

Flowdirection

200 400 600 800 1000 12001500

2000

2500

3000

3500

4000

4500

5000

pressure at centre line inner pressure outer pressure

Pre

ssur

e [P

a]

Channel length [µm]Re = 99

21

,21 2

wd

Lppp

ii

ih

ii

ρζλ ⋅⎟⎟⎠

⎞⎜⎜⎝

⎛+=−=Δ ∑

8.12.1;Re2 1

* −===Δ⇒ nmwmp nnρ

Intro

Fluid properties

Fluid dynamics

Heat transfer

Mass transfer

Chemical reactions

Conclusions

Micro Process Engineering, Dr.-Ing. Norbert Kockmann, Slide 24

Simulation of the heat transfer in a micro channel: Constant wall heat flux, 50 W/cm2,

Single phase flow, water,

Definition of the Nusselt number:

Laminar developed flow:

Entrance flow and bend flow lead to vortices:→ Nu number increases.

Heat Transfer – Laminar Flow

( )FW

hhqq TTk

dq

k

dh

−==Nu

Tin = 300K, water, Rein = 26

dh = 100µm, water

heated areaq = 50 W/cm2

flow direction

300K

356K

q = const. → Nu = const. = 4.3

Intro

Fluid properties

Fluid dynamics

Heat transfer

Mass transfer

Chemical reactions

Conclusions

hq ≈ 25.8 kW/m2K

Micro Process Engineering, Dr.-Ing. Norbert Kockmann, Slide 25

Heat Transfer – Curved Flow

Heat transfer in a T-joint micro channelwith constant heat flux: Streamlines and temperature

fields, Rein = 155, Reout = 109,Tin = 300 K

L

dhq RePr664.0Nu 3/1=

flow direction

Heat transfer enhancementdue to vortices.

Analytical calculation fordeveloping flow consitions:

Comparison simulation - theory300K

336K

Nuq ≈ 20 → hq ≈ 120 kW/m2K

Intro

Fluid properties

Fluid dynamics

Heat transfer

Mass transfer

Chemical reactions

Conclusions

Micro Process Engineering, Dr.-Ing. Norbert Kockmann, Slide 26

Heat Transfer – Curved Flow

Microchannels with bends and joints:

Entrance flow at each bendleads to vortices:→ Nu number is increased.

Dimensionless length X+

Mean Nu number for the channel

( )6/16/1Pr432.2tanh

NuNu +=

Xm

me

X+

PrRePe ⋅==+

hh d

L

d

LX

Good agreement betweensimulation and analyticalresults.

300K

356K

Intro

Fluid properties

Fluid dynamics

Heat transfer

Mass transfer

Chemical reactions

Conclusions

Micro Process Engineering, Dr.-Ing. Norbert Kockmann, Slide 27

Channel networks

Layout acc. to Bejan‘s „constructal“ design method:- element of 0th. order

- systems setup

design of complex structures

uni-direktional

bi-direktional

but: high pressure loss

301 K

367 K

Reout = 61

detail

Intro

Fluid properties

Fluid dynamics

Heat transfer

Mass transfer

Chemical reactions

Conclusions

Micro Process Engineering, Dr.-Ing. Norbert Kockmann, Slide 28

Cross sections in channel systems

Biological structures follow a certain pattern

Murray‘s Law (also W.R. Hess, 1914)

