Mitglied der H
eelmholtz-G
emeinschaft
Chemical ReactionsChemical Reactions in a µ-fluidic T-Sensor: Numerical Comparison of 2D and 3D Models
15 October 2009 | Remo Winz
Presented at the COMSOL Conference 2009 Milan
The Cµ Research Group
Why Cµ was formed: focus & merge expertise (chemistry, microsystems)
Cµ mission: explore chemical processes under develop of intelligent microsystem devices
e.g. for lab-on-chip technology.
5cmLab-on-Chip Systems:y
Combining fluidic parts with (electro-) analytical ones
14 July 2009 Slide 25cm
Fluidic Microchip, by Cμ-team Prof. Dr. M. Böhm, Nov. 2005
Content Introduction Cµ & Lab-on-Chip T-Sensor T Sensor 3D Model and 2D Projections
Implementation Implementation System Equations Special requirements in 2D case
Numerical considerations in Comsol
Comparison 2D / 3D
Conclusion & Outlook
14 July 2009 Slide 3
Conclusion & Outlook
3D T-Sensor with Reaction
Sensor Overflow
Adsorption atSensor
Concentration q
ores
cenc
e
q
Fluo
Wavelength(nm)
14 July 2009 Slide 4
Sensor Design
DiffusionA
Sensor
New sensor design
y
New sensor design
Signal
occu
panc
y
60%
80%
Inte
gral
o20%
40%
14 July 2009 Slide 5
Liquid phase concentration10 100 1000
Projections from 3D to 2DP j ti P
P2
Projection P1:
P1
Molecules are adsorbed
A Bx
yz
Sensor Load:
P1x
z
P2x
y
14 July 2009 Slide 6
x
Winz et. al. [2007]
The Mathematical Model
Navier Stokes Convection & Diffusion Langmuir Kinetic
Convection
Functionalized SurfaceVelocity Profile
Convection
Concentration Plug
DiffusionAdsorption
DV P V FDt
cV
qkqqckdtdq
desads )( max
Functionalized SurfaceVelocity Profile Concentration Plug
c V c D c St
( )c
dt
dtdqS
Diffusion: 0.45e-9 m²/s Inlet Concentration: 1e-3 mol/m³Diffusion: 0.45e-9 m²/s Inlet Concentration: 1e-3 mol/m³
14 July 2009 Slide 7
Velocity: 6.6e-4 m/s Receptors density: 3.32e-6 mol/m²Adsorption: 4.4e4 m³/mol/s ≈ 2 rec./nm²Desorption: 1e-1 1/s Degrees of Freedom: ~ 650.000 (P2)
Velocity: 6.6e-4 m/s Receptors density: 3.32e-6 mol/m²Adsorption: 4.4e4 m³/mol/s ≈ 2 rec./nm²Desorption: 1e-1 1/s Degrees of Freedom: ~ 650.000 (P2)
Reaction, Film Diffusion and Adsorption
Reaction EquationReaction Equation
CcN N
B r
N
N
N
NZn
N N
B r
N
N
N
NZn
Film DiffusionFilm Diffusion
BAreactC cckt
c
kreact
N N
N
N
N
NZn
N N
N
N
N
NZn
2+Zn
)( fCfilmf cckt
c
N N
B r
N N
Z n2+
N N
B r
N N
Z n2+
kfilm
N N
N
N
N
NZn
Ligand
N N
N
N
N
NZn
Fluorescent Sorption KineticSorption Kinetic
NNN
N N
Br
N
N
N
NZ n
Z n
NNN
B r
Z n2+
C86H73BrN6Zn2
NNN
N N
Br
N
N
N
NZ n
Z n
NNN
B r
Z n2+
C86H73BrN6Zn2
kads
qkqqckdtdq
desfads )( max
14 July 2009 Slide 8
SS SS
kdesReceptor Adsorption Desorption
Numerics & Implementation
Refined mesh in the region of strong kinetics
Aim: Receive a stable and precise solutionAim: Receive a stable and precise solution
Refined mesh in the region of strong kinetics
Fluid Flow
Quad mesh better suited forlongitudinal flow Fluid Flow
Numerical stabilization techniques
nce
ntra
tion
cent
ratio
n
Add artificialdiffusion
14 July 2009 Slide 9x
Con
xCon
c
Direct vs. iterative Solvers
Solvers: PARDISO and GMRES (with ILU precond.) Computational Times: GMRES increasingly slow Accuracy: negligible influence Accuracy: negligible influence
14 July 2009 Slide 10
Numerical Considerations:Time Discretization
Computation Times
fixed time steps increasing effort
Accuracy 10%
1% 10% 10%
compared with‘best’ solution
1%
0.1% 1%
0.1%
1%
0.1%
no significantimprovement
major error at plug
14 July 2009 Slide 11
j p g
Numerical Considerations:Space Discretization
Computation Times
variable time steps
Accuracy 10%
1% 10% 10%
compared to nextrefined solution
1%
0.1%
%
1%
0.1%
10%
1%
0.1%
better at plugs improvement on
refinement steps
14 July 2009 Slide 12
p
OutlookInlet Compound ACompound A
S
Diffusion Zonepossible: Reaction
Sensorwith Receptors
Fluid Flow
Outlet
panc
y
80%
New sensor design
Inlet Compound B
Signal
egra
l occ
u
20%
40%
60%
14 July 2009 Slide 16Liquid phase concentration
Inte 20%
10 100 1000
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