U.S. patent application number 17/501772 was filed with the patent office on 2022-02-10 for non-planar and non-symmetrical piezoelectric crystals and reflectors.
The applicant listed for this patent is FloDesign Sonics, Inc.. Invention is credited to Kedar Chitale, Brian Dutra, Rudolf Gilmanshin, Thomas J. Kennedy, III, Bart Lipkens, Dane Mealey, Walter M. Presz, JR., David Sokolowski.
Application Number | 20220040733 17/501772 |
Document ID | / |
Family ID | |
Filed Date | 2022-02-10 |
United States Patent
Application |
20220040733 |
Kind Code |
A1 |
Lipkens; Bart ; et
al. |
February 10, 2022 |
NON-PLANAR AND NON-SYMMETRICAL PIEZOELECTRIC CRYSTALS AND
REFLECTORS
Abstract
An acoustophoretic device is disclosed. The acoustophoretic
device includes an acoustic chamber, an ultrasonic transducer, and
a reflector. The ultrasonic transducer includes a piezoelectric
material driven by a voltage signal to create a multi-dimensional
acoustic standing wave in the acoustic chamber emanating from a
non-planar face of the piezoelectric material. A method for
separating a second fluid or a particulate from a host fluid is
also disclosed. The method includes flowing the mixture through an
acoustophoretic device. A voltage signal is sent to drive the
ultrasonic transducer to create the multi-dimensional acoustic
standing wave in the acoustic chamber such that the second fluid or
particulate is continuously trapped in the standing wave, and then
agglomerates, aggregates, clumps, or coalesces together, and
subsequently rises or settles out of the host fluid due to buoyancy
or gravity forces, and exits the acoustic chamber.
Inventors: |
Lipkens; Bart; (Hampden,
MA) ; Presz, JR.; Walter M.; (Wilbraham, MA) ;
Chitale; Kedar; (Little Rock, AR) ; Kennedy, III;
Thomas J.; (Wilbraham, MA) ; Gilmanshin; Rudolf;
(Framingham, MA) ; Mealey; Dane; (Somers, CT)
; Dutra; Brian; (Granby, CT) ; Sokolowski;
David; (Wilbraham, MA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
FloDesign Sonics, Inc. |
Wilbraham |
MA |
US |
|
|
Appl. No.: |
17/501772 |
Filed: |
October 14, 2021 |
Related U.S. Patent Documents
|
|
|
|
|
|
Application
Number |
Filing Date |
Patent Number |
|
|
15206244 |
Jul 9, 2016 |
11179747 |
|
|
17501772 |
|
|
|
|
62190715 |
Jul 9, 2015 |
|
|
|
International
Class: |
B06B 1/02 20060101
B06B001/02; B01D 21/28 20060101 B01D021/28; B06B 1/06 20060101
B06B001/06; B01D 21/00 20060101 B01D021/00; B06B 3/04 20060101
B06B003/04; C12M 1/00 20060101 C12M001/00; H03H 9/17 20060101
H03H009/17 |
Claims
1. An acoustic reflector, comprising a reflective portion for
reflecting acoustic energy, the reflective portion including a
non-planar face that is faceted.
2. The reflector of claim 1, further comprising a planar face
opposite the non-planar face.
3. The reflector of claim 2, further comprising the reflective
portion being composed of piezoelectric material.
4. The reflector of claim 3, further comprising the piezoelectric
material being poled in a direction substantially perpendicular to
the planar face of the reflector.
5. The reflector of claim 1, wherein the non-planar face of the
reflector includes a shape that is defined by a step function or a
smooth function.
6. The reflector of claim 2, wherein the non-planar face of the
reflector includes a plurality of adjoining portions, each of which
are located at respective distances from a respective closest
portion of the planar face, the respective distances being
different.
7. The reflector of claim 6, wherein the respective distance of
each adjoining portion from the respective closest portion of the
planar face defines a resonance for the acoustic energy.
8. The reflector of claim 7, wherein the collective respective
distances define a plurality of distinct resonances that match
resonances for the acoustic energy as resonance conditions for the
acoustic energy vary.
9. The reflector of claim 1, further comprising the faceted
non-planar face being configured to scatter the reflected acoustic
energy.
10. The reflector of claim 9, further comprising the faceted
non-planar face being configured to disrupt resonance of the
acoustic energy.
11. A method for forming an acoustic field, comprising: generating
acoustic energy using an ultrasonic transducer; reflecting the
acoustic energy with an acoustic reflector that comprises a
reflective portion for reflecting acoustic energy, the reflective
portion including a non-planar face that is faceted; and causing
the generated acoustic energy and reflected acoustic energy to
interact to form the acoustic field.
12. The method of claim 11, wherein the acoustic reflector further
comprises a planar face opposite the non-planar face.
13. The method of claim 12, wherein the reflective portion further
comprises piezoelectric material.
14. The method of claim 13, further comprising the piezoelectric
material being poled in a direction substantially perpendicular to
the planar face of the reflector.
15. The method of claim 11, further comprising defining a shape of
the non-planar face of the reflector by a step function or a smooth
function.
16. The method of claim 12, wherein the non-planar face of the
reflector includes a plurality of adjoining portions, each of which
are located at respective distances from a respective closest
portion of the planar face, the respective distances being
different.
17. The method of claim 11, further comprising scattering the
reflected acoustic energy using the faceted non-planar face.
18. The method of claim 11, further comprising disrupting resonance
of the acoustic field using the faceted non-planar face.
19. An acoustic system, comprising: an acoustic chamber; an
ultrasonic transducer coupled to the acoustic chamber that includes
a piezoelectric material that is configured to be excited to
generate an acoustic wave in the acoustic chamber; and a reflector
located across the acoustic chamber from the at least one
ultrasonic transducer, the reflector including a faceted surface
that faces the at least one ultrasonic transducer.
20. The system of claim 19, wherein the faceted, non-planar face of
the reflector includes a plurality of facet clusters.
21. The system of claim 19, wherein the faceted, non-planar face of
the reflector includes a plurality of wells.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application claims priority to U.S. patent application
Ser. No. 15/206,244, filed on Jul. 9, 2016 which claims priority to
U.S. Provisional Patent Application Ser. No. 62/190,715, filed on
Jul. 9, 2015, the disclosure of each of which is hereby fully
incorporated by reference in its entirety.
