simulation of chromatographic band transport · 2008/10/10 · ©2007 waters corporation...
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©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
©2007 Waters Corporation 3
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
©2007 Waters Corporation 4
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
++=
©2007 Waters Corporation 10
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
)
©2007 Waters Corporation 12
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
©2007 Waters Corporation 15
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:
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