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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