BACKGROUND
[0002] The present disclosure relates to the use of ultrasonically
generated acoustic standing waves to achieve trapping,
concentration, and separation of suspended-phase components and
thereby remove such contaminants from a fluid medium such as water.
The acoustic standing waves may be created by exciting the
piezoelectric crystal of an ultrasonic transducer.
[0003] Piezoelectric crystals may be composed of any material that
is able to generate a piezoelectric effect, i.e. vibrate when
subjected to an external voltage. A conventional material that is
used to make piezoelectric crystals is lead zirconate titanate
(PZT). Piezoelectric ceramics are traditionally a mass of
perovskite ceramic crystals composed of a small, tetravalent metal
ion (e.g., titanium, zirconium) in a lattice of larger, divalent
metal ions (e.g., lead, barium) and oxygen ions.
[0004] A piezoelectric PZT crystal can be made by mixing fine
powders of the component metal oxides in specific proportions. This
mixture is then heated to form a uniform powder. An organic binder
is mixed with the metal oxides and formed into desired shapes
(e.g., plates, rods, discs). The formed materials are heated at
high temperatures that sinter the mixture and form a dense
crystalline structure. The sintered parts are then cooled and
subsequently shaped or trimmed to desired specifications.
Electrodes are applied to the appropriate surfaces of the PZT
crystal using processes such as electroless nickel plating or a
silver/glass bead mixture coating that is heated and fused on the
surface of the crystal.
[0005] Exposing the piezoelectric crystal to an electric charge
(i.e. voltage) either in air or a liquid fluid generates pressure
waves. A function generator may be used to apply a specific
frequency or group of frequencies to the piezoelectric crystal such
that the pressure waves have a specific frequency. An amplifier may
be used to apply higher voltages to the piezoelectric crystal at
the frequencies generated by the function generator.
Conventionally, the face of the piezoelectric crystal is flat and
thus the waves generated from the piezoelectric crystal are uniform
across the face of the crystal.
[0006] A flat-faced piezoelectric crystal can be perturbed in a
multi-mode fashion so as to generate multi-dimensional acoustic
standing waves. These higher order modes of the piezoelectric
crystal allow for multiple trapping lines to be formed in the
acoustic standing wave, thus forming a multi-dimensional acoustic
standing wave.
[0007] It would be desirable to provide a piezoelectric crystal
that can be perturbed by a single excitation, yet still generate a
multi-dimensional acoustic standing wave(s).
BRIEF DESCRIPTION
[0008] The present disclosure relates, in various embodiments, to
acoustophoretic devices and methods of separating a second fluid or
a particulate from a host fluid. Briefly, a multi-dimensional
acoustic standing wave(s) emanating from a non-planar face of a
piezoelectric material is used to continuously trap the second
fluid or particulate, which then agglomerates, aggregates, clumps,
or coalesces together, and subsequently rises or settles out of the
host fluid due to buoyancy or gravity forces, and exits the
acoustic chamber. The non-planar piezoelectric material only needs
to be exposed to a single frequency, rather than a group of
frequencies, to generate a multi-dimensional acoustic standing
wave.
[0009] Disclosed in various embodiments herein are acoustophoretic
devices, comprising: an acoustic chamber having at least one inlet
and at least one outlet; at least one ultrasonic transducer located
on a wall of the acoustic chamber; and a reflector located on a
wall on the opposite side of the acoustic chamber from the at least
one ultrasonic transducer. The at least one ultrasonic transducer
includes a piezoelectric material driven by a voltage signal to
create a multi-dimensional acoustic standing wave in the acoustic
chamber emanating from a non-planar face of the piezoelectric
material.
[0010] In certain embodiments, the non-planar face of the
piezoelectric material is poled in a direction substantially
perpendicular to a second face of the piezoelectric material. The
non-planar face of the piezoelectric material can be defined by a
step function or a smooth function.
[0011] In certain embodiments, the reflector also has a non-planar
surface, which can be defined by a step function or a smooth
function.
[0012] In certain embodiments, the piezoelectric material may be
planar and the reflector will have a non-planar surface.
[0013] The at least one ultrasonic transducer can have a
non-symmetrical shape, such as a trapezoidal shape. The reflector
can also have a non-symmetrical shape, such as a trapezoidal
shape.
[0014] Also disclosed herein are methods for separating a second
fluid or a particulate from a host fluid. The methods comprise
flowing a mixture of the host fluid and the second fluid or
particulate through an acoustophoretic device. The acoustophoretic
device comprises an acoustic chamber having at least one inlet and
at least one outlet; at least one ultrasonic transducer located on
a wall of the acoustic chamber; and a reflector located on a wall
on the opposite side of the acoustic chamber from the at least one
ultrasonic transducer. The at least one ultrasonic transducer
includes a piezoelectric material driven by a voltage signal to
create a multi-dimensional acoustic standing wave in the acoustic
chamber emanating from a non-planar face of the piezoelectric
material. The methods further comprise sending a voltage signal to
drive the at least one ultrasonic transducer to create the
multi-dimensional acoustic standing wave in the acoustic chamber
such that the second fluid or particulate is continuously trapped
in the standing wave, and then agglomerates, aggregates, clumps, or
coalesces together, and continuously rises or settles out of the
host fluid due to enhanced buoyancy or gravity forces, and exits
the acoustic chamber.
[0015] The voltage signal can be a sinusoidal, triangular, pulsed
or similar waveform. The voltage signal can have a frequency of
from about 100 kHz to about 20 MHz.
[0016] In certain embodiments, the mixture of the host fluid and
the second fluid or particulate is continuously flowed through the
acoustic chamber. The second fluid or particulate can include at
least one cell selected from the group consisting of CHO cells,
T-cells, and yeast cells. Flow rates through the acoustic chamber
can be from about 1 mL per minute to about 50 liters per hour. The
methods and devices of the present disclosure may be capable of
separation efficiencies of 90% and more for cell concentrations
from as low as 50,000 cells per milliliter of fluid to 80,000,000
cells per milliliter of fluid.