Example: Fork-shaped structure1. Level z-Level

3/0,,

3/10,1, 2;2 z

hzhhh dddd −− ==

Constant wall shear stresses τW

Biggest resistance at the smallest parts

Stabilized flow and homogeneous flow distribution

∑= i ihh dd 3,

30,

Lungenflügel, www.uni-ulm.de/klinik/chirurgie2/ images/SPL-009.jpg

Intro

Fluid properties

Fluid dynamics

Heat transfer

Mass transfer

Chemical reactions

Conclusions

Micro Process Engineering, Dr.-Ing. Norbert Kockmann, Slide 29

Channel networks: Pressure loss

Fork-shaped device

•No influence of single branches

Conventional device

•Half of the pressureloss

T- tree device

•Has the highestpressure loss

•Wedges reduce thepressure loss by10-15%

Intro

Fluid properties

Fluid dynamics

Heat transfer

Mass transfer

Chemical reactions

Conclusions

Micro Process Engineering, Dr.-Ing. Norbert Kockmann, Slide 30

Channel networks: Heat transfer

Fork-shaped device

•Wider branches have a higher heattransfer rate

•Pressure optimized versions reducethe heat transfer significantly

•T- tree device

•More levels increase the heattransfer significantly

•Pressure optimized versions reducethe heat transfer significantly

Intro

Fluid properties

Fluid dynamics

Heat transfer

Mass transfer

Chemical reactions

Conclusions

Micro Process Engineering, Dr.-Ing. Norbert Kockmann, Slide 31

Experimental results: Comparison

Absorbed heat

•18% higher heat transfer rate at equal pumping power

•26% higher heat transfer rate at equal mass flow rate

Thermal resistance

•38% lower thermal resistance at equal pumping power

•41% lower thermal resistance at equal mass flow rates

( )Q

ATTR chipfluidchip

th &⋅−

=

k ≈ 4 kW/m2K

Intro

Fluid properties

Fluid dynamics

Heat transfer

Mass transfer

Chemical reactions

Conclusions

Micro Process Engineering, Dr.-Ing. Norbert Kockmann, Slide 32

Overview mixing principles

Mixing in microfluidics byadvection, convection, and diffusion

Main goal: reduction of diffusion length

Control of striation thickness

Mixing Principles

diffusive

2/1)( tDx ∝

laminar turbulent

chaoticadvection

herringbonetype

SAR split & recombine

impingingjet

convectivelaminar

02 dx n−∝

Interdigitalmeanderchannel

Focus mixer

lamellar width

lamellaeengineering

geometry& flow repetition

geometry &flow momentum

distributive convective

injectionmixer

acc. Nguyen, Wu, 2005

4/1)/( εν∝x

ReM = 0.01

ReM = 1000

Intro

Fluid properties

Fluid dynamics

Heat transfer

Mass transfer

Chemical reactions

Conclusions

Micro Process Engineering, Dr.-Ing. Norbert Kockmann, Slide 33

Mixing in sharp 90° bend

Simulation: streamlines and concentration fields► 90° sharp bend (100×100 µm2)► Re = 99, w = 0,85 m/s► Re > 10 vortex generation

residence time:u

ltP =

diffusion time:( )

D

d

D

dtD 82

2/ 22

==

l

d

l

d

t

t

P

D

8

PeScRe

8=⋅=

Pe

1

ScRe

1=∝α

2/1

2ReDn ⎟

⎠⎞

⎜⎝⎛=

R

dhDean numberD

ν=ScSchmidt number

0.01 0.1 1 10 1000

5

10

15

20

25

30

35

40

L100x100 L200x200 L500x500 L200x50 L500x50

Mix

ing

Qua

lity α

[%]

Reynolds Number Re [-]

At 1000µm channel length

500µm

100µm

0 µm

C = 1

0

Inlet

Intro

Fluid properties

Fluid dynamics

Heat transfer

Mass transfer

Chemical reactions

Conclusions

Micro Process Engineering, Dr.-Ing. Norbert Kockmann, Slide 34

Channel structures, T-mixer

transient flow in T-shaped micromixersgeneration of vortex pairs and vortex shedding, wake flow

symmetrical mixing 1:1

asymmetrical flow for Re > 140

periodic vortex pulsation for 240 < Re < 400

quasi-periodic pulsation for 400 < Re < 500

chaotic pulsations for 500 < Re < 1000 (min.)

0 140 Re240

straightlaminar

Dean vortex

EngulfmentS-vortexsteady

400 ?

turbulent

aperiodic,chaotic

vortex generation

10 500

quasi-periodicvortex

pulsation

S-vortexperiodicpulsation

1000

Intro

Fluid properties

Fluid dynamics

Heat transfer

Mass transfer

Chemical reactions

Conclusions

Micro Process Engineering, Dr.-Ing. Norbert Kockmann, Slide 35

Transient flow regimes

transient flow regimes in T-mixers, rectangular cross sectiontypical frequencies

Influence on mixingMixing quality

~ 500 Hz for T600x300x300, dh = 400µm~ 4500 Hz for T200x100x100, dh = 133µm

0

100

200

300

400

500

600

700

800

200 250 300 350 400

Re

f / H

z

Re = 300, channel depth 300 µmmixing channel width 600 µmf = 440 Hzfluorescence color Uranin

2.0Sr Zahl-Strouhal h ≈⋅

=w

df

2max

2 /1 σσα −=

Intro

Fluid properties

Fluid dynamics

Heat transfer

Mass transfer

Chemical reactions

Conclusions

Micro Process Engineering, Dr.-Ing. Norbert Kockmann, Slide 36

Mixing regimes: Influence on the mixing quality

Mixing quality (after 2 mm) depending on Re:

– straight laminar und vortex flow: residence time is important

– Engulfment and periodic pulsation: lamellae generation

– chaotic flow: separation interface with bursts

100080060040020010010.01

1

0.8

0.6

0.4

0.2

0

ReRe (log)

