U.S. patent application number 10/731399 was filed with the patent office on 2005-06-16 for method of using unbalanced alternating electric field in microfluidic devices.
Invention is credited to Dukhin, Andrei S., Dukhin, Stanislav.
Application Number | 20050129526 10/731399 |
Document ID | / |
Family ID | 34652749 |
Filed Date | 2005-06-16 |
United States Patent
Application |
20050129526 |
Kind Code |
A1 |
Dukhin, Andrei S. ; et
al. |
June 16, 2005 |
Method of using unbalanced alternating electric field in
microfluidic devices
Abstract
The applicant describes a new method of generating directed
motion of the liquid in the microfluidic device by applying
"un-balanced" AC electric field for generating electroosmosis and
related hydrodynamic flow in the chamber with any symmetry of the
elements, including spherical or cylindrical symmetry, and any
relative position of these elements. Direction of the flow depends
on the phase of the "un-balanced" electric field, which opens a
simple way to operate flow and create a desirable flow pattern.
Inventors: |
Dukhin, Andrei S.; (Goldens
Bridge, NY) ; Dukhin, Stanislav; (Goldens Bridge,
NY) |
Correspondence
Address: |
Dr. Andrei S. Dukhin
12 Branch Street
Goldens Bridge
NY
10526
US
|
Family ID: |
34652749 |
Appl. No.: |
10/731399 |
Filed: |
December 10, 2003 |
Current U.S.
Class: |
417/53 |
Current CPC
Class: |
H02N 11/006
20130101 |
Class at
Publication: |
417/053 |
International
Class: |
F04B 001/00 |
Claims
What is claimed is:
1. Method of generating directed motion of liquid by applying
un-balanced alternating electric field, which is AC electric field
with a zero time averaged component and finite time averaged of the
higher than one powers of the electric field strength, to the
system of material objects with arbitrary symmetry for inducing
electroosmotic flow on the object-liquid interfaces.
2. Method of the claim 1, wherein the frequency of the AC electric
field exceeds Warburg frequency of the several KHz for eliminating
Faraday current but is lower than hydrodynamic relaxation
frequency
3. Method of the claim 1, wherein the electroosmosis generating
objects have either spherical or cylindrical symmetry and size not
exceeding 10 microns.
4. Method of the claim 1, wherein the system of electroosmosis
generating objects is microfluidics device with array of the metal
electrodes.
5. Method of the claim 1, wherein the system of electroosmosis
generating objects is microfluidics device with array of the metal
obstacles and electric field is applied by the means of external
electrodes systems.
Description
FIELD OF THE INVENTION
[0001] This invention describes a method for generating directed
relative motion of liquid in microfluidic device by applying
uniform alternating electric field with "unbalanced" time
dependence to the system of the charged micro-obstacles that
experience non-linear polarization in the applied electric field,
which causes non-linear electro-osmosis.
BACKGROUND OF THE INVENTION
[0002] Electric field influence on the charged surfaces generates
relative motion of the phases in heterogeneous systems. In the case
of "electrophoresis", particles or macromolecules move relative to
the liquid, whereas in the case of "electroosmosis", liquid moves
relative to the solid matrix. These "electrokinetic phenomena" are
known for 200 years and are the basis of several important
technologies. One of the recent important technological
developments exploiting these phenomena is "microfluidics", which
is technology of operating motion of the small volumes of liquid.
There is a version of mocrofluidic devices that uses electroosmosis
as driving force initiating liquid motion. There are several
reviews describing current level of microfluidic development: 1.
"Microfluidics: Basis Issues, Applications and Challenges", by H.
A. Stone and S. Kim, AIChE Journal, vol. 47, 6, pp. 1250-1254,
2001; 2. "Micro Total Analysis Systems. Introduction, Theory and
Technology", by D. R. Reyes, D. Iossifidis, P. A. Auroux, A. Manz,
Anal. Chem, 74, 2623-2636, 2002; 3. "Flexible Methods for
Microfluidics", by G. W. Whitesides and A. D. Stroock, Physics
Today, 42-48, June 2001.
