Finite Element Simulations of the Injection Process

Charles Emrich
May 2003
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The orthogonal injection process is really what makes microdevice CE a faster and lower-volume technique it's monolithic capillary counterpart. This is because the injected volume (plug size) can be preceisely tailored by:
i) the geometry of the channels at the injection cross, and
ii) the electric fields that drive the injection process.

For typical micro-CE applications, the volume at the cross is generally in the 10-1000 pL range for channels etched from 5 to 50 microns deep. Bear in mind that this wide range of volumes from a narrow range of depths is because of the isotropic etching that is used to form the channels.

A low-volume cross injection may not always be the ideal situation, however, and electrokinetic control of the plug size can be employed to further shape the plug. Even with extremely sensitive confocal fluorescence detection systems, too small of a plug of a low concentration could yield peaks of undetectably-low intensity. This is especially true for analytes for which there is a good deal of dispersion (e.g. high D, wall interactions).

The Movies
The following simulations present some typical injections through a cross-injector and the effects of varying the electric fields and their timing.Each of the simulations was performed on the same 400 x 400 um cross. The reservoirs are as follows:
Sample - bottom, Waste - top, Cathode - left, Anode - right

Standard Pinched Injection
(no back bias)
 
Standard Pinched Injection
("full" back bias field 100% of run field)

inject: V(S) = 0, V(W) = 8, V(C,A) = 2
run: V(C) = 0, V(A) = 2, V(S,W) = float

The pinching field is 75% of the injection field.
Higher pinching fields give smaller plugs.
A large diffusional smear trails the plug absent back biasing
inject: V(S) = 0, V(W) = 8, V(C,A) = 2
run: V(C) = 0, V(A,S,W) = 2

Applying potential to the sample and waste reservoirs during
the run, draws analytes back into those channels, hence
preventing diffusional leakage into the separation column.
Movies
Movies

large (600x600)
small (300x300)

still pictures: gif archive

large (600x600)
small (300x300)

still pictures: gif archive

   
High Back Bias
( back bias field 125% of run field)
 
Too Much Back Bias
(back bias field 150% of run field)
gif animation
gif animation
inject: V(S) = 0, V(W) = 8, V(C,A) = 2
run: V(C) = 0, V(A) = 2, V(S,W) = 2.5

The plug volume decreases as the back bias field increases.
inject: V(S) = 0, V(W) = 8, V(C,A) = 2
run: V(C) = 0, V(A,S,W) = 3

The plug can't escape the cross at this back bias field.
Movies
Movies

large (600x600)
small (300x300)

still pictures: gif archive

large (600x600)
small (300x300)

still pictures: gif archive

   
Too Much Back Bias
(back bias field 200% of run field)
 
Floated Injection
(with full back bias)
gif animation
gif animation
inject: V(S) = 0, V(W) = 8, V(C,A) = 2
run: V(C) = 0, V(A) = 2, V(S,W) = 4

This back bias field fully thwarts the run field.
inject: V(S) = 0, V(W) = 8, V(C,A) = float
run: V(C) = 0, V(A,S,W) = 2,

The plug can be made significantly larger by floating C,A
during the injection. Back biasing removes the trailing edge.
Movies
Movies

large (600x600)
small (300x300)

still pictures: gif archive

large (600x600)
small (300x300)

still pictures: gif archive

   
Delayed Back Bias
(full back bias delayed 1 s)
 
High Diffusivity
(D=1e-6 cm^2/, floated injection)
gif animation
gif animation
inject: V(S) = 0, V(W) = 8, V(C,A) = 2
delay: V(C) = 0, V(A) = 2, V(S,W) = float
run: V(C) = 0, V(A) = 2, V(S,W) = 2

The plug is allowed to escape from the cross region before
back biasing can reduce its volume
inject: V(S) = 0, V(W) = 8, V(C,A) =float
run: V(C) = 0, V(A,S,W) = 2

Diffusive dispersion will broaden this wide plug, but
the effect will be small in proportion to the plug length.
Movies
Movies

large (600x600)
small (300x300)

still pictures: gif archive

large (600x600)
small (300x300)

still pictures: gif archive

   
High Diffusivity
(D=1e-6 cm^2/, pinched injection)
 
gif animation

All of these movies were created using a custom
colormap in Tecplot.

Black is zero concentration
Blue is 33% concentration
Green is 100% concentration
and a linear gradient exists between each.

Movies using the standard "small rainbow"
colormap can be found on this page
[coming soon]

inject: V(S) = 0, V(W) = 8, V(C,A) = 2
run: V(C) = 0, V(A) = 2, V(S,W) = 2

Diffusive band broadening is clearly evident for this small plug
 
Movies

large (600x600)
small (300x300)

still pictures: gif archive

 

   

Computation Details
All results were generated with Coventorware 2003. The model used has channels 400 um long (from end to end) and 20 um wide. The model was meshed at high resolution as parabolic (quadratic) hexahedra using a Manhattan algorithm (3900 elements, 49000 nodes). All simulations were carried out in 2D using the FEM solver (FIDAP) with a 0.01 s timestep, a residual tolerance of 1e-4, and solutions were output every 0.1 s. The mobile species used had a mobility of 1.5 e-4 cm^2/Vs (which is approximately that of the 1.3 kbp fragment from a HaeIII digest of phiX 174 in 1.0 w/v % HEC, with 1X TBE, and 1 uM of the intercalating dye, thiazole orange), and a diffusion constant of 1e-8 cm^2/s (effectively no diffusion) except where noted. Injection field strengths used were 200 V/cm and run fields were 50 V/cm. Run field strengths are higher (~200 V/cm) in practice but were lowered to optimize simulation conditions. Solutions of temporally-segmented simulations of "fast" moving species generally will give bad results unless the mesh density is increased, but too much of an increase can lead to solution non-convergence or datasets that are simply too large for the computer.

Movie Details
The movies were exported from the Tecplot-based viewer on Coventorware as 2000x1746 pixel AVI's encoded with the terrible Microsoft RLE codec. Each movie is recorded at 5 frames per second (fps), which is not real-time, but one-half real time (the output timestep was 0.1 s, giving a true 10 fps output). I chose to slow down the frame rate to make the movies easier to see. The movies were then cropped to a 1:1 aspect ratio and resized to 608x608 or 288x288 pixels and recompressed with the MPEG-1 codec using TMPGEnc. The MPEG format was chosen beacuse it offers high compression with low distortion, and is uniformly compatible.

Additionally, every frame from each movie is available as an archived collection of gif images ('tarballs' in Unix speak). Very old and very modern computers should be able to read these files. If you can't, you're probably wearing pleated khaki pants.

Copyright
This work can be used for educational or non-profit aims, but not without acknowledgement of the author. This work may not be reproduced in any form without written consent of the author.

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