α

α mean

α min

α max

Intro

Fluid properties

Fluid dynamics

Heat transfer

Mass transfer

Chemical reactions

Conclusions

Micro Process Engineering, Dr.-Ing. Norbert Kockmann, Slide 37

Results from chemical reactions

Mixing in T-shaped device

unsteady flow behavior in micromixers

mixing in convective mixers

particle precipitation BaSO4

parallel-competitive reaction

comparable behavior in precipitation and chemical reaction

advanced devices necessary

good mixing

Re = 300T600x300x300

Re = 300T600x300x300

Intro

Fluid properties

Fluid dynamics

Heat transfer

Mass transfer

Chemical reactions

Conclusions

Micro Process Engineering, Dr.-Ing. Norbert Kockmann, Slide 38

Channel structures, mixer

Cyclone

Vortex mixer

Tesla valve, fluidic oszillator

cyclone insert, FZK, Germany

www.imt.tu-bs.de

www.ltf-gmbh.de

Intro

Fluid properties

Fluid dynamics

Heat transfer

Mass transfer

Chemical reactions

Conclusions

Micro Process Engineering, Dr.-Ing. Norbert Kockmann, Slide 39

Channel structures, axial dispersion

mean residence time, plug flow

axial dispersion by diffusion and laminar convection

Bodenstein number Bo

residence time distribution

z

cADJ axn ∂∂

−=2

2

z

cD

z

cw

t

cax ∂∂

+∂∂

−=∂∂

2*

*2

*

*

*

*

Boz

c

z

c

t

c

∂

∂+

∂∂

−=∂∂

axD

Lw ⋅=Bo

wLtP /=

mD

hmax DC

dwDD

⋅+=

22

210192 −≈DC

Intro

Fluid properties

Fluid dynamics

Heat transfer

Mass transfer

Chemical reactions

Conclusions

Micro Process Engineering, Dr.-Ing. Norbert Kockmann, Slide 40

Chemical reactions in continuous flow

reaction rate

chemical reaction with diffusion and convection

typical time scales- reaction time

- residence time

- diffusive mixing time

time scale ratio is expressed by Damköhler numbers

∏

∑

±=

⋅=⋅=−

i

mijj

jj

ijmiii

ickr

rVRVnn

with

0, νρ&&

∑ ⋅+∂∂

+∂∂

−=∂∂

jjijax r

z

cD

z

cw

t

c ν2

2

kr

ct

i

iR /1~

υ=

w

Lt RP =

( )mm

D D

b

D

bt

82

2/ 22

==

L

b

x

z

y

h

„turbulent“ micro mixing2/1

3.17 ⎟⎠⎞

⎜⎝⎛=εν

Et

Intro

Fluid properties

Fluid dynamics

Heat transfer

Mass transfer

Chemical reactions

Conclusions

Micro Process Engineering, Dr.-Ing. Norbert Kockmann, Slide 41

Characteristic times of reaction and transport

reactions and mass transfer- residence time

- diffusive mixing time

design criteria

reaction heat ΔHr and heat transfer- heat capacity of fluids

- convective heat transfer

design criteria

DaII

DaI

2

==

==

mi

hi

R

m

i

i

R

P

Dc

dr

t

twc

Lr

t

t

ν

ν

DaI > 1 complete reactionDaII < 1 fast mixing, „pre-mixed“ reaction

DaIII ~ 1 isothermal reactionDaIV < 1 mitigation of hot spots

DaIV

DaIII

2

=Δ

Δ

=ΔΔ

Ww

hrm

zp

rm

T

drH

wTc

LrH

λρρρ

Intro

Fluid properties

Fluid dynamics

Heat transfer

Mass transfer

Chemical reactions

Conclusions

Micro Process Engineering, Dr.-Ing. Norbert Kockmann, Slide 42

Summary

Why micro process engineering?

Scaling and fluid behavior

Laminar flow regime and vortex generation

Channel elements

Microfluidic devices withchemical reactions

Intro

Fluid properties

Fluid dynamics

Heat transfer

Mass transfer

Chemical reactions

Conclusions

Micro Process Engineering, Dr.-Ing. Norbert Kockmann, Slide 43

Thanks to

Funding by the DFG (German Research Foundation) in the

Priority program SPP1141 „Strömungsmischer“

Research project „Effective micromixer“

Thank You for Your Attention!