[0017] Separation of materials may also include particulates
separated from a primary fluid. This would include microspheres,
microbubbles, microcarriers and the like. These materials may be
solid or hollow and have a positive or negative contrast
factor.
[0018] Also in various embodiments herein are acoustophoretic
devices, comprising: an acoustic chamber having at least one inlet
and at least one outlet; at least one ultrasonic transducer located
on a wall of the acoustic chamber; and a reflector located on a
wall on the opposite side of the acoustic chamber from the at least
one ultrasonic transducer. The at least one ultrasonic transducer
includes a piezoelectric material driven by a voltage signal to
create a multi-dimensional acoustic standing wave in the acoustic
chamber emanating from a first face of the piezoelectric material,
and the reflector includes a faceted surface. The first face of the
ultrasonic transducer can be planar. The faceted surface of the
reflector can include a plurality of facet clusters or a plurality
of wells.
[0019] In particular embodiments, the multi-dimensional standing
wave results in an acoustic radiation force having an axial force
component and a lateral force component that are the same order of
magnitude. In particular embodiments, the acoustic standing wave
may be a multi-dimensional acoustic standing wave (e.g., a
three-dimensional acoustic standing wave). Examples of such
multi-dimensional acoustic standing waves can be found in commonly
owned U.S. Pat. No. 9,228,183, the entire contents of which are
hereby fully incorporated by reference. In other embodiments, the
acoustic standing wave can be a planar acoustic standing wave.
Further yet, in particular embodiments, the acoustic standing wave
may be a combination of a planar acoustic standing wave and a
multi-dimensional acoustic standing wave, such as where the planar
acoustic standing wave and multidimensional acoustic standing wave
are super-positioned on each other.
[0020] These and other non-limiting characteristics are more
particularly described below.
BRIEF DESCRIPTION OF THE DRAWINGS
[0021] The following is a brief description of the drawings, which
are presented for the purposes of illustrating the exemplary
embodiments disclosed herein and not for the purposes of limiting
the same.
[0022] FIG. 1 is a graph showing the relationship of the acoustic
radiation force, gravity/buoyancy force, and Stokes' drag force to
particle size. The horizontal axis is in microns (.mu.m) and the
vertical axis is in Newtons (N).
[0023] FIG. 2A illustrates a first embodiment of a piezoelectric
material according to the present disclosure. The piezoelectric
material is a perovskite crystal at a temperature above the Curie
point.
[0024] FIG. 2B illustrates a second embodiment of a piezoelectric
material according to the present disclosure. The piezoelectric
material is a perovskite crystal at a temperature below the Curie
point.
[0025] FIG. 3 illustrates a first embodiment of a non-planar face
of a piezoelectric material according to the present disclosure.
The non-planar face of the piezoelectric material is defined by a
smooth function.
[0026] FIG. 4 illustrates a second embodiment of a non-planar face
of a piezoelectric material according to the present disclosure.
The non-planar face of the piezoelectric material is defined by a
stepped function formed by facets.
[0027] FIG. 5 illustrates a third embodiment of a non-planar face
of a piezoelectric material according to the present disclosure.
The non-planar face of the piezoelectric material is defined by a
stepped function formed by facets.
[0028] FIG. 6 illustrates a cross-sectional view of an acoustic
chamber of an acoustophoretic device according to the present
disclosure. The device includes a piezoelectric material having a
planar first face and a reflector having a faceted surface.
[0029] FIG. 7A illustrates a first exemplary configuration of the
faceted surface of the reflector of FIG. 6.
[0030] FIG. 7B illustrates a second exemplary configuration of the
faceted surface of the reflector of FIG. 6.
[0031] FIG. 7C illustrates a third exemplary configuration of the
faceted surface of the reflector of FIG. 6.
[0032] FIG. 8 illustrates a magnified view of a facet cluster of
the faceted surface of FIG. 7C, showing the height differential
between a central facet and four surrounding outer facets.
[0033] FIG. 9 illustrates a fourth exemplary configuration of the
faceted surface of the reflector of FIG. 6.
[0034] FIG. 10 illustrates a magnified view of the faceted surfaces
depicted in FIG. 9.
[0035] FIG. 11 is a graph illustrating the separation efficiency of
a faceted reflector versus a flat, planar reflector at varied
impedance levels. The left-hand y-axis is impedance in thousands of
rayls. The two lines marked as "flat reflector" and "faceted
reflector" are read against the left-hand y-axis. The right-hand
y-axis is efficiency. The points labeled "1 mission" and "1e6 flat"
(triangular and X-shaped points) are read against the right-hand
y-axis. The x-axis is in units of ten thousand Hertz.
[0036] FIG. 12 is a graph illustrating the separation efficiency of
a faceted reflector versus a flat, planar reflector over time at a
frequency of 2.185 MHz and two different powers (5 W and 10 W).
[0037] FIG. 13 illustrates a third embodiment of a piezoelectric
material according to the present disclosure. The piezoelectric
material has a non-symmetrical, trapezoidal shape.
[0038] FIGS. 14A-140 illustrate the non-planar face of the
trapezoidal piezoelectric material of FIG. 13 upon which asymmetric
excitation patterns are generated at four different
frequencies.
[0039] In FIG. 14A, the excitation pattern is generated at a
frequency of 2.217 MHz. The right-hand scale is in units of
10.sup.-9, and ranges from 0.55 to 1 in intervals of 0.05. The
maximum value is 2.25.times.10.sup.-9, and the minimum value is
2.18.times.10.sup.-11.
[0040] In FIG. 14B, the excitation pattern is generated at a
frequency of 2.302 MHz. The right-hand scale is in units of
10.sup.-10, and ranges from 3 to 6 in intervals of 0.5. The maximum
value is 1.38.times.10.sup.-9, and the minimum value is
1.64.times.10.sup.-11.
[0041] In FIG. 14C, the excitation pattern is generated at a
frequency of 2.32 MHz. The right-hand scale is in units of
10.sup.-10, and ranges from 2.5 to 6 in intervals of 0.5. The
maximum value is 1.11.times.10.sup.-9, and the minimum value is
1.4.times.10.sup.-11.
