18.Electrophoresis and
Magnetohydrodyanamics:
Lab on a Chip
Streaming Potentia
Micro-electromechanical systems
goal- “Lab on a chip” integrated sensors and measurements
Based on variety of phenomena that operate at the macro scale
And can be applied at the microscale, but where the application
Results in altered mathematical descriptors because of the small
Spatial arrangement.
Here we will look at only Two aspects of microfluidics:
1. Electrokinetically driven liquid micro flow
2. Magnetically altered electrochemical microflows
J  kC gradient 
Flux is moles/Area-time
It is equal to some constant x conc. X
gradient
Flux due to migration
J mi
d
d
 ui Ci
 ui* Ci
dx
dx
J mi  electrophoretic flux
  tortuosity
  porosity
ui*  effective electrophoretic mobility
The whole volume is not pore space
The distance is tortuous
Ions migrating pull with them their water
Anode
Vapp
Charged Surface
Yo
Jm
+
+
+
+
+
+
+
+
X=0
+
Jo
Jm
Cathode
+
Movement of ions: electroosmotic velocity of
solution
eo 
a f (o )

f is a function
Based on shape
ueof 
eo  electroosmotic solution velocity
  applied electric field
  zeta potential
  solution vis cos ity
(  o )

Electroosmotic mobility
Electrosmostic Flux (carried by solution moving due to ions)
Jeo,i  ueoCi
J eo ,i
 d
Cw
Ci
 d
Ci
d

o

ke
dx Cw
 dx Cw
dx
Ci
d

ke
Cw
dx
where
o  ke
Flux due to migration
J mi
d
d
*
 ui Ci
 ui Ci
dx
dx
J mi

J eo
u '* Cw
j
ke

u *j
ke
u *j
ke

2 o 

3
 o
 2

3
J mi

J eo
u '* Cw
j
ke

u *j
ke
Data is for soils
Table 3: Relative migration and electroosmotic fluxes
Species
uj * (cm2 /V s)
ke
Jmi/Jei
H+
7.6x10-4
Na+
1.09x10-4
1.1x10-4
0.99
Ca2+
1.3x10-4
Cd2+
61.55x10-4
0.1x10-4
15.5
Pb2+
1.88x10-4
0.1x10-4
18.8
0.1 m apply 10 V
eo 
a f (o )

Assume f = 2/3
Calculation of electroOsmotic flow in a soil
with 10 V applied 0.1 m apart:
V
  100
m
C
 o  10
Vm
9
  10
3
kg  s
m  s2
  10mV
C 
V


2109
0
.
01
V
100







2o
V m
m
7 CVs
v

 6.6 x10
3
kg  m
 3 kg 
310


m  s
Typical
values
Potential
At the shear
Plane of
A soil colloid
V
 9 C 

210
 0.01V 100 


2o
CVs
V  m
m
v

 6.6 x107
kg 
3
kg  m

3103


m  s
CV  J 
kg (m2 )
s2
kg (m2 )
6.6 x10 7
s
2
CVs
cm
7
7 m
s
 6.6 x10
 6.6 x10
6
kg  m
kg  m
s
day
Solution will move through soil (in presence of 100 V/m) at
A rate of 6 cm/day.
Electrode Reactions to carry the current

2 H2 O  2e  2OH  H2( gas)

2 H2 O  4 H  4e  O2( gas)
++ H+
Mobilities
Species
uj* (cm2 /V s)
H+
7.6x10-4
Na+
1.09x10-4
Ca2+
1.3x10-4
Cd2+
61.55x10-4
Pb2+
1.88x10-4
Cathode
Anode
OH-
Pb2+
Precipitation reaction
Pb2   2OH   Pb(OH ) 2
-
Electroosmotic flow used for
Electrospray ionization Mass Spec
+
Electron transfer reactions may
Occur if the Electrode potentials
Are large: this can create positive ions which move into the mass spec
Since the system is an electrochemical
One – the radicals, cations, etc. produced
Can be attacked and/or stabilized by the solution
(remember the Gutman donor/acceptor values?)
Here the solvent CH2CN
Is nucleophilic and attaches
Itself to the metal complex
Another way to get
Ions for the mass
Spec is to allow
Electrochemical
Reactions with donors
And or acceptors
TMPD can be used as
A donor for PAH, while
Dicyanodichloroquinone
DDQ is used as an
acceptor
Nice exam question,
Why?
Capillary Electrophoresis
eo 
a (  o )

Flow is a “plug” which does not have the capillary drag
At the edges so it gives much cleaner (less peak broadened)
Separations.
Pressure
As driving
force
ElectroOsmotic
flow
To get movement of a neutral analyte incorporate into
A micelle; modulate the charge on the micelle using
pH
zi e
u
6r
a (omicelle ) f a (ocapillary )
micelle  ep  eo 



Where f is the shape function
Lab on a Chip Electrophoresis
J. Wang, M. Pumera / Talanta 69 (2006) 984–987
Fig. 1. Microchip system for FIA with
electrochemical detection: (a) run buffer
reservoir, (b) sample reservoir, (c)
unused/second sample reservoir, (d)
detection
reservoir, (e) platinum cathode for FIA, (f)
Ag/AgCl wire reference electrode,
(g) platinum counter electrode and (h)
detection electrode.
Vickers, Electrophoresis, 2005
Goal use electrochemical detectin
For a miniature electrochemical separatin
Device, requires decoupling of the
Hold
Detection
current from the separation sys
At ground
for separation
Lab on a Chip Stripping Analysis
Large volume
Small volume
Emily A. Clark and Ingrid Fritsch, Factors influencing redox
Magnetohydrodynamic-induced convection for enhancement of stripping
analysis Anal. Chem. 2006, 78, 3745-3751
Small volume
Smaller enhancements in the small volume system using a permanent
magnet
Emily A. Clark and Ingrid Fritsch, Factors influencing redox
Magnetohydrodynamic-induced convection for enhancement of stripping
analysis Anal. Chem. 2006, 78, 3745-3751
Use of magnetic fields to drive enhanced flux

F Lorentz




  J   B


Deposit large number of ions into mercury NOT of interest to generate
A large flux, J, to the surface.
If done in the presence of a magnetic field (B)
Then you get a lorentz force (N/m^3) on the charge carrying ions which
Operates by the right handed rule to generate a magneto hydrodynamic
Convection toforce soluton to the surface.
Emily A. Clark and Ingrid Fritsch, Anodic Stripping Voltammetric
Enhancement by Redox Magnetohydrodynamics Anal. Chem. 2004, 76,
2415-2418
Magnetic field generated by a small electromagnet
Emily A. Clark and Ingrid Fritsch, Anodic Stripping Voltammetric
Enhancement by Redox Magnetohydrodynamics Anal. Chem. 2004, 76,
2415-2418
Fritsch JES 2006
B
Fritsch JES 2006
Magnetic field pushes fluid down
Fritsch JES 2006
Magnetic field pushes fluid up
Removes much of the diffusional
Shape to the voltammogram
Which will allow for more
Robust measurement of
Concentration and/or kinetics
Flow rate in the microchannel
Fritsch JES 2006
Fritsch JES 2006
Anal. Chem. 2007 79 5746-5752
Magnetic Field Switching of
Nanoparticles
between Orthogonal Microfluidic
Channels
Figure 2. Absorbance versus time curves
for a plug (concentration,
7.7 mg/mL) of Fe2O3 nanoparticles
injected into the lower flow stream
at a flow rate of 15 íL/min. Monitoring the
upper channel with (red
- - -) and without (red s), and bottom
channel with (blue - - -) and
without (blue s), the applied magnetic field.
Asterisk indicates the
point where the magnetic field was
removed. Inset: Au nanoparticles
eluting from the lower channel with (blue - -) and without (blue s) a
magnetic field under equivalent conditions.
Anal. Chem. 2007 79 5746-5752
Magnetic Field Switching of
Nanoparticles
between Orthogonal Microfluidic
Channels
Andrew H. Latham, Anand N. Tarp
and Mary Elizabeth Williams*
Using the ability to move magnetic particles, we envision
microfludic devices in which external magnetic fields, generated
Figure 7. Absorbance versus time for both
by electromagnets or permanent magnets, can be used to
the upper and lower
perform
separations, injections, and manipulations in microfluidic
channels while pulsating the magnetic field
channels.
(10 s on/20 s off) with
Given the already widespread use of magnetic beads in
biological
a continuous stream of Fe2O3
development of compatible analytical and microscale
nanoparticles flowing through the upperassays,
approaches would be of great use. These initial experiments
show
channel at a flow rate of 15 íL/min.
that standard operations for microfluidic devices such as
injection/
removal, mixing, separation, concentration, and fluid/particle
handling are all possible with correctly functionalized magnetic
particles and the appropriate field strength and flow rates.
Leventis Anal. Chem. 2001
Magnetohydrodynamic Electrochemistry in the
Field of Nd-Fe-B Magnets. Theory, Experiment,
and Application in Self-Powered Flow Delivery
Systems
Two kinds of magnetic force
Moving charges
Magnetic dipoles

F Lorentz
   
 q  E  v B 




Electromagnetic force on moving
Charge is related to q the charge
And the velocity of the particle,
The intensity of the electric field and
The magnetic induction, B
Anions and cations experience
same

 direction
Of force:

 Moving ions transfer momentum to the solvent


Causing it to behave as if it were subject to the
q v q v
Leventis Anal. Chem. 2001
Magnetohydrodynamic Electrochemistry in the
Field of Nd-Fe-B Magnets. Theory, Experiment,
and Application in Self-Powered Flow Delivery
Systems
For dipoles the average magnetic moment per dipole
Leventis Anal. Chem. 2001
Magnetohydrodynamic Electrochemistry in the
Field of Nd-Fe-B Magnets. Theory, Experiment,
and Application in Self-Powered Flow Delivery
Systems
Leventis Anal. Chem. 2001
Magnetohydrodynamic Electrochemistry in the
Field of Nd-Fe-B Magnets. Theory, Experiment,
and Application in Self-Powered Flow Delivery
Systems
Leventis Anal. Chem. 2001
Magnetohydrodynamic Electrochemistry in the
Field of Nd-Fe-B Magnets. Theory, Experiment,
and Application in Self-Powered Flow Delivery
Systems
current
Leventis Anal. Chem. 2001
Magnetohydrodynamic Electrochemistry in the
Field of Nd-Fe-B Magnets. Theory, Experiment,
and Application in Self-Powered Flow Delivery
Systems
JACS 2005