Funding by Country Baden-Württemberg

„Integrated Processes with Microreactors“

Many of the presented results have been funded and supportedby the following organizations:

Lonza AG, Visp, R&D Exclusive Synthesis

Intro

Fluid properties

Fluid dynamics

Heat transfer

Mass transfer

Chemical reactions

Conclusions

Micro Process Engineering, Dr.-Ing. Norbert Kockmann, Slide 44

Literature

Textbooks and MonographsG.K. Batchelor, An Introduction to Fluid Dynamics, Cambridge University Press, 2000

P. Tabeling, Introduction to Microfluidics, Oxford University Press, 2005

N. Kockmann, Transport Phenomena in Micro Process Engineering, Springer, 2007

N. Kockmann (Ed.), Micro Process Engineering, Wiley-VCH, 2006

J.J. Brandner et al., Microfabrication in Metals and Polymers, Chap. 10 in Micro Process Engineering, N. Kockmann (Ed.), Wiley-VCH, 2006

O. Tonomura, Simulation and analytical modeling for microreactor design, Chap. 8 in Micro Process Engineering, N. Kockmann (Ed.), Wiley-VCH, 2006

F. Goldschmidtböing et al., Silicon microfabrication for microfluidics, Chap. 11 in Micro Process Engineering, N. Kockmann (Ed.), Wiley-VCH, 2006

Y. Sone, Kinetic theory and fluid dynamics, Birkhäuser, 2002

C. Cercignani, The Boltzmann equation and its applications, Springer, 1988

M. Gad-el-Hak, The MEMS Handbook, CRC Press, 2006

A. Bejan, Shape and Structure, from Engineering to Nature, Cambridge University Press, 2000

H.D. Baehr, K. Stephan, Wärme- und Stoffübertragung, Springer, 2004

W. Albring, Angewandte Strömungslehre, Akademie-Verlag, 1988

Micro Process Engineering, Dr.-Ing. Norbert Kockmann, Slide 45

Literature

Journal and conference papersM. Schlüter, M. Hoffmann, N. Räbiger, Theoretische und experimentelle Untersuchun-gen der Mischvorgänge in T-förmigen Mikroreaktoren – 2: Experimentelle Untersu-chungen des Strömungsmischens, Chemie-Ingenieur-Technik 76 (2004) 1682-1688

N. Kockmann, M. Engler, P. Woias, Theoretische und experimentelle Untersuchun-gen der Mischvorgänge in T-förmigen Mikroreaktoren – 3: Konvektives Mischen und chemische Reaktionen, Chemie-Ingenieur-Technik 76 (2004) 1777-1783

S. Nedea et al. Density distribution for a dense hard-sphere gas in micro/nano-channels: Analytical and simulation results, J. Comp. Physics 219 (2006) 532–552

R.W. Barber, D.R. Emerson, Challenges in Modeling Gas-Phase Flow in Microchannels: From Slip to Transition, ICNMM2005-75074, 2005

J.B. Taylor, A.L. Carrano, S.G. Kandlikar, Characterization of the Effect of SurfaceRoughness and Texture on Fluid, ICNMM2005-75075, 2005

L. Cheng, D. Mewes, Review of two-phase flow and flow boiling of mixtures in smalland mini channels, Int. J. Multiphase Flow 32 (2006) 183-207

E.V. Rebrov et al. Header Design for Flow Equalization in Microstructured Reactors, AIChE J. 53 (2007) 28-38

S. Chen, G.D. Doolen, Lattice Boltzmann Method for Fluid Flows, Annu. Rev. FluidMech. 30 (1998) 329-364

G. Hetsroni, A. Mosyak, E. Pogrebnyak, L.P. Yarin, Fluid flow in microchannels, Int. J. Heat Mass Transfer, 48 (2005) 1982-1998

D.J. Quinn et al. A Systematic Approach to Process Selection in MEMS, J. MEMS 15 (2006) 1039-1050

Micro Process Engineering, Dr.-Ing. Norbert Kockmann, Slide 46

Length scales

typical regimes

micro structures enlarge the process spaceon small length scales, the behavior of single atoms ormolecules becomes importantfluid properties may change!

Kockmann 2006

Intro

Fluid properties

Fluid dynamics

Heat transfer

Mass transfer

Chemical reactions

Conclusions

Micro Process Engineering, Dr.-Ing. Norbert Kockmann, Slide 47

Typical dimensions, where pulsations do occur?

periodic fluctuations at 240 < Re < 400

typical frequencies of 500 Hz, Sr ≈ 0,2

typical channel dimensions 100 < dh < 1000 µmfor water at 20 °C

Re number

frequency [Hz]turbulence

low frequencies

Intro

Fluid properties

Fluid dynamics

Heat transfer

Mass transfer

Chemical reactions

Conclusions

high frequencies