[0042] In FIG. 14D, the excitation pattern is generated at a
frequency of 2.34 MHz. The right-hand scale is in units of
10.sup.-10, and ranges from 3 to 5 in intervals of 0.5. The maximum
value is 9.23.times.10.sup.-10, and the minimum value is
8.98.times.10.sup.-12.
[0043] FIG. 15 is a diagram illustrating an acoustophoretic
separation method according to the present disclosure for a second
fluid or particle less dense than a host fluid.
[0044] FIG. 16 is a diagram illustrating an acoustophoretic
separation method according to the present disclosure for a second
fluid or particle denser than a host fluid.
[0045] FIG. 17 is a cross-sectional diagram of a conventional
ultrasonic transducer.
[0046] FIG. 18 is a cross-sectional diagram of an ultrasonic
transducer according to the present disclosure. An air gap is
present within the transducer, and no backing layer or wear plate
is present.
[0047] FIG. 19 is a cross-sectional diagram of an ultrasonic
transducer according to the present disclosure. An air gap is
present within the transducer, and a backing layer and wear plate
are present.
DETAILED DESCRIPTION
[0048] The present disclosure may be understood more readily by
reference to the following detailed description of desired
embodiments and the examples included therein. In the following
specification and the claims which follow, reference will be made
to a number of terms which shall be defined to have the following
meanings.
[0049] Although specific terms are used in the following
description for the sake of clarity, these terms are intended to
refer only to the particular structure of the embodiments selected
for illustration in the drawings, and are not intended to define or
limit the scope of the disclosure. In the drawings and the
following description below, it is to be understood that like
numeric designations refer to components of like function.
[0050] The singular forms "a," "an," and "the" include plural
referents unless the context clearly dictates otherwise.
[0051] The term "comprising" is used herein as requiring the
presence of the named component and allowing the presence of other
components. The term "comprising" should be construed to include
the term "consisting of", which allows the presence of only the
named component, along with any impurities that might result from
the manufacture of the named component.
[0052] Numerical values should be understood to include numerical
values which are the same when reduced to the same number of
significant figures and numerical values which differ from the
stated value by less than the experimental error of conventional
measurement technique of the type described in the present
application to determine the value.
[0053] All ranges disclosed herein are inclusive of the recited
endpoint and independently combinable (for example, the range of
"from 2 grams to 10 grams" is inclusive of the endpoints, 2 grams
and 10 grams, and all the intermediate values). The endpoints of
the ranges and any values disclosed herein are not limited to the
precise range or value; they are sufficiently imprecise to include
values approximating these ranges and/or values.
[0054] The modifier "about" used in connection with a quantity is
inclusive of the stated value and has the meaning dictated by the
context. When used in the context of a range, the modifier "about"
should also be considered as disclosing the range defined by the
absolute values of the two endpoints. For example, the range of
"from about 2 to about 10" also discloses the range "from 2 to 10."
The term "about" may refer to plus or minus 10% of the indicated
number. For example, "about 10%" may indicate a range of 9% to 11%,
and "about 1" may mean from 0.9-1.1.
[0055] It should be noted that many of the terms used herein are
relative terms. For example, the terms "upper" and "lower" are
relative to each other in location, i.e. an upper component is
located at a higher elevation than a lower component in a given
orientation, but these terms can change if the device is flipped.
The terms "inlet" and "outlet" are relative to a fluid flowing
through them with respect to a given structure, e.g. a fluid flows
through the inlet into the structure and flows through the outlet
out of the structure. The terms "upstream" and "downstream" are
relative to the direction in which a fluid flows through various
components, i.e. the flow fluids through an upstream component
prior to flowing through the downstream component. It should be
noted that in a loop, a first component can be described as being
both upstream of and downstream of a second component.
[0056] The terms "horizontal" and "vertical" are used to indicate
direction relative to an absolute reference, i.e. ground level.
However, these terms should not be construed to require structures
to be absolutely parallel or absolutely perpendicular to each
other. For example, a first vertical structure and a second
vertical structure are not necessarily parallel to each other. The
terms "top" and "bottom" or "base" are used to refer to surfaces
where the top is always higher than the bottom/base relative to an
absolute reference, i.e. the surface of the earth. The terms
"upwards" and "downwards" are also relative to an absolute
reference; upwards is always against the gravity of the earth.
[0057] The term "parallel" should be construed in its lay sense of
two surfaces that maintain a generally constant distance between
them, and not in the strict mathematical sense that such surfaces
will never intersect when extended to infinity.
[0058] The present application refers to "the same order of
magnitude." Two numbers are of the same order of magnitude if the
quotient of the larger number divided by the smaller number is a
value of at least 1 and less than 10.
[0059] Acoustophoresis is the separation of particles and secondary
fluids from a primary or host fluid using high-intensity acoustic
standing waves, and without the use of membranes or physical size
exclusion filters. It has been known that high intensity standing
waves of sound can exert forces on particles in a fluid when there
is a differential in both density and/or compressibility, otherwise
known as the acoustic contrast factor. The pressure profile in a
standing wave contains areas of local minimum pressure amplitudes
at its nodes and local maxima at its anti-nodes. Depending on the
density and compressibility of the particles, they will be trapped
at the nodes or anti-nodes of the standing wave. Generally, the
higher the frequency of the standing wave, the smaller the
particles that can be trapped due the pressure of the standing
wave.
[0060] When acoustic standing waves propagate in liquids, the fast
oscillations may generate a non-oscillating force on particles
suspended in the liquid or on an interface between liquids. This
force is known as the acoustic radiation force. The force
originates from the non-linearity of the propagating wave. As a
result of the non-linearity, the wave is distorted as it propagates
and the time-averages are nonzero. By serial expansion (according
to perturbation theory), the first non-zero term will be the
second-order term, which accounts for the acoustic radiation force.
The acoustic radiation force on a particle, or a cell, in a fluid
suspension is a function of the difference in radiation pressure on
either side of the particle or cell. The physical description of
the radiation force is a superposition of the incident wave and a
scattered wave, in addition to the effect of the non-rigid particle
oscillating with a different speed compared to the surrounding
medium thereby radiating a wave. The following equation presents an
analytical expression for the acoustic radiation force on a
particle, or cell, in a fluid suspension in a planar standing
wave.
F R = 3 .times. .pi. .times. P 0 2 .times. V P .times. .beta. m 2
.times. .lamda. .times. .phi. .function. ( .beta. , .rho. ) .times.
sin .function. ( 2 .times. kx ) ( 1 ) ##EQU00001##
where .beta..sub.m is the compressibility of the fluid medium,
.rho. is density, .phi. is acoustic contrast factor, V.sub.p is
particle volume, A is wavelength, k is 2.pi./.lamda., P.sub.0 is
acoustic pressure amplitude, x is the axial distance along the
standing wave (i.e., perpendicular to the wave front), and
.phi. .function. ( .beta. , .rho. ) = 5 .times. .rho. .rho. - 2
.times. .rho. m 2 .times. .rho. .rho. + .rho. m - .beta. .rho.
.beta. m ##EQU00002##
where .rho..sub.p is the particle density, .rho..sub.m is the fluid
medium density, .beta..sub.p is the compressibility of the
particle, and .beta..sub.m is the compressibility of the fluid
medium.
[0061] In a typical experiment, the system is operated at a voltage
such that the particles are trapped in the ultrasonic standing
wave, i.e., remain in a stationary position. The axial component of
the acoustic radiation force drives the particles, with a positive
contrast factor, to the pressure nodal planes, whereas particles
with a negative contrast factor are driven to the pressure
anti-nodal planes. The radial or lateral component of the acoustic
radiation force is the force that traps the particle. It therefore
must be larger than the combined effect of fluid drag force and
gravitational force. For small particles or emulsions, the drag
force F.sub.D can be expressed as:
F D = 4 .times. .pi. .times. .mu. f .times. R P .function. ( U f -
U p ) [ 1 + 3 2 .times. .mu. ^ 1 + .mu. ^ ] ( 1 ) ##EQU00003##
where U.sub.f and U.sub.p are the fluid and particle velocity,
R.sub.p is the particle radius, .mu..sub.f and .mu..sub.p are the
dynamic viscosity of the fluid and particle, and {circumflex over
(.mu.)}=.mu..sub.p/.mu..sub.f is the ratio of dynamic viscosities.
The buoyancy force F.sub.B is expressed as:
F.sub.B=4/3.pi.R.sub.P.sup.3(.rho..sub.f-.rho..sub.p)g (2)
where R.sub.p is the particle radius, .rho..sub.f is the fluid
density, .rho..sub.p is the particle density, and g is the
universal gravitational constant.
[0062] For a particle to be trapped in the ultrasonic standing
wave, the force balance on the particle must be zero, and therefore
an expression for lateral acoustic radiation force F.sub.LRF can be
found, which is given by:
F.sub.LRF=F.sub.D+F.sub.B (3)
[0063] For a particle of known size and material property, and for
a given flow rate, this equation can be used to estimate the
magnitude of the lateral acoustic radiation force.
[0064] The theoretical model that is used to calculate the acoustic
radiation force is the formulation developed by Gor'kov, where the
primary acoustic radiation force F.sub.R is defined as a function
of a field potential U, F.sub.R=-.gradient.(U), where the field
potential U is defined as
U = V O .function. [ p 2 .function. ( x , y , z ) 2 .times. .rho. f
.times. c f 2 .times. f 1 - 3 .times. .rho. f .times. v 2
.function. ( x , y , z ) 4 .times. f 2 ] ##EQU00004##
and f.sub.1 and f.sub.2 are the monopole and dipole contributions
defined by
f 1 = 1 - 1 .LAMBDA. .times. .sigma. 2 .times. .times. f 2 = 2
.times. ( .LAMBDA. - 1 ) 2 .times. .LAMBDA. + 1 ##EQU00005##
where
.sigma. = c p c f .times. .times. .LAMBDA. = p p p f .times.
.times. .beta. f = 1 .rho. f .times. c f 2 ##EQU00006##
where p is the acoustic pressure, u is the fluid particle velocity,
.LAMBDA. is the ratio of cell density .rho..sub.p to fluid density
.rho..sub.f, .sigma. is the ratio of cell sound speed c.sub.p to
fluid sound speed c.sub.f, V.sub.0=.pi.R.sub.p.sup.3 is the volume
of the cell, and < > indicates time averaging over the period
of the wave.
[0065] For a one dimensional standing wave, where the acoustic
pressure is expressed as
p=A cos(kx)cos(.omega.t) (4)
where A is the acoustic pressure amplitude, k is the wavenumber,
and .omega. is the angular frequency. In this case, there is only
the axial component of the acoustic radiation force F.sub.ARF,
which is found to be
F A .times. R .times. F = V O .times. k .times. X .times. A 2 4
.times. .rho. f .times. c f 2 .times. sin .function. ( 2 .times. k
.times. x ) ( 5 ) ##EQU00007##
where X is the contrast factor given by
X = ( 5 .times. .LAMBDA. - 2 1 + 2 .times. .LAMBDA. - 1 .sigma. 2
.times. .LAMBDA. ) ##EQU00008##
[0066] Particles with a positive contrast factor will be driven to
the pressure nodal planes, and particles with a negative contrast
factor will be driven to the pressure anti-nodal planes. In this
way, the generation of a multi-dimensional acoustic standing wave
in an acoustic chamber results in the creation of tightly packed
clusters of particles in the acoustic chamber, typically
corresponding to the location of the pressure nodes or anti-nodes
in the standing wave depending on acoustic contrast factor.
[0067] Gork'ov's model is for a single particle in a standing wave
and is limited to particle sizes that are small with respect to the
wavelength of the sound fields in the fluid and the particle. It
also does not take into account the effect of viscosity of the
fluid and the particle on the radiation force. As a result, this
model cannot be used for macro-scale ultrasonic separators since
particle clusters can grow quite large.
[0068] FIG. 1 is a log-log graph (logarithmic y-axis, logarithmic
x-axis) that shows the scaling of the acoustic radiation force,
fluid drag force, and buoyancy force with particle radius.
