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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

Mean Sensor Load 3D Simulation

14 July 2009 Slide 13

Mean Sensor Load 2D Simulation

14 July 2009 Slide 14

Adjusting kf

14 July 2009 Slide 15

time time

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

14 July 2009 Slide 17

Comparison of Comsol and deal.II

Comsol Model Streamline diffusion used

deal.II Model uses Upwind scheme fi d i i fixed time stepping

Concentrations Concentrations < 0.1 % of cmax dropped

Comparison of

14 July 2009 Slide 18

concentrations