[0003] All devices that employ this effect can be considered as
combination of material objects, such as electrodes, canals,
valves, etc, and electric field. Accordingly, there are three
approaches to achieve specified goals:
[0004] either to arrange material objects at certain appropriate
design and order
[0005] or apply electric field with appropriate properties.
[0006] or use both ways together.
[0007] U.S. Pat. No. 5,976,336 "Microfluidic devices incorporating
improved channel geometries" by R. S. Dubrow, C. B. Kennedy, L. J.
Bousse, 1999, might serve as an example of the first approach. In
this patent we do not consider material construction of the
microfluidic device at all.
[0008] In this patent we are dealing exclusively with the second
approach.
[0009] In the general, electric field strength E is characterized
with frequency .omega., amplitude A and phase .psi. as
following:
E(x, t)=A(x, t) sin(.omega.t+.psi.) (1)
[0010] where x and t are some space coordinate and time
respectively.
[0011] There are two modes of the electric field depending on the
frequency:
[0012] DC field at the zero frequency
[0013] AC field at non-zero frequency
[0014] The first and most used version is DC field. There are
several US Patents dealing with this type of electrokinetic
microfluidic devices: by S. J. Salvatore, U.S. Pat. No. 4,908,112
"Silicon semiconductor wafer for analyzing micronic biological
samples" in 1990; by P. K. Dasgupta, U.S. Pat. No. 5,660,703
"Apparatus for capillary electrophoresis having an auxiliary
electroosmotic pump" in 1997, by J. W. Parce, U.S. Pat. No.
6,394,759 "Micropump" and U.S. Pat. No. 6,012,902 "Micropump" in
2000, by Kopf-Sill, U.S. Pat. No. 6,617,823 "Systems for monitoring
and controlling fluid flows rates in microfluidic systems" in
2003.
[0015] This mode of the electric field has a big disadvantage of
being associated with Faraday current on electrodes. This current
is related to electrochemical reactions on electrodes. These
reactions generate chemical species, which could cause
contamination.
[0016] It is possible to prevent, or at least to minimize this
contamination managing design of material objects as it is
suggested, for instance, by P. K. Dasgupta, U.S. Pat. No. 5,660,703
"Apparatus for capillary electrophoresis having an auxiliary
electroosmotic pump" in 1997.
[0017] Replacing DC field with AC field offers much simpler
solution to this problem. In this mode of the electric field, it is
possible to eliminate electrochemical reactions completely if
frequency is high enough.
[0018] However, application of the AC field requires a special
means for creating directed motion of the liquid. Just regular
linear electroosmosis in symmetrical system does not generate the
directed motion of liquid and useless for pumping. This problem
could be resolved by introducing asymmetry into the system. This
idea is widely known in the generating directed motion of the
particles by AC electric field. Non-uniformly spaced AC electric
field with the space coordinate x dependent amplitude generates
directed motion of the particles known as "dielectrophoresis".
There is a large bulk of literature on dielectrophoresis. One of
the most recent patents on this subject is by F. F. Becker, P. R.
C. Gascoyne, Y. Huang and X. B. Wang, U.S. Pat. No. 6,641,708
"Method and apparatus for fractionation using conventional
dielectrophoresis and field flow fractionation", 2003.
[0019] The same idea can be introduced for generating directed
motion of the liquid. Space dependence of the AC electric field
amplitude A(x) is induced by special arrangements of electrodes.
Application of this idea to the microfluidics is described in the
several recent papers: by A. Ajdari "Pumping liquids using
asymmetric electrode arrays", Physical Review E, vol. 61, 1, pp.
45-48, 2000, by A. B. D. Brown, C. G. Smith, and A. R. Rennie
"Pumping of water with ac electric fields applied to asymmetric
pairs of microelectrodes", Physical Review E, vol. 63, 016305,
2000.
[0020] This approach to the microfluidic pumping is complicated by
the problem of the changing direction of the liquid motion.
Asymmetry of the material objects in the device determines this
direction. It means that such devices could pump liquid only in one
direction. Voltage modulation suggested by A. Ajdari "Pumping
liquids using asymmetric electrode arrays", Physical Review E, vol.
61, 1, pp. 45-48 introduces a constant, time independent component
of the current, which constituents return to the DC field with all
related problems.
[0021] In addition, it might be hard to control asymmetry of the
elements on this small scale of dimensions.
[0022] In this patent we evoke an old idea expressed many years ago
in Russian literature for eliminating linear effects in
electrophoresis with purpose of investigating non-linear components
of electrophoretic motion. It was suggested by S. S. Dukhin, A. K.
Vidybida, A. S. Dukhin and A. A. Serikov "Aperiodic
Electrophoresis. Directed drift of dispersed particles in a uniform
anharmonic alternating electric field", Kolloidnyi Zh., vo. 49, 5,
752-755, 1988, English.
[0023] Instead of the asymmetry of the material object, this idea
suggests to use a special time dependence of the electric field,
keeping its amplitude uniform, space independent. This type of
electric field is called "un-balanced". It does not have constant,
time independent component. This eliminates linear effects, Faraday
current, prevents possible contamination by electrochemical
reactions residue. At the same time it generates directed motion of
the particles, which depends on the non-linear terms in
electrophoretic mobility. There is a general definition of this
field and some examples given in the detailed description of this
patent.
[0024] This idea has never been before suggested for electroosmosis
and related microfluidic applications.
BRIEF SUMMARY OF INVENTION
[0025] The applicant describes a new method of generating directed
motion of the liquid in the microfluidic device by applying
"un-balanced" AC electric field for generating electroosmosis and
related hydrodynamic flow in the chamber with any symmetry of the
elements, including spherical or cylindrical symmetry, and any
relative position of these elements. Direction of the flow depends
on the phase of the "un-balanced" electric field, which opens a
simple way to operate flow and create a desirable flow pattern.
BRIEF DESCRIPTION OF THE DRAWINGS
[0026] FIG. 1. Two examples of the "un-balanced" AC electric
field.
DETAILED DESCRIPTION OF INVENTION
[0027] Microfluidics is rather new discipline with a purpose of
creating new means for operating motion of liquid on very small
scales of hundreds microns and below. Microfluidics is closely
linked to electrokinetics, which is scientific discipline regarding
various phenomena that occur in the heterogeneous systems under
influence of electric field. In particular, electrokinetic effect
of electroosmosis is of great interest for microfluidics because it
could be defined as motion of the liquid generated by the electric
field influence on interfacial electric charges.
[0028] Electroosmosis is closely related to electrophoresis, which
is motion of the solid particles relative to the liquid induced by
the external electric field.
[0029] These electrokinetic phenomena are known for almost 200
years with most attention paid to electrophoresis in both
experimental and theoretical aspects. Some of this knowledge could
be transferred and expanded now from electrophoresis to
electroosmosis for microfluidics related purposes.
[0030] Both effects are characterized with a speed of the motion.
In the case of electrophoresis it is motion of particle relative to
the liquid V.sub.eph, in the case of electroosmosis it is opposite,
motion of liquid relative to the immobile solid phase V.sub.eo. In
the imaginary case of the collection of the separate particles in
the liquid, speed of electrophoresis is equal to the speed of
electroosmosis in magnitude but opposite in sign, because they are
simply different due to the difference in the immobile frame of
reference.
V.sub.eo=-V.sub.eph (2)
[0031] In the classical electrokinetic theory (see Dukhin, S. S.
and Derjaguin, B. V. "Electrokinetic Phenomena" in "Surface and
Colloid Science", E. Matijevic (Ed.), John Wiley & Sons, NY, v.
7 (1974)) electrophoresis and electroosmosis are linear effects in
regard to the electric field strength. It happens because external
field electric potential drop associated with a small colloidal
particle 2Ea is much less than typical potential in the particles
double layers RTIF.apprxeq.25 m V. Here a is particle radius, R is
a gas constant, T is absolute temperature, F is Faraday constant.
This usually expressed as the following non-equality: 1 EFa RT <
1 ( 3 )
[0032] For particle with 1 micron radius this restrict E to be
below 250 V/cm. The typical value of electric field strength in
classical electrokinetics is below 10 V/cm, which explains why
electrophoresis and electroosmosis are assumed to be linear with
electric field strength. A special notion of "electrophoretic
mobility" as coefficient proportionality between speed of
electrophoresis and electric field strength has been
introduced:
V.sub.eph=.mu..sub.ephE (4)
[0033] About 2 decades ago it became clear that assumption of
linearity does not work in some cases. The notion of "non-linear
electrophoresis" was introduce. Review of these earlier works was
given by S. S. Dukhin, A. K. Vidybida, A. S. Dukhin and A. A.
Serikov "Aperiodic Electrophoresis. Directed drift of dispersed
particles in a uniform anharmonic alternating electric field",
Kolloidnyi Zh., vo. 49, 5, 752-755, 1988, English. The speed of
non-linear electrophoresis contains two terms, classical linear and
term proportional to the third power of the electric field
strength:
V.sub.eph=.mu..sub.ephE+.mu..sub.eph,3+E.sup.3 (5)
[0034] Importance of the non-linear term depends on the value of
the non-linear electrophoretic mobility .mu..sub.eph,3. There were
theories developed for general non-conducting particles and for two
special cases when this parameter is particularly large: 1) porous
charged particles such as ionite or polyelectrolyte; 2) metal
ideally polarized particles.
[0035] For general non-conducting particles (oxides, latex,
pigments, etc) non-linear term is related to the polarization of
the double layer caused by surface conductivity. There is a
dimensionless parameter called "Dukhin number", (see Lyklema, J.,
"Fundamentals of Interface and Colloid Science", vol. 1-3, Academic
Press, London-NY, (1995-2000), which determines the magnitude of
this effect. This number is reciprocally proportional to the
particle size. In the case of microfluidics the size of obstacles
is rather large, certainly exceeding micron. This leads to the
small Dukhin number, negligible double layer polarization and
small, even hardly measurable non-linear electrophoretic term if
obstacles are made from non-conducting material.
[0036] For the purpose of this patent the most important is the
case of metal particles. Non-linear electrophoresis is the most
pronounced in this case. The non-linear term in this case is
related to the difference in conductivities between particle and
liquid.
[0037] Theory of non-linear electrophoresis of metal ideally
polarized particles was developed by A. S. Dukhin "Biospecific
mechanism of double layer formation and peculiarities of cell
electrophoresis", Colloids and Surfaces A, 73, pp. 29-48, 1993. He
derived the following expression for this effect: 2 V eph = m o E -
9 m 0 a 2 8 C dl ( C dl ) = E 3 ( 6 )
[0038] where .epsilon..sub.m and .epsilon..sub.0 are dielectric
permittivities of media and vacuum, .eta. is dynamic viscosity,
.phi. is electric potential, C.sub.dl id double layer capacitance,
.zeta. is electrokinetic potential of particles, which is measure
of their equilibrium electric charge.
[0039] This simple theory can be directly used for estimating speed
of the liquid flow in the microfluidic device with collection of
the metal electrodes for generating electroosmotic flow under
influence of DC electric field. There is just one difference.
Instead of particles moving relatively to the liquid, liquid moves
relatively to the fixed cylindrical or spherical electrodes. 3 V eo
= - V eph = - m 0 E + 9 m 0 a 2 8 C dl ( C dl ) = E 3 ( 7 )
[0040] This expression allows us to compare linear and non-linear
effects. For instance, it turns out that for particle size 10
microns, non-linear term becomes larger than linear term at the
electric field strength exceeding only approximately 25 V/cm. In
the case of 100 microns particles this critical field is only 2.5
V/cm.
[0041] These simple approximate calculations indicate that
non-linear electroosmosis could be used as a basis for microfluidic
device. It is very fortunate because it opens way to replace DC
field with AC field. This replacement is desirable very much
because it allows to eliminate Faraday current and related
contamination by products of electrochemical reactions.
[0042] In order to determine the optimum way to apply AC electric
field we again turn our attention to the existing theory of
electrophoresis.
[0043] Fifteen years ago a group of Ukrainian scientists suggested
to use so-called "un-balanced" AC electric field for eliminating
linear term in the speed of the particle motion and creating
particle drift with the speed that depends only on the non-linear
mobility: S. S. Dukhin, A. K. Vidybida, A. S. Dukhin and A. A.
Serikov "Aperiodic Electrophoresis. Directed drift of dispersed
particles in a uniform anharmonic alternating electric field",
Kolloidnyi Zh., vo. 49, 5, 752-755, 1988, English.
[0044] The definition of the "un-balanced" electric field could be
given in the form of the following two equations: 4 0 T E t = 0 ( 8
) 0 T E 3 t 0 ( 9 )
[0045] The first equation means that there should be no time
independent component of the current in the system. The second one
is required for retaining the non-linear term in the particle
drifting motion. FIG. 1 shows 2 examples of "un-balanced" AC
electric field. The top example illustrates the following AC field,
which is sum of two harmonics shifted by certain phase:
E=E.sub.1 sin(.omega.t)+E.sub.2 sin(2.omega.t+.PSI.) (10)
[0046] If we would apply electric field like this to the real
dispersion, particle start to drift with the speed that depends on
the non-linear mobility only. Consequently, in the case of
microfluidic device, liquid would exhibit drifting motion with the
following speed: 5 V eo drift = 1 T e 0 Te V eo t = 3 4 ef , 3 E 1
2 E 2 sin = 27 32 m 0 a 2 C dl ( C dl ) = E 1 2 E 2 sin ( 11 )
[0047] where T.sub.e is the time period of the electric field.
[0048] Direction of the motion depends on the phase shift between
harmonics. This gives an easy way to operate with liquid
motion.
[0049] There is infinite number of the various "un-balanced" AC
electric fields. We just showed only two examples on the FIG. 1.
This fields must satisfy conditions (8) and (9) and there is also
certain restrictions of the frequency.
[0050] First of all, frequency must be above critical frequency of
Warburg impedance .omega..sub.W in order to eliminate Faraday
current. It is usually several KHz.
[0051] Secondly, frequency must be below Maxwell-Wagner frequency
.omega..sub.MW that depends mostly on conductivity of the liquid
K.sub.m, (see Dukhin, S. S. and Shilov V. N. "Dielectric phenomena
and the double layer in dispersed systems and polyelectrolytes",
John Wiley and Sons, NY, (1974)): 6 MW = K m m 0 ( 12 )
[0052] This frequency characterizes relaxation of the double layer.
Polarization charges that cause non-linear effect require some time
to develop completely. This condition specifies Maxwell-Wagner
frequency. For conductivity of liquid K.sub.m=0.01 S/m, this
critical frequency equals roughly to 2.2 MHz.
[0053] Third condition requires frequency to be below frequency of
the electroosmotic field relaxation .omega..sub.eo: 7 eo = v D
MW
[0054] where v is kinematic viscosity of the liquid, D is effective
diffusion coefficient of the electrolyte.
[0055] This condition reflects the fact that electric field should
change in time slow enough for allowing electroosmotic flow to
develop completely within the double layer. This restriction is not
essential in aqueous systems where because kinematic viscosity
exceeds diffusion coefficient several order of magnitude. This
means that this frequency is much larger than Maxwell-Wagner
frequency.
[0056] However, there is one more important frequency of
hydrodynamic nature. Electroosmotic flow establishes quickly itself
within the thin Double Layer. This flow makes liquid to move beyond
the double layer. It takes some time for this bulk flow to develop.
This critical time depends on the size of the object that generates
initial electroosmotic flow. Corresponding frequency of this
hydrodynamic relaxation .omega..sub.h is given as following: 8 h =
v a 2
[0057] This hydrodynamic relaxation limits available frequency
range very substantially in the case of microfluidics. The larger
size of the electroosmosis generating obstacles the lower this
frequency becomes. For instance, for 100 micron generating
electrodes it is only about 0.1 KHz. This means that for large
microfluidic device obstacles of hundreds microns in size, it is
practically impossible to take advantage of all benefits related
with AC field. Hydrodynamic flow would not have sufficient time to
develop completely if frequency high is enough to eliminate Faraday
current.
[0058] It looks like the size of the electroosmosis generating
obstacles should not exceed 10 microns. Hydrodynamic relaxation
frequency corresponding to this size is about 10 KHz. This opens
the frequency window between Warburg frequency .omega..sub.W
(several KHz) and hydrodynamic relaxation frequency .omega..sub.h
(about 10 KHz).
* * * * *