Calculations are done for a typical mammalian cell used in
experiments. In the experiment, the mammalian cell had a density
(.rho..sub.p) of 1,050 kg/m.sup.3 and a cell sound speed (c.sub.p)
of 1,550 m/s. The fluid in which the particle was flowed was water
having a density (.rho..sub.w) of 1000 kg/m.sup.3, a fluid sound
speed (c.sub.f) of 1500 m/s, and a flow rate (v.sub.f) of 4 cm/min.
The experiment used 33 PZT-8 ultrasonic transducers driven at a
frequency (f) of 2.2 MHz at a pressure (p) of 1 MPa. As explained
above, the gravity/buoyancy force is a particle volume dependent
force, and is therefore negligible for particle sizes on the order
of micron, but grows, and becomes significant for particle sizes on
the order of hundreds of microns. The fluid drag force scales
linearly with fluid velocity, and therefore typically exceeds the
buoyancy force for micron sized particles, but is negligible for
larger sized particles on the order of hundreds of microns. The
acoustic radiation force scaling is different. When the particle
size is small, Gor'kov's equation is accurate and the acoustic
trapping force scales with the volume of the particle. Eventually,
when the particle size grows, the acoustic radiation force no
longer increases with the cube of the particle radius, and will
rapidly vanish at a certain critical particle size. For further
increases of particle size, the radiation force increases again in
magnitude but with opposite phase (not shown in the graph). This
pattern repeats for increasing particle sizes.
[0069] Initially, when a suspension is flowing through the system
with primarily small micron sized particles, it is necessary for
the acoustic radiation force to balance the combined effect of
fluid drag force and buoyancy force for a particle to be trapped in
the standing wave. In FIG. 1, this happens for a particle size of
about 3.5 micron, labeled as Rel. The graph then indicates that all
larger particles will be trapped as well. Therefore, when small
particles are trapped in the standing wave, particles
coalescence/clumping/aggregation/agglomeration takes place,
resulting in continuous growth of effective particle size. As the
particle size grows, the acoustic radiation force reflects off the
particle, such that large particles will cause the acoustic
radiation force to decrease. Particle size growth continues until
the buoyancy force becomes dominant, which is indicated by a second
critical particle size, R.sub.c2, at which size the particles will
rise or sink, depending on their relative density with respect to
the host fluid. Thus, FIG. 1 explains how small particles can be
trapped continuously in a standing wave, grow into larger particles
or clumps, and then continuously will rise or settle out because of
enhanced buoyancy or gravity forces.
[0070] The models that were implemented in the present disclosure
are based on the theoretical work of Yurii Ilinskii and Evgenia
Zabolotskaya as described in AIP Conference Proceedings, Vol.
1474-1, pp. 255-258 (2012). These models also include the effect of
fluid and particle viscosity, and therefore are a more accurate
calculation of the acoustic radiation force.
[0071] The acoustophoretic separation technology of the present
disclosure employs multi-dimensional ultrasonic acoustic standing
waves, planar acoustic standing waves or combinations of planar and
multidimensional acoustic standing waves (collectively referred to
herein simple as acoustic standing waves) to trap particles or a
secondary fluid in a volume of fluid containing said
particles/secondary fluid.
[0072] Turning now to FIG. 2A, a first embodiment of a
piezoelectric material 200 is shown. In the embodiment depicted in
FIG. 2A, the piezoelectric material 200 is a perovskite crystal at
a temperature above the Curie point. The piezoelectric material 200
is in the shape of a cubic lattice with a symmetrical arrangement
of positive and negative charges. FIG. 2B shows a second embodiment
of a piezoelectric material 250. In the embodiment depicted in FIG.
2B, the piezoelectric material 250 is a perovskite crystal at a
temperature below the Curie point. The piezoelectric material 250
is in the shape of a tetragonal (orthorhombic) lattice with an
electric dipole. Both of the piezoelectric materials 200, 250
depicted in FIG. 2A and FIG. 2B are comprised of divalent metal
ion(s) (e.g., lead, barium), oxygen ion(s), and tetravalent metal
ion(s) (e.g., titanium, zirconium). The dipole expansion and
contraction of the piezoelectric materials 200, 250 depicted in
FIG. 2A and FIG. 2B allow for the piezoelectric effect to occur,
resulting in the generation of pressure waves.
[0073] The Curie point is a critical temperature at which each
perovskite crystal in a piezoelectric material exhibits a simple
cubic symmetry with no dipole moment. However, at temperatures
below the Curie point, such as is depicted in FIG. 2B, each crystal
has tetragonal or rhombohedral symmetry and a dipole moment.
Adjoining dipoles form regions of local alignment are called
domains. The alignment of the crystals gives a net dipole moment to
the domain in the crystal and, as a result, generates a net
polarization. The polarization, however, is still random and thus
there is no overall direction that the piezoelectric crystal will
change in shape when an electrical impulse is applied.
[0074] In operation, a strong, direct current electric field,
usually at a temperature slightly below the Curie point, is applied
to the crystal. Through this poling (polarization) treatment, the
domains of the piezoelectric crystal most nearly aligned with the
electric field expand at the expense of domains that are not
aligned with the field, and the piezoelectric crystal expands in
the direction of the strong electrical field. When the electric
field is removed, most of the dipoles are locked into a
configuration of near alignment. The piezoelectric crystal now has
a permanent polarization (i.e., the crystal can be considered
"poled"). Thus, upon supplying an electrical charge to the crystal,
the crystal will expand and contract in the direction that it is
now poled.
[0075] In a conventional flat/planar piezoelectric surface, a
single frequency can be used to excite a multi-dimensional acoustic
standing wave. In accordance with the present disclosure, it has
been found that a piezoelectric material having a non-planar (i.e.,
non-flat) face can be electrically excited by a single frequency to
further enhance the expansion and contraction in the poled
direction of the crystal, such that differential vibrations (as
opposed to uniform vibrations) emanate from the surface of the
non-planar face of the piezoelectric material to generate a
multi-dimensional acoustic standing wave. Through proper shaping of
the non-planar surface, a multi-dimensional acoustic standing wave
can be generated as desired (e.g., with a desired strength, shape,
intensity).
