©2007 Waters Corporation

Simulation of chromatographic band transport

Bernard Bunner, Antoni Kromidas, Marianna Kele, Uwe Neue

Waters Corp

October 10, 2008Boston Comsol Conference

Presented at the COMSOL Conference 2008 Boston

©2007 Waters Corporation 2

Outline

1. About chromatography2. Detector cell: Band transport in open fluid

→ Navier-Stokes + convection-diffusion

3. Microfluidic chip: Band transport in a packed bed:+ Darcy’s law

4. Thermal effects in 2.1 mm column+ heat equation

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What is chromatography?

Pass a mixture of chemical species dissolved in a liquid mobile phase through a stationary phase physically located in a column

Depending on chemical affinity of the different species with the stationary phase, they elute at different times ⇒ separation

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An HPLC system

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Detector

0.0025” Ø0.005” Ø

200 um Ø200 um Ø

flow in

geometry mesh

flow out

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Governing equations

Incompressible Navier-Stokes

Convection-diffusion for analyte band

numerical vs physical diffusion

uuutu

2. ∇=∇+∂∂ µρρ

CDCutC 2. ∇=∇+∂∂

t

inlet

outlet

2inσ 2

outσ

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Velocity field

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Band transport

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Transport in a packed bed

Solvent: Darcy’s law

superficial velocity

permeability void fraction

Solute:

linear velocity

evolution of concentration

effective diffusion coefficient

plate height (Van Deemter)

02 =∇ P

( )232

1180 εε−

= pdk

PkUs ∇−=µ

tot

m

VV

=ε

CDCutC

eff2. ∇=∇+

∂∂

t

sUuε

=

2uHDeff =

( ) uDd

uDduH

mol

pmolp 6

5.12

++=

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Microfluidic chip: inlet/outlet vias

Dvia 500 um

75 um

25 um

bed

fluid

t=0

t=22.5 s

t=20 s

t=17.5 s

t=15 s

t=12.5 s

t=10 s

t=5 s

t=0.5 s

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Microfluidic chip: inlet/outlet vias

0

5

10

15

20

25

50 100 150 200 250

Dvia (um)

Hef

f (um

)

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Microfluidic chip: bends

6.75

7

7.25

7.5

7.75

8

0 0.5 1 1.5

R (mm)

Hef

f (um

)

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Thermal effects in 2.1 mm columns

2.1 mm ID columnpacked with

1.7 um particles

retainingfrit

retainingfrit

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Temperature field

adiabatic BCs

∆Tmax=16.6 K

isothermal BCs

∆Tmax=1.7 K

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Performance

Heating and the temperature dependence of viscosity and diffusion coefficient can combine to create a significant drop of performance

0

2000

4000

6000

8000

10000

12000

14000

0.000 0.200 0.400 0.600 0.800 1.000 1.200 1.400

Q (ml/min)

N adiabaticisothermal

©2007 Waters Corporation 16

0

2000

4000

6000

8000

10000

12000

14000

0.000 0.200 0.400 0.600 0.800 1.000 1.200

Q (ml/min)

plat

e he

ight

no artificial diffusiond_id=0.01

Concluding remark

Effect of artificial and numerical diffusion in convection-diffusion problems: