U.S. patent application number 17/720687 was filed with the patent office on 2022-08-25 for methods of particle manipulation and analysis.
The applicant listed for this patent is The Trustees of Princeton University, University of Hawaii, UT-BATTELLE, LLC. Invention is credited to Jesse AULT, Jie FENG, Sangwoo SHIN, Howard A. STONE, Patrick WARREN.
Application Number | 20220268731 17/720687 |
Document ID | / |
Family ID | |
Filed Date | 2022-08-25 |
United States Patent
Application |
20220268731 |
Kind Code |
A1 |
AULT; Jesse ; et
al. |
August 25, 2022 |
METHODS OF PARTICLE MANIPULATION AND ANALYSIS
Abstract
Methods described herein, in some embodiments, permit extraction
of particle structural and/or surface charge data from gradient
induced particle motion in channels. In one aspect, a method of
manipulating particle motion comprises introducing a fluid into a
channel, the fluid comprising particles, and driving particle
accumulation to a preselected location in the channel by setting
advective velocity of the fluid to offset diffusiophoretic mobility
of the particles at the preselected location.
Inventors: |
AULT; Jesse; (Knoxville,
TN) ; SHIN; Sangwoo; (Honolulu, HI) ; STONE;
Howard A.; (Princeton, NJ) ; FENG; Jie;
(Princeton, NJ) ; WARREN; Patrick; (Wirral,
GB) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
The Trustees of Princeton University
UT-BATTELLE, LLC
University of Hawaii |
Princeton
Oak Ridge
Honolulu |
NJ
TN
HI |
US
US
US |
|
|
Appl. No.: |
17/720687 |
Filed: |
April 14, 2022 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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16915651 |
Jun 29, 2020 |
11307170 |
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17720687 |
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16210760 |
Dec 5, 2018 |
10697931 |
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16915651 |
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62594871 |
Dec 5, 2017 |
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62682449 |
Jun 8, 2018 |
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International
Class: |
G01N 27/447 20060101
G01N027/447; G01N 15/14 20060101 G01N015/14; G01N 15/00 20060101
G01N015/00 |
Goverment Interests
STATEMENT OF GOVERNMENT RIGHTS
[0002] This invention was made with government support under Grant
No. DE-AC05-000R22725 awarded by the Department of Energy and Award
No. CBET1702693 awarded by the National Science Foundation. The
government has certain rights in the invention.
Claims
1. A method of determining zeta potential of channel walls
comprising: establishing a solute concentration gradient to induce
a wall slip boundary condition in the channel; measuring pressure
drop over the channel length; determining channel wall
diffusiophoretic mobility of the slip boundary condition from the
measured pressure drop; and deriving the zeta potential of the
channel walls from the wall diffusiophoretic mobility.
2. The method of claim 1, wherein the wall diffusiophoretic
mobility is derived from a relation between the measured pressure
drop and wall slip velocity of the boundary condition.
3. A zeta potentiometer comprising: at least one flow channel; at
least one light source for illuminating the flow channel; an
imaging device positioned to observe the illuminated flow channel;
and a sample storage location adapted to provide sample to the at
least one flow channel.
4. The zeta potentiometer of claim 3, wherein the imaging device
comprises a microscope.
Description
RELATED APPLICATION DATA
[0001] The present application is a divisional application of U.S.
patent application Ser. No. 16/915,651 filed Jun. 29, 2020, which
is a continuation application of U.S. patent application Ser. No.
16/210,760 filed Dec. 5, 2018, now U.S. Pat. No. 10,697,931, which
claims priority pursuant to 35 U.S.C. .sctn. 119(e) to U.S.
Provisional Patent Application Ser. No. 62/594,871 filed Dec. 5,
2017 and U.S. Provisional Patent Application Ser. No. 62/682,449
filed Jun. 8, 2018, each of which is incorporated herein by
reference in its entirety.
FIELD
[0003] The present invention relates to methods of particle
manipulation and analysis and, in particular, to methods employing
solute gradients for particle manipulation and analysis.
BACKGROUND
[0004] Particle motion or transport in suspensions and colloids is
important in many applications including drug delivery,
disinfection, filtration and fluid sample analysis. Several
mechanisms exist to induce directed motion of colloidal particles,
such as employment of one or more external forces. External forces
can include electrostatic, dielectric, magnetic, acoustic, optical
and/or inertial effects. Effective application of external forces
can necessitate apparatus of complex architecture and design.
Additionally, use of external forces often fails to reveal
meaningful information of particle systems, such as zeta potential
and particle size.
SUMMARY
[0005] In view of the foregoing deficiencies, new methods of
particle manipulation and analysis are needed. Methods described
herein, in some embodiments, permit extraction of particle
structural and/or surface charge data from gradient induced
particle motion in channels. In one aspect, a method of
manipulating particle motion comprises introducing a fluid into a
channel, the fluid comprising particles, and driving particle
accumulation to a preselected location in the channel by setting
advective velocity of the fluid to offset diffusiophoretic velocity
of the particles at the preselected location. In some embodiments,
fluid advective velocity and diffusiophoretic velocity of the
particles are equal or substantially equal, resulting in cessation
of particle movement in the fluid at the preselected location. In
other embodiments, the difference between fluid advective velocity
and particle diffusiophoretic velocity is sufficiently small,
thereby permitting particle accumulation at the preselected
location for a defined period of time. Additionally,
non-accumulated particles can be passed out of the channel by the
advective velocity of the fluid.
[0006] In another aspect, methods of particle separation are
described. A method of particle separation comprises introducing a
fluid into a channel, the fluid comprising a mixture of particle
species. The particle species are separated in the fluid by driving
accumulation of the particle species to preselected locations in
the channel via setting advective velocity of the fluid to offset
diffusiophoretic velocity of a particle species at each of the
preselected locations. In some embodiments, one or more of the
separated particle species can be analyzed or characterized in the
channel. Moreover, one or more of the separated particle species
can be selectively removed from the channel.
[0007] In another aspect, methods of particle analysis are
described. A method of particle analysis comprises introducing a
fluid into a channel and determining the presence of analyte
particles in the fluid sample by driving accumulation of the
analyte particles to a preselected location in the channel. The
analyte particles are driven to the preselected location by setting
advective velocity of the fluid sample to offset diffusiophoretic
velocity of the analyte particles at the preselected location. The
presence of the analyte particles at the preselected location is
subsequently detected. In other embodiments, a method of particle
analysis comprises introducing a fluid sample into a channel. The
presence of a plurality of analyte particle species in the fluid
sample is determined by driving accumulation of the analyte
particle species to preselected locations in the channel. The
analyte particle species are driven by setting advective velocity
of the fluid to offset diffusiophoretic velocity of an analyte
particle species at each of the preselected locations. The presence
of the analyte particles at each of the preselected locations is
then detected.
[0008] In a further aspect, methods of determining particle zeta
potential are described. A method of determining particle zeta
potential, in some embodiments, comprises introducing a fluid into
a channel, the fluid having an advective velocity and solute
concentration gradient. Particles are introduced into the fluid and
accumulated at a location in the channel where the advective
velocity of the fluid is offset by diffusiophoretic velocity of the
particles. The diffusiophoretic mobility of the particles is
calculated from this location in the channel, and the particle zeta
potential is derived from the diffusiophoretic mobility.
[0009] In other embodiments, a method of determining particle zeta
potential comprises providing at least one dead-end pore containing
solute having a first solute concentration and introducing a
plurality of colloidal particles into the dead-end pore, the
colloidal particles having positive diffusiophoretic mobility and a
second solute concentration less than the first solute
concentration. The image intensity in the dead-end pore is
measured, and the maximum colloidal density is determined based on
the image intensity. Particle zeta potential is derived from the
maximum colloidal density. In some embodiments, the image intensity
is measured after migration of the colloidal particles in the
dead-end pore reaches a quasi-steady state.
[0010] In another aspect, methods of determining the zeta potential
of channel surfaces and/or walls are described. In some
embodiments, a method of determining surface or wall zeta potential
comprises providing at least one dead-end pore containing a solute
having a first solute concentration and introducing a plurality of
colloidal particles having a second solute concentration less than
the first solute concentration. The plurality of colloidal
particles migrate into the dead-end pore, and the image intensity
of the dead-end pore is measured prior to the colloidal particle
migration reaching a quasi-steady state. The transient peak
position is determined from the image intensity, and zeta potential
of the pore wall is determined from the transient peak position. In
some embodiments, wall zeta potential is determined by fitting the
transient peak position to a power law curve, obtaining a power law
exponent, and comparing the effective power law exponent to results
from a two-dimensional computer simulation.
[0011] In another aspect, methods of determining the zeta potential
of channel walls or surfaces via pressure measurements are
described. A method of determining zeta potential of channel walls
or surfaces, in some embodiments, comprises establishing a solute
concentration gradient to induce a wall slip boundary condition in
the channel. The pressure drop along the channel is measured, and
channel wall diffusiophoretic mobility of the slip boundary
condition is derived from the measured pressure drop. The zeta
potential of the channel walls or surfaces is derived from this
wall diffusiophoretic mobility. In some embodiments, for example,
the wall diffusiophoretic mobility is derived from a relation
between the measured pressure drop and the wall slip velocity of
the boundary condition.
[0012] Zeta potentiometers are also described herein. In some
embodiments, a zeta potentiometer comprises at least one flow
channel, at least one light source for illuminating the flow
channel, and an imaging device positioned to observe the
illuminated flow channel. A sample storage location is adapted to
provide a sample to the at least one flow channel for analysis.
[0013] These and other embodiments are further described in the
following detailed description.
BRIEF DESCRIPTION OF THE DRAWINGS
[0014] FIGS. 1A-C illustrate principles of particle manipulation
according to some embodiments described herein.
[0015] FIG. 2 illustrates peak particle concentration location
(x.sub.p) in the channel as a function of solute Peclet number for
a variety of diffusiophoretic mobilities (.GAMMA..sub.p/D.sub.s)
according to some embodiments.
[0016] FIG. 3 illustrates suspended concentration profiles for
particles with differing diffusiophoretic mobilities according to
some embodiments.
[0017] FIG. 4A illustrates introduction of colloidal particles with
solute concentration c.sub.o in a dead-end pore that initially
contains higher solute concentration c.sub.i.
[0018] FIG. 4B illustrates migration of the colloidal particles
into the pore via diffusiophoresis.
[0019] FIG. 4C illustrates the condition after solute equilibration
across the pore where the quasi-steady state location of the
maximum colloidal density (x.sub.m.sup..infin.) is determined from
the experimental image intensity (I).
[0020] FIG. 4D illustrates particle zeta potential .zeta..sub.p as
a function of x.sub.m.sup..infin..
[0021] FIG. 5A illustrates colloid particle migration into a
dead-end pore induced by solute gradients.
[0022] FIG. 5B illustrates the corresponding fluorescence intensity
distribution of the colloidal particles migrating into the dead-end
pore.
[0023] FIG. 5C illustrates the normalized location of the maximum
intensity (x.sub.m/L) over time.
[0024] FIG. 5D is an image sequence of time-dependent colloidal
particle distribution in the dead-end pore.
[0025] FIG. 5E illustrates the cross-section averaged colloidal
particle density distribution in the dead-end pore normalized by
the maximum density (n/n.sub.m.sup..infin.) at 300 s.
[0026] FIG. 5F illustrates the maximum intensity distribution over
time using 3D, 2D, and 1D-simulation results.
[0027] FIG. 6 illustrates 1D-simulations of maximum intensity
location (x.sub.m/L) over time for .zeta..sub.p ranging from -40 mV
-100 mV with a step of 10 mV. The inset indicates
x.sub.m.sup..infin./L at 300 s versus .zeta..sub.p, where the
dashed curve corresponds to 1D-simulation results and the solid
curves correspond to 2D-simulation results.
[0028] FIG. 7A illustrates particle trajectories in the presence of
diffusioosmotic flow induced by nonzero wall zeta potential
.zeta..sub.w.
[0029] FIG. 7B illustrates a 2D simulation of particle distribution
in a channel with wall slip flow.
[0030] FIG. 7C illustrates a 2D simulation of particle distribution
in a channel without wall slip flow. FIG. 7D provides 2D numerical
results of x.sub.m/L over time plotted in log-log scale for various
.zeta..sub.w (-20 to -80 mV) with .zeta..sub.p of -80 mV. The
dashed curve represents 1D results, which neglect fluid flow. The
inset is .beta. versus .zeta..sub.w at early times (t<60 s) for
a wide range of .zeta..sub.p,w values.
[0031] FIG. 7E illustrates a comparison of colloidal particle
migration in bare and plasma treated PDMS channels. The scale bar
is 50 .mu.m.
[0032] FIG. 7F illustrates corresponding particle peak locations
over time in the plasma treated and untreated channels of FIG. 7e.
The curve in the inset indicates .beta. versus .zeta..sub.w with
.zeta..sub.p=-80 mV.
[0033] FIGS. 8A and 8B illustrate a system setup for determining
wall zeta potential of a channel via pressure measurements, wherein
ends of the channel are coupled to larger main channels.
[0034] FIG. 9 illustrates a system design for measuring zeta
potential of channel walls or surfaces according to some
embodiments.
[0035] FIG. 10 illustrates a zeta potentiometer according to some
embodiments.
DETAILED DESCRIPTION
[0036] Embodiments described herein can be understood more readily
by reference to the following detailed description and examples and
their previous and following descriptions. Elements, apparatus and
methods described herein, however, are not limited to the specific
embodiments presented in the detailed description and examples. It
should be recognized that these embodiments are merely illustrative
of the principles of the present invention. Numerous modifications
and adaptations will be readily apparent to those of skill in the
art without departing from the spirit and scope of the
invention.
[0037] In one aspect, methods of manipulating particle motion are
provided. A method of manipulating particle motion comprises
introducing a fluid into a channel, the fluid comprising particles,
and driving particle accumulation to a preselected location in the
channel by setting advective velocity of the fluid to offset
diffusiophoretic velocity of the particles at the preselected
location. In some embodiments, fluid advective velocity and
diffusiophoretic velocity of the particles are equal or
substantially equal, resulting in cessation of particle movement in
the fluid at the preselected location. In other embodiments, the
difference between fluid advective velocity and particle
diffusiophoretic velocity is sufficiently small, thereby permitting
particle accumulation at the preselected location for a defined
period of time. Additionally, non-accumulated particles can be
passed out of the channel by the advective velocity of the
fluid.
[0038] As detailed herein, diffusiophoretic velocity of the
particles is a function of particle size, particle surface charge,
strength of the solute gradient in the fluid and/or various
combinations thereof. In particular, diffusiophoretic velocity is
equal to the product of particle diffusiophoretic mobility
(.GAMMA..sub.r) and gradient log solute concentration,
.mu..sub.dp=.GAMMA..sub.p.gradient.lnc. In some embodiments, the
solute gradient is established by connecting the channel with a
second channel transporting fluid having a differing solute
concentration. FIGS. 1A-C illustrate principles of particle
manipulation according to some embodiments described herein. As
illustrated in FIG. 1A, a side channel 10 containing particles is
in fluid communication with a second or main channel 11. The solute
concentration in the fluid of the side channel 10 differs from the
solute concentration in the main channel 11, thereby establishing a
solute gradient in the side channel 10. Inside the side channel 10,
particle motions are governed by a combination of the fluid
velocity (.mu..sub.f) and the diffusiophoretic velocity
(.mu..sub.dp) resulting from the solute concentration gradient.
With appropriately chosen parameters for the particles of interest,
the fluid and diffusiophoretic velocities can be designed to act in
opposite or offsetting directions, resulting in a stable position
in the pore (x.sub.p) where particles can accumulate. The location
of the site of accumulation can be preselected by knowing the
diffusiophoretic velocity of the particles and setting the fluid
velocity to offset the diffusiophoretic velocity at the preselected
location. Equation (1), for example, can be employed in some
embodiments to select one or more particle accumulation sites
(x.sub.p) in the channel.
x P = Pe s - 1 .times. ln [ .beta. - e P .times. e s ( 1 + .GAMMA.
p D s ) .times. ( .beta. - 1 ) ] ( 1 ) ##EQU00001##
where Pe.sub.s is the Peclet number, .beta. is solute concentration
at the channel outlet, c(l, y, t), and D.sub.s is solute
diffusivity. Alternatively, depending on various underlying
assumptions, other equation(s) may be used for determining one or
more particle accumulations sites (x.sub.p) according to methods
described herein. In some embodiments, the fluid velocity can be
set to flow particles not of interest out of the channel, thereby
isolating particles of interest in the channel. Subsequent to
accumulation at a location in the channel, the particles can be
characterized and/or selectively removed from the channel. The
particles, for example, may be characterized by one or more
spectroscopic techniques, in some embodiments.
[0039] Any desired particle type or species not inconsistent with
the principles of the present invention can be employed with
methods described herein. In some embodiments, the particles are
colloidal or otherwise suspended in the fluid. Particles may
include charged inorganic particles and/or charged organic
particles, such as polymeric particles. In other embodiments,
particles comprise one or more biomolecular species including, but
not limited to, small molecule drugs, nucleic acids, proteins,
vesicles and pathogens such as viruses, bacterial and other
microbial species. Particles may also comprise emulsions.
[0040] In another aspect, methods of particle separation are
provided. A method of particle separation comprises introducing a
fluid into a channel, the fluid comprising a mixture of particle
species. The particle species are separated in the fluid by driving
accumulation of the particle species to preselected locations in
the channel via setting advective velocity of the fluid to offset
diffusiophoretic velocity of a particle species at each of the
preselected locations. In some embodiments, one or more of the
separated particle species can be analyzed or characterized in the
channel. Moreover, one or more of the separated particle species
can be selectively removed from the channel. FIG. 2 illustrates
peak particle concentration location (x.sub.p) in the channel as a
function of solute Peclet number for a variety of diffusiophoretic
mobilities .GAMMA..sub.p/D.sub.s, where .GAMMA..sub.p is
diffusiophoretic mobility and D.sub.s is the solute diffusivity. As
illustrated in FIG. 2, particles with differing diffusiophoretic
mobilities can be driven to differing locations in the channel
according to offsetting interaction with the fluid advection
velocity. With reference to Equation (1) herein, for a given
.GAMMA..sub.p/D.sub.s, both solute Peclet number and .beta. can be
tuned to selectively determine the channel position at which
particles accumulate. Note that for x.sub.p<0, particle
diffusiophoresis is too strong relative to fluid advection, and
particles will be continuously pumped upstream without accumulating
in the channel.
[0041] FIG. 3 illustrates suspended concentration profiles for
particles with differing diffusiophoretic mobilities according to
some embodiments. As can be seen, particles with larger
.GAMMA..sub.p/D.sub.s experience diffusiophoresis more strongly and
are able to propagate further upstream towards the channel inlet.
As time progresses, particles continue to focus at separate
locations, and particle concentrations will continue to grow in the
separate locations. Another way to interpret the results of FIG. 3
is to consider a channel simultaneously filled with uniform dilute
concentrations of five different types of particles with the values
.GAMMA..sub.p/D.sub.s specified in the figure. Due to the combined
influences of fluid advection and diffusiophoresis, as time passes,
the particle concentration will begin to separate and focus at
different locations, forming distinct concentration peaks,
effectively sorting and focusing each of the particles based on
their .GAMMA..sub.p/D.sub.s. For example, since the peak
concentration locations are steady in time after an initial
transient time t=O(l), and those locations are uniquely determined
by the system parameters Pe.sub.s, .GAMMA..sub.p/D.sub.s, and
.beta., it is straightforward to establish .GAMMA..sub.p of the
particles. In a microfluidic experiment with fixed .beta. and
Pe.sub.s, the position of peak concentration (x.sub.p) with unknown
.GAMMA..sub.p can be measured. The unknown diffusiophoretic
mobility, in some embodiments, can subsequently be directly
calculated from Equation (2):
.GAMMA. p = D s ( .beta. - e P .times. e s e P .times. e s .times.
x p ( .beta. - 1 ) - 1 ) ( 2 ) ##EQU00002##
This configuration, therefore, has potential applications ranging
from particle sorting, separation, and focusing, to diagnostic and
measurement applications. In some embodiments, fluid advective
velocity and diffusiophoretic velocity of the particles are equal
or substantially equal resulting in cessation or suspension of
particle movement in the fluid at one or more channel locations. In
other embodiments, the difference between fluid advective velocity
and particle diffusiophoretic velocity is sufficiently small,
thereby permitting particle accumulation at the preselected
location for a period of time.
[0042] In another aspect, methods of particle analysis are
described. A method of particle analysis comprises introducing a
fluid into a channel and determining the presence of analyte
particles in the fluid sample by driving accumulation of the
analyte particles to a preselected location in the channel. The
analyte particles are driven by setting advective velocity of the
fluid sample in the channel to offset diffusiophoretic velocity of
the analyte particles at the preselected location. The presence of
the analyte particles at the preselected location is subsequently
detected. In some embodiments, the fluid sample comprises a
plurality of analyte particle species. In such embodiments, the
presence of analyte particle species is determined by driving
accumulation of the analyte particle species to preselected
locations in the channel via setting advective velocity of the
fluid in the channel to offset diffusiophoretic velocity of an
analyte particle species at each of the preselected locations. The
presence of the analyte particles at each of the preselected
locations is then detected.
[0043] In the present methods of particle analysis, advective fluid
velocity and solute gradients can be selected to isolate particles
of interest in a fluid sample. For example, an investigator can
determine or classify particles of interest based on their
diffusiophoretic velocities. Advective fluid velocity is then
selected, such that any particles having the desired
diffusiophoretic velocities are isolated in the channel at one or
more locations. According to the principles described herein, the
location(s) of particle isolation are calculated based on fluid
advective velocity and diffusiophoretic velocity. Particles not
exhibiting diffusiophoretic velocities of interest can pass out of
the channel or be isolated at another location in the channel. In
this way, particles of interest in an unknown sample can be
isolated and identified and/or characterized. One of more species
of isolated particles may also be selectively removed from the
channel.
[0044] In a further aspect, methods of determining particle zeta
potential are described. In some embodiments, a method of
determining particle zeta potential comprises introducing a fluid
into a channel, the fluid having an advective velocity and solute
concentration gradient. The particles are accumulated at a location
in the channel where the advective velocity of the fluid is offset
by diffusiophoretic velocity of the particles. The diffusiophoretic
mobility (.GAMMA..sub.r) of the particles is calculated using this
location in the channel (x.sub.p), and the zeta potential of the
particles is derived from the diffusiophoretic mobility. In some
embodiments, for example, particle zeta potential (.zeta..sub.p) is
derived from diffusiophoretic mobility according to Equations
(3)-(5):
.GAMMA. p = 2 .times. .eta. .times. ( k B .times. T Z .times. e ) 2
.times. u o 1 - u 1 / ( u 0 .times. .kappa. .times. a ) ( 3 )
##EQU00003##
where is the permittivity of the medium, .eta. is the viscosity of
the medium, k.sub.B is the Boltzman constant, Tis the absolute
temperature, and e is the elementary charge. .mu..sub.0 and
.mu..sub.1 are functions of zeta potential and when estimating
k.sup.-1, the concentration is assumed to be (c.sub.i+c.sub.o)/2.
Here,
u 0 = 2 .times. ( D - - D + D - + D + ) .times. Z .times. e .times.
.zeta. p k B .times. T + 8 .times. ln .times. cosh .function. ( Z
.times. e .times. .zeta. p k B .times. T ) ( 4 ) ##EQU00004##
where D- and D+ are, respectively, the diffusivities of cations and
anions. .mu..sub.1 is a series of exponential integrals where the
lengthy expressions can be found in Prieve et al., J Fluid Mech.,
148:247-269, 1984. For very large particles or vanishingly thin
Debye layer (.kappa..alpha..fwdarw..infin.),
.GAMMA. p = .eta. .times. ( k B .times. T Z .times. e ) 2 .times. (
( D - - D + D - + D + ) .times. Z .times. e .times. .zeta. p k B
.times. T + 4 .times. ln .times. cosh .function. ( Z .times. e
.times. .zeta. p 4 .times. k B .times. T ) ) ( 5 ) ##EQU00005##
where .zeta..sub.p is particle zeta potential. As described herein,
the solute gradient can be established, in some embodiments, by
connecting the channel with a second channel transporting fluid
having a differing solute concentration.
[0045] In another aspect, a method of determining particle zeta
potential comprises providing at least one dead-end pore containing
solute having a first solute concentration and introducing a
plurality of colloidal particles into the dead end pore, the
colloidal particles having positive diffusiophoretic mobility and a
second solute concentration less than the first solute
concentration. The image intensity in the dead-end pore is
measured, and the maximum colloidal density is determined based on
the image intensity. Particle zeta potential is derived from the
maximum colloidal density. In some embodiments, the image intensity
is measured after migration of the colloidal particles in the
dead-end pore reaches a quasi-steady state.
[0046] An overview of this zeta potentiometry technique is provided
in FIGS. 4A-D. Colloidal particles with solute concentration
c.sub.o are introduced to a dead-end pore containing higher solute
concentration c.sub.i, as illustrated in FIG. 4A, leading to
diffusiophoretic particle migration into/from the dead-end pore
FIG. 4B. The direction of motion is determined by the particle
surface charge and by the diffusivity difference between anions and
cations. The particle motion is also influenced by the presence of
the wall surface charge, which induces diffusioosmosis that results
in a circulating fluid flow. During migration, the particles
accumulate near the colloidal front since the particle velocity
.mu..sub.p is proportional to the gradient of the logarithmic
solute concentration, i.e. .mu..sub.p=.GAMMA..sub.p.gradient.lnc,
where .GAMMA..sub.p is the particle diffusiophoretic mobility,
which strongly depends on the particle zeta potential .zeta..sub.p
as shown in Equation 5 and FIG. 4B. After the solute equilibrates
across the pore, the colloidal distribution becomes quasi-steady
since the particle's diffusivity is negligible compared to that of
the solute. The quasi-steady location of the maximum colloidal
density x.sub.m.sup..infin. is highly sensitive to .zeta..sub.p.
Thus, by locating x.sub.m.sup..infin. from the intensity
distribution, .zeta..sub.p can be obtained as provided in FIGS.
4C-D.
[0047] The foregoing principles are illustrated via the migration
of fluorescent colloidal particles (polystyrene, diameter=0.99
.mu.m) into a dead-end pore via NaCl gradient
(c.sub.i=10.times.10.sup.-3 M, c.sub.o=0.1.times.10.sup.-3 M). The
polystyrene particle migration is illustrated in FIG. 5A. NaCl is a
favorable solute choice because it can generate significant LJP.
Furthermore, the induced electrophoresis and chemiphoresis are in
the same direction under practical conditions, enabling relatively
strong diffusiophoresis. As mentioned, particles accumulate near
the colloidal front due to the logarithmic dependence on the solute
gradient. To identify the location of the maximum colloidal density
x.sub.m(t), the particle distribution can be inferred from the
fluorescence intensity distribution along the pore as shown in FIG.
5B. Over time, x.sub.m asymptotically approaches its quasi-steady
final position within a few minutes (FIG. 5C). The location of the
quasi-steady maximum colloid density x.sub.m.sup..infin. is defined
as the peak location at three times the solute diffusion time scale
.tau..sub.s, which in the present case is 300 s
( .tau. s .apprxeq. l 2 D s .apprxeq. 100 .times. s ,
##EQU00006##
where l=400 .mu.m is the pore length and D.sub.s=1600 .mu.m.sup.2
s.sup.-1 is the solute ambipolar diffusivity).
[0048] Although diffusiophoresis is a complex interfacial
phenomenon occurring over nanometer length scales for individual
particles, the macroscopic particle dynamics can be predicted by
solving advection-diffusion equations as follows. The transient
particle dynamics in a dead-end pore can be modeled by solving
advection-diffusion equations for the solute and the particles. The
equations for the solute c and the particles n are, respectively,
given as:
.differential. c .differential. t = D s .times. .gradient. 2 c -
.gradient. ( u f .times. c ) ( 6 ) ##EQU00007## .differential. n
.differential. t = D p .times. .gradient. 2 n - .gradient. ( u p
.times. n ) ( 7 ) ##EQU00007.2##
where .mu..sub.f is the fluid velocity and
.mu..sub.p=.mu..sub.f+.mu..sub.dp is the particle velocity, which
is the sum of the fluid advection (.mu..sub.f) and the particle
diffusiophoresis (.mu..sub.dp). D.sub.s is the ambipolar
diffusivity of the solute and D.sub.p is the particle diffusivity,
which is obtained from the Stokes-Einstein relation to obtain
D.sub.p.
[0049] The length, width, and height of the dead-end pore are, L,
w, and 2h, respectively. The coordinates in length, width, and
height are denoted as, respectively, x, y, and z, where the origin
is located at the center of the pore inlet. The boundary conditions
at the inlet are c(x=0, y, z, t)=c.sub.o and n(x=0, y, z, t)=1
while a no flux condition is imposed at the channel walls. Initial
conditions are c(x, y, z, 0)=c.sub.i and n(x, y, z, 0)=0. Since the
flow speed in the dead-end pore is due to the circulating flow (10
.mu.m/s), the Peclet number in the transverse direction to the pore
axis of the solute migrating into a dead-end pore is far less than
unity, indicating diffusion dominant transport. Thus, for the
reduced order modeling (1D and 2D), the influence of flow advection
on the solute distribution is neglected and diffusion for the
solute transport is only considered. Due to the boundary condition,
the solution simplifies to c(x, y, z, t)=c(x, t).
[0050] The analytical solution to the transient solute
concentration in a dead-end pore is given by Equation (8):
c .function. ( x , t ) = c o + ( c i - c o ) .times. n = 0 .infin.
b n .times. sin .function. ( .lamda. n .times. x L ) .times. e
.lamda. n 2 .times. D s .times. t / L 2 ( 8 ) ##EQU00008##
where b.sub.n=2(1-1 cos .lamda..sub.n)/.lamda..sub.n and
.lamda..sub.n=(2n+1).pi./2. However, for full 3D modeling, the
influence of flow advection on the solute distribution is accounted
for, and the full advection diffusion equation is solved.
[0051] To account for the fluid advection induced by
diffusioosmosis, an effective wall slip velocity
.mu..sub.w=-.GAMMA..sub.w.gradient.lnc is imposed along the channel
surface. For reduced order modeling (2D), the analytical solution
to the flow profile in the length (x) and height (z) directions is
obtained by using the lubrication approximation with a zero net
volume flux constraint across the cross-section of the channel. The
velocity field .mu..sub.f(x,z)=(.mu..sub.f,x(x,z),
.mu..sub.f,z(x,z) is given by Equations (9a) and (9b):
u x ( x , z ) = - .GAMMA. w 2 .times. d .times. ln .times. c d
.times. x [ 3 .times. ( z h ) 2 - 1 ] ( 9 .times. a ) ##EQU00009##
u z ( x , z ) = .GAMMA. w 2 .times. d 2 .times. ln .times. c d
.times. x 2 [ z .function. ( ( z h ) 2 - 1 ) ] ( 9 .times. b )
##EQU00009.2##
Using these equations for the flow advection, the
advection-diffusion equation for the particles is numerically
solved using MATLAB in the reduced order simulations.
[0052] By solving equations for both solute and particle suspension
inside a dead-end pore and considering the fluid advection due to
the diffusioosmosis, the time-dependent particle distribution
(FIGS. 5D and 5E) including x.sub.m(t) (FIG. 5F) can be predicted
with excellent agreement with the experimental results illustrated
in FIGS. 5a-c.
[0053] Due to the anisotropic geometry of the pore
(length.times.width.times.height=400 .mu.m.times.48 .mu.m.times.10
.mu.m), reduced-order modeling gives excellent agreement with full
3D numerical results. For example, 1D modeling, which only
considers the length dimension, provides good agreement for
x.sub.m.sup..infin. (see 1D curve in FIG. 5F), while 2D modeling,
which accounts for the diffusioosmotic flow induced by the wall
surface charge, also successfully predicts the transient dynamics
(2D curve in FIG. 5f). Since x.sub.m.sup..infin. is only considered
when determining .zeta..sub.p, 1D modeling is sufficient, offering
computational efficiency and simplicity.
[0054] By solving the 1D advection-diffusion equation for the
particles as described herein, where advection is due only to
diffusiophoresis, x.sub.m(t) can be calculated for various particle
zeta potentials as shown in FIG. 6. The results indicate that
x.sub.m.sup..infin. is sensitive to .zeta..sub.p, as shown in the
inset of FIG. 6. Thus x.sub.m.sup..infin. is measured
experimentally and .zeta..sub.pis extracted by comparison with one
or more simulations, including 1D simulations. Zeta potentials
(.zeta..sub.p,DP) of a variety of particles were measured according
to this solute gradient method. The results compared well with the
zeta potentials (.zeta..sub.ELS) measured by standard
electrophoretic light scattering as evidenced in Table I.
TABLE-US-00001 TABLE I Zeta Potentials of various colloidal
particles measured via solute gradients and electrophoretic light
scattering Particle 2a (.mu.m).sup.1 .zeta..sub.p, DP (mV)
.zeta..sub.p, ELS (mV) Solution conditions.sup.2 Polystyrene (Bangs
Lab) 0.99 -80.1 .+-. 5.3 -67.5 .+-. 4.9 Polystyrene (Invitrogen)
1.1 -81.4 .+-. 3.4 -79.2 .+-. 6.8 Polystyrene (Spherotech) 0.91
-87.2 .+-. 4.0 -72.5 .+-. 5.4 Carboxylate-modified polystyrene 1.2
-72.1 .+-. 5.2 -74.7 .+-. 6.7 Sulfate-modified polystyrene 0.53
-85.6 .+-. 3.9 -59.1 .+-. 4.9 Amine-modified polystyrene 1.1 61.2
.+-. 4.4 58.8 .+-. 4.7 Decane 0.53 -88.7 .+-. 5.7 -104.3 .+-. 8.2
50 mM NaCl, 1 mM SDS .lamda.-DNA 0.29 -57.9 .+-. 6.4 -30.4 .+-.
10.9 pH = 8.3 Unilamellar lipid vesicles 0.86 -54.2 .+-. 13.3 -89.5
.+-. 10.4 pH = 7.2, 1 mM NaCl Non-fluorescent polystyrene 0.92
-84.5 .+-. 4.3 -68.8 .+-. 6.6 Polymethyl methacrylate 1.3 -52.1
.+-. 6.6 -61.2 .+-. 7.8 .sup.1Measured by dynamic light scattering
.sup.2c = (c.sub.i + c.sub.o)/2 .apprxeq. 5 mM NaCl and pH
.apprxeq. 6.0 unless otherwise noted.
[0055] In view of the foregoing methods, zeta potentiometers are
also described herein. In some embodiments, a zeta potentiometer
comprises at least one flow channel, at least one light source for
illuminating the flow channel, and an imaging device positioned to
observe the illuminated flow channel. A sample storage location is
adapted to provide a sample to the at least one flow channel for
analysis. FIG. 10 illustrates a zeta potentiometer according to
some embodiments.
[0056] The zeta potentiometer in FIG. 10 employs a USB microscope
as the imaging device and light emitting diode (LED) backlight for
channel illumination. The microscope and LED are positioned
opposite one another. Additionally, the sample storage location is
located above the channel, permitting sample flow to the channel
via hydrostatic pressure. The zeta potentiometer of FIG. 10 can
require small sample volumes, generally less than 100 .mu.m, while
providing fast analytical times, generally less than 5 minutes. In
some embodiments, zeta potentiometers described herein do not
employ any external forces in the zeta potential analysis. Prior
zeta potentiometers, for example, have employed external electric
and/or magnetic fields in the particle analysis. Electro-acoustic
forces have also been used in prior zeta potentiometers for
particle analysis. As shown herein, the described zeta
potentiometers and associated diffusiophoretic methods obviate the
need for these external forces in particle analysis.
[0057] In another aspect, methods of determining zeta potential of
channel surfaces and/or walls are described. In some embodiments, a
method of determining surface or wall zeta potential comprises
providing at least one dead-end pore containing a solute having a
first solute concentration and introducing a plurality of colloidal
particles having a second solute concentration less than the first
solute concentration. The plurality of colloidal particles migrate
into the dead-end pore, and the image intensity of the dead-end
pore is measured prior to the colloidal particle migration reaching
a quasi-steady state. The transient peak position is determined
from the image intensity, and zeta potential of the pore wall is
determined from the transient peak position. In some embodiments,
wall zeta potential is determined by fitting the transient peak
position to a power law curve, obtaining a power law exponent, and
comparing the effective power law exponent to results from a
two-dimensional computer simulation.
[0058] Whereas the quasi-steady location of the maximum particle
density x.sub.m.sup..infin. was used to determine .zeta..sub.p, the
transient particle dynamics during early times contain information
about wall zeta potential .zeta..sub.w due to the presence of
diffusioosmotic flow induced by the solute gradients. Although the
net fluid flow in a dead-end pore is zero due to confinement,
nonzero local flow velocities exist because of balance between
diffusioosmosis and induced pressure gradients driving opposite
motions. For example, the curved colloidal front of FIG. 5a further
confirms the contribution of pressure-driven flow. This flow
balance results in circulating flow with magnitude proportional to
|.gradient.lnc| that propagates along the solute diffusion. For a
negatively charged wall exposited to a solute gradient directed in
the pore, the resulting flow diverges from the center to the wall
as illustrated in FIG. 7A. This flow pushes the particles, which
have entered at the early stage, away from the center toward the
wall retarding the overall migration toward the end of the pore
(FIG. 7A).
[0059] Particle dynamics under such a circulating fluid flow are
simulated by imposing a wall slip velocity,
.mu..sub.w=-.GAMMA..sub.w.gradient.lnc, where .GAMMA..sub.w is the
wall diffusiophoretic mobility, which is determined by
.zeta..sub.w. Due the channel's narrow cross-section, it may be
treated as a 2D system considering the dimensions in the length (x)
and height (z) directions, thereby reducing computational costs.
The 2D approximation further allows analytical solutions for
circulating fluid flow to be obtained using the lubrication
approximation. Particle distributions calculated from 2D
simulations are presented in FIGS. 7B and 7C, showing the influence
of this fluid flow on the particle dynamics. The presence of this
circulating flow advects the particles toward the wall, retarding
the motion of x.sub.m(t), especially at times early times, such as
less than 60 s. However, the circulating flow is weakened over
time, and the transverse flow component exists only far from the
inlet. Consequently, particles entering the in the late stage are
hardly influenced by fluid advection, ultimately resulting in
similar x.sub.m.sup..infin. regardless of .zeta..sub.w.
[0060] During this time-dependent behavior, at early times (<60
s) the transient peak position deviates from diffusive ingress
(x.sub.m(t).about.t.sup.1/2) in a power-law-like behavior (i.e.,
x.sub.m(t).about.t.sup..beta.), as shown in FIG. 7D. The effective
power law exponent (.beta.) is empirically observed to be sensitive
to both .zeta..sub.p and .zeta..sub.w since the transient dynamics
are a consequence of interplay between the particle
diffusiophoresis and the diffusiophoretic fluid advection. The
exponent .beta. is given the inset of FIG. 7D for a wide range of
.zeta..sub.p and .zeta..sub.w and can be used to determine
.GAMMA..sub.p from a known .GAMMA..sub.p.
[0061] A prerequisite for measuring .zeta..sub.w using this method
is that .GAMMA..sub.p must be larger than .GAMMA..sub.w. If
.GAMMA..sub.w.gtoreq..GAMMA..sub.p, the constant particle inlet
condition for the simulations becomes invalid, since the number of
particles leaving the pore due to the circulating flow is greater
than the number entering the pore.
[0062] This method is demonstrated by performing experiments with
polystyrene particles in bare and plasma-treated
poly-(dimethylsiloxane) (PDMS) channels (FIG. 7E). Plasma treatment
significantly increases the surface charge, thereby increasing
.zeta..sub.w. As predicted, the plasma-treated channel exhibits
much slower migration in the early stage compared to the untreated
surface, although x.sub.m.sup..infin. is similar for both cases.
.zeta..sub.w was determined by obtaining .beta. (FIG. 7F) and
comparing to simulation results (inset of FIG. 7f). The results are
approximately -55 mV for the untreated -72 mV for the
plasma-treated PDMS surfaces, which are in good agreement with
prior literature values.
[0063] In another aspect, methods of determining the zeta potential
of channel walls or surfaces via pressure measurements are
described. A method of determining zeta potential of channel walls
or surfaces, in some embodiments, comprises establishing a solute
concentration gradient to induce a wall slip boundary condition in
the channel. The pressure drop along the channel is measured, and
channel wall diffusiophoretic mobility of the slip boundary
condition is derived from the measured pressure drop. The zeta
potential of the channel walls or surfaces is derived from this
wall diffusiophoretic mobility. In some embodiments, for example,
wall diffusiophoretic mobility is derived from a relation between
the measured pressure drop and the wall slip velocity of the
boundary condition.
[0064] The solute concentration gradient can be established by any
means consistent with the methods described herein. In some
embodiments, for example, the solute gradient is established by
coupling each channel end to a larger channel, wherein the larger
channels carry solute concentrations at different speeds. FIGS. 8A
and 8B illustrate such a setup wherein ends of a channel 80 are
coupled to larger main channels (Channel 1 and Channel 2). In the
embodiment of FIGS. 8a-b, Channel 1 carries a nondimensional solute
concentration of c=1 at a mean speed of at a mean speed of
.sub.main,1 and Channel 2 carries a nondimensional solute
concentration of c=.beta. at a mean speed of .sub.main,2. Dynamics
within the pore are established by driving the main flows in
Channels 1 and 2 at different speeds. For example, with
.sub.main,1> .sub.main,2, a pressure gradient along the channel
80 will drive flow through the channel 80 at a mean speed of >0.
With steady inlet/outlet conditions, a steady-state solute
concentration gradient will develop within the channel 80 on a
timescale of L.sup.2/D.sub.s, where for low Reynolds numbers the
flow is quasi-steady with respect to the solute dynamics, and
wherein L is channel 80 length and D.sub.s is solute diffusivity.
As this solute gradient develops, slip boundary conditions at the
channel 80 walls drive recirculating secondary flows through
diffusioosmosis, which cause deviations in the pressure gradient
along the channel 80. This pressure gradient is directly related to
the zeta potential of the channel 80 walls, making possible the use
of such a system to perform zeta potentiometry of surfaces using
fluid measurements. FIG. 8b is a magnified view of the channel 80
of dimensions 2h.sub.1.times.2h.sub.2 wherein the solid arrows
denote the direction of flow.
[0065] The equations governing the coupled fluid/solute dynamic
include the Navier-Stokes and continuity equations, as well as the
advection-diffusion equation for the dissolved solute dynamics.
Analytical solutions can be achieved via the lubrication
approximation for the case of long narrow channels. The unique
feature that differentiates methods and systems described herein,
including that illustrated in FIGS. 8a and 8b, from a traditional
pressure-driven Poiseuille flow calculation is the addition of wall
slip boundary conditions on the pore walls due to the action of
diffusioosmosis that is driven by local solute concentration
gradients. The slip boundary conditions result in deviations of the
pressure gradient within the channel from the Poiseuille flow case
with no-slip boundaries. As shown below, zeta potential of the
channel surfaces can be calculated directly from the total pressure
drop along the channel.
[0066] The pressure drop along the channel .DELTA.p=p(1)-p(0) is
given by Equation (10):
.DELTA. .times. p = 3 3 .times. C * - 1 .times. ( 1 + .GAMMA. w L
.times. U _ .times. ln .times. .beta. ) ( 10 ) ##EQU00010##
Therefore, the pressure drop is uniquely specified by the solute
concentration ratio .beta., the channel aspect ratio
h.sub.1/h.sub.2 (through C*), and the dimensionless diffusioosmotic
mobility of the channel walls
.GAMMA. w L .times. U , ##EQU00011##
where .GAMMA..sub.w is channel wall or channel surface
diffusioosmotic mobility. For a typical system, h.sub.1/h.sub.2 and
.beta. will be given system design parameters. Equation 10 then
directly relates the diffusioosmotic mobility of the channel walls
with the total pressure drop .DELTA.p along the length of the
channel, which may be measured. Therefore, in practice, the
measurement of a single pressure drop in a microfluidic system is
sufficient to determine wall diffusioosmotic mobility
.GAMMA..sub.w, wherein zeta potential of the channel walls or
channel surfaces can be derived from .GAMMA..sub.w.
[0067] Zeta potential (.zeta.)can be proportional to the logarithm
of the solute concentration for the case of symmetric electrolytes
with a valence of one for a wide range of solute concentrations.
Specifically, if the cations do not show specific adsorption, the
zeta potential is given as
.zeta. = - a 1 .times. ln .times. c ##EQU00012##
where a.sub.1 is a constant of proportionality. Then neglecting
corrections due to finite Debye layer effects, the diffusioosmotic
mobility can be written as Equation (11):
.GAMMA. w = .mu. .times. ( k B .times. T Z .times. e ) 2 [ ( D + -
D - D + + D - ) .times. Z .times. e .times. .zeta. k B .times. T +
4 .times. ln .times. cosh .function. ( Z .times. e .times. .zeta. 4
.times. k B .times. T ) ] ( 11 ) ##EQU00013##
where is the permittivity of the medium, .mu. is the dynamic
viscosity of the medium, k.sub.B is the Boltzman constant, T is the
absolute temperature, e is the elementary charge, Z is the valence
of the solute, D+ and D- are the diffusivity of cations and anions
respectively, and .zeta. is zeta potential of the channel walls or
surfaces.
[0068] FIG. 9 illustrates a system design for measuring zeta
potential of channel walls or surfaces according to some
embodiments. As illustrated in FIG. 9, the channel or pore of
interest is connected to two main channels as in FIG. 8. Notably,
the pore extends through the two main channels for connection to
pressure measurement ports. The system also provides holes or ports
for connecting the main channels to flow pumps.
[0069] Channels employed in one or more of the methods described
herein can have any dimensions not inconsistent with the objectives
of the present invention. In some embodiments, channels are of
dimensions suitable for microfluidic analysis. Additionally, fluid
advective velocities in the channels can be controlled with one or
more pumps. As detailed herein, fluid advective velocity can
include a diffusioosmotic component or contribution, which is a
function of at least channel wall zeta potential. Moreover,
diffusioosmotic velocity is fluid velocity at the channel wall and
is incorporated into fluid advective velocity along with the
pressure induced flow. In some embodiments, fluids employed in the
present methods are one or more biological fluids. In other
embodiments, the fluids are non-biological fluids.
[0070] Particle manipulation and/or separation methods and systems
described herein can be employed in a variety of applications
including, but not limited to, fluid filtration, such as water
filtration, particle sorting, separation, and focusing, and
diagnostic and measurement applications.
[0071] Various embodiments of the invention have been described in
fulfillment of the various objectives of the invention. It should
be recognized that these embodiments are merely illustrative of the
principles of the present invention. Numerous modifications and
adaptations thereof will be readily apparent to those skilled in
the art without departing from the spirit and scope of the
invention.
* * * * *