[0076] FIG. 3 shows a first embodiment of such a piezoelectric
material 300 in which a non-planar first face 310 of the
piezoelectric material 300 is defined by a smooth function. In this
way, the non-planar face 310 of the piezoelectric material 300 is
poled in a direction 320 substantially perpendicular to a second
face 330 of the piezoelectric material 300. In the piezoelectric
material 300 depicted in FIG. 3, the non-planar face 310 and the
second face 330 are located on opposite sides of the crystal. The
second face is planar, and provides the reference against which the
non-planarity of the first face 310 is determined. As seen here,
the first face 310 is formed from a series of peaks 312 and valleys
314. The transition between the peaks and valleys is smooth. A
smooth function is a function having a derivative that is
continuous.
[0077] A single electrode can be used on each side of the
piezoelectric material. The electrode may be coated by several
means, such as plating with electroless nickel or spray coating
with a conductive coating, such as a silver-containing coating. The
electrodes must be separated so that there is a positive terminal
and a negative terminal to energize the piezoelectric material.
[0078] In contrast to FIG. 3, FIG. 4 shows a second embodiment of a
piezoelectric material 400 in which a non-planar first face 410 of
the piezoelectric material 400 is defined by a stepped function.
Again, the non-planar face 410 of the piezoelectric material 400 is
poled in a direction 420 substantially perpendicular to a second
face 430 of the piezoelectric material 400. A stepped function is a
piecewise constant function. As seen here, the overall shape of the
first face 410 is made up of a series of smaller flat surfaces 412,
also referred to herein as facets.
[0079] FIG. 5 shows a third embodiment of a piezoelectric material
500 in which a non-planar face 510 of the piezoelectric material
500 is defined by a stepped function. Yet again, the non-planar
first face 510 of the piezoelectric material 500 is poled in a
direction 520 substantially perpendicular to a second face 530 of
the piezoelectric material 500. The main difference between FIG. 4
and FIG. 5 is that the adjacent smaller flat surfaces 512 (i.e.
facets) vary much more in their difference in height (relative to
the second face 530).
[0080] It is also contemplated that the reflector located on an
opposite side of the acoustic chamber from the
transducer/piezoelectric material can also have a non-planar
surface, which can be likewise defined by a smooth or stepped
function. The non-planar face of the transducer/piezoelectric
material and the non-planar surface of the reflector may be
described as being faceted, such as is depicted in FIG. 6. In FIG.
6, the piezoelectric material 600 has a flat, planar first face
610, and the reflector 650 has a faceted surface 660. The faceted
surface 660 of the reflector 650 is defined by flat surfaces or
facets 662, similar to the facets 512 of the piezoelectric material
500 of FIG. 5 and the facets 412 of the piezoelectric material 400
of FIG. 4. That is, as depicted in FIG. 6, the facets 662 in the
faceted surface 660 of the reflector 650 can be stepped, such that
adjacent facets are located different distances from a first face
610 of the piezoelectric material 600. For example, facet 670 is
located distance L.sub.1 from the first face 610 of the
piezoelectric material 600, while facet 680 is located distance
L.sub.2 from the first face 610 of the piezoelectric material 600,
with L.sub.1 being greater than L.sub.2. It is to be understood
that the facets 662 may be dimensioned as desired. For example,
facet 670 typically has a width 672 selected to maximize the
reflected energy. Similarly, the distance between adjacent facets,
such as distance L.sub.3 between facet 670 and facet 680, is
typically selected to minimize the distance between the director of
a natural vibration mode of the piezoelectric material and adjacent
facets. The distance between a facet and the first face 610 of the
piezoelectric material 600 (e.g., distance L.sub.1 for facet 670
and distance L.sub.2 for facet 680) typically corresponds to a half
wavelength to accommodate for all possible resonance conditions in
the acoustic chamber.
[0081] As will be appreciated by those skilled in the art, the
facets 662 can be arranged as desired to create an acoustic
standing wave having a desired mode pattern. FIGS. 7A-7C depict
various exemplary configurations of the faceted surface 660 of the
reflector 650. For example, FIG. 7A shows a design in which the
faceted surface 660 of the reflector 650 includes flat surfaces or
facets 662 that extend along the length of the reflector 650. The
height of a given facet generally differs from the height of an
adjacent facet by a fraction of the generated acoustic standing
wave. The design in FIG. 7A implements a degenerated
one-dimensional pattern of intermittent steps.
[0082] FIG. 7B shows a design in which the faceted surface 660 of
the reflector 650 includes wells 664 having flat bottoms 666. In
the exemplary embodiment of FIG. 7B, the wells 664 are all of equal
depth. The distribution of the wells 664 on the faceted surface 660
of the reflector 650 corresponds to the distribution of the
3.times.3 mode pattern emitted by the reflector 650. The wells are
distributed in a regular pattern along the faceted surface.
[0083] Finally, FIG. 7C and FIG. 8 show a design in which the
faceted surface 660 of the reflector 650 includes multiple facet
clusters 668. In this exemplary embodiment, each facet cluster 668
is comprised of a pyramid-shaped group of five facets, with four
outer facets 673, 674, 675, 676 differing from a central facet 670
by a multiple of 0.1 wavelengths. That is, if the central facet 670
corresponds to the 0 position, the four outer facets 673, 674, 675,
676 are deeper by 0.1, 0.2, 0.3, and 0.4 wavelengths, respectively.
For example, central facet 670 in FIG. 8 corresponds to position 0,
outer facet 673 is located 70 .mu.m below the surface of the
central facet 670, outer facet 674 is located 140 .mu.m below the
surface of the central facet 670, outer facet 675 is located 210
.mu.m below the surface of the central facet 670, and outer facet
676 is located 240 .mu.m below the surface of the central facet
670. The distribution of the facet clusters 668 corresponds to the
distribution of the 9.times.9 mode pattern reflected by the
reflector, though it is to be understood that such a design could
also be used with a 3.times.3 mode pattern. It is further
contemplated that the pattern of the facets in the faceted surface
660 of the reflector 650 may influence the mode selection for
various frequencies. The number of facets or facet levels within a
single facet cluster is typically selected to ensure smooth
adjustment to the changing resonance conditions within the acoustic
chamber (i.e., more facets or facet levels for more gradual
transitions), with the facets or facet levels differing from one
another by a fraction of the acoustic wavelength, as previously
explained. The number of facets or facet levels should, however,
generally be limited to minimize the total number of facets,
thereby increasing the reflecting area per facet. As will be
appreciated by those skilled in the art, the piezoelectric material
may likewise have a faceted front face, similar to the faceted
surface of the reflector depicted in FIG. 6 and FIGS. 7A-7C. In
such embodiments, the first face of the piezoelectric material is
faceted, while the surface of the reflector is generally kept
planar or flat.
[0084] FIG. 9 and FIG. 10 depict another exemplary embodiment of a
faceted surface 660 of the reflector 650. FIG. 9 shows the entire
reflector, while FIG. 10 provides a magnified view of a portion of
the faceted surface 660 of the reflector 650. As best seen in FIG.
10, the surface is divided into multiple facets that provide four
different heights. A dotted line is used to indicate the facet
cluster 690. The central facet 691 is surrounded by a second facet
692, a third facet 693, and a fourth facet 694. The second facet
692 has approximately twice the surface area of the third facet or
the fourth facet. The third facet 693 is the lowest of these
facets, followed by the second facet 692, then the fourth facet
694, with the central facet 691 being the highest of these
facets.
[0085] It is noted that in FIGS. 4-10, the facets are generally
illustrated as being surfaces with a square-shaped perimeter. This
is not a requirement, and the facets may be of any suitable shape,
e.g. rectangular, circular, etc.
[0086] As will be explained in greater detail herein, the operation
of the acoustophoretic devices of the present disclosure includes
generation of acoustic standing waves in an acoustic chamber. The
acoustic standing waves can be at a fixed frequency throughout the
period of operation, and the frequency may be selected to match the
mode distribution of the piezoelectric material to the facet
distribution of the reflector. The maximal amplitude of the
acoustic standing wave is achieved under the resonance conditions
that occur when the wave frequency f satisfies the condition
f=nc/2L, where c is the speed of sound in the medium, n is a
positive integer, and L is the distance between the transducer and
the reflector. Optimal cell separation is achieved under the
resonance conditions at the maximal amplitude of the acoustic
pressure for a fixed emitter power. The maximal acoustic pressure
in turn leads to the maximal acoustic radiation force, which is the
result of the acoustic field gradients, and to the most efficient
cell trapping. When particles (e.g., cells) accumulate within the
acoustophoretic device (or more generally due to inhomogeneous
conditions), the speed of sound c changes and the resonance
conditions are destroyed. The speed of sound may also change due to
the change of temperature of the suspension. The temperature change
may be a result of the acoustic operation or due to the change of
the feed solution temperature. The resonance conditions can be
changed also for different suspension compositions. These are most
typical, but not all the possible, mechanisms of the resonance
destruction.
[0087] FIG. 11 graphically illustrates some of the advantages of
using a reflector having a faceted surface over a flat, planar
reflector. In FIG. 11, the lowest two lines (i.e., the lines having
square and diamond-shaped points) represent the impedance of a
faceted reflector and flat reflector in thousands of Rayls along
the left y-axis, and the upper two lines (i.e., the lines having
triangular and X-shaped points) represent the efficiency of a
faceted reflector and a flat reflector in values of percentage
along the right y-axis. The x-axis of FIG. 11 represents various
operating frequencies in ten thousands of Hertz. FIG. 11 shows that
for a yeast concentration of 1.times.10.sup.6 cells/mL, the
efficiency of a faceted reflector was noticeably greater than the
efficiency of a flat, planar reflector. A similar result is noticed
in FIG. 12, which graphically illustrates the efficiency of a
faceted reflector versus the efficiency of a flat, planar reflector
at a frequency of 2.185 MHz across a period of 80 minutes.
[0088] Referring back to FIG. 6, when the resonance is destroyed
for facet 670 separated by distance L.sub.1 from the piezoelectric
material 600, the standing wave "hops" to nearby facet 680, which
corresponding L.sub.2 distance from the piezoelectric material 600
satisfies the resonance conditions at the new speed of sound.
Therefore, the device is a self-tuning system capable of
readjusting to maintain a strong multi-dimensional (e.g.,
three-dimensional) acoustic field regardless of the changing
properties of the processed suspension, and capable of working at
the same operation frequency. Put another way, the use of a
reflector having a faceted surface improves the acoustophoretic
device by shortening or completely eliminating the undesirable time
periods during which the frequency of the device must be scanned
and, therefore, out of tune.
[0089] The use of a reflector having a faceted surface also
optimizes the performance at uneven cell mass distribution. As the
cell density and concentration can be different along the paths
between the piezoelectric material/transducer and the reflector at
different positions across the resonator cross section, the
resonance conditions can be different along these paths. With a
reflector having a faceted surface, different facets are available
to re-tune the resonator along these paths in accordance to these
local conditions. This level of optimization does not exist in a
flat transducer-flat reflector system, even with agile frequency
tuning.
[0090] Moreover, the use of a reflector having a faceted surface
suppresses the standing wave corresponding to the "piston" mode of
the flat piezoelectric material/transducer regardless of the
frequency. Therefore, the range of operation frequencies available
with the reflector having a faceted surface is wider than with a
flat transducer-flat reflector system.
[0091] The differential vibrations of the non-planar face of the
piezoelectric material allow for differential pressure waves to be
generated from the non-planar face of the piezoelectric material
using a single voltage input from the function generator and the
amplifier into the piezoelectric material. This, in turn, allows
for the creation of a multi-dimensional acoustic standing wave and
further allows for local wave fronts with varying amplitudes to
come from the non-planar face of the piezoelectric material with a
single frequency input to then generate the multi-dimensional
standing wave in the fluid.
[0092] In certain embodiments, the piezoelectric material and/or
reflector may be non-symmetrical or asymmetric in shape. This
refers to the shape of the piezoelectric material as defined by its
perimeter. Put another way, the perimeter of the piezoelectric
material forms an irregular polygon, or the piezoelectric material
does not have any axis of symmetry. The piezoelectric crystal of
FIG. 3, for example, is a square, which is symmetrical. However,
piezoelectric material 1300 depicted in FIG. 13 has a trapezoidal
shape with four different angles. Designing the piezoelectric
material to have a non-symmetrical shape allows for an acoustic
standing wave created by the piezoelectric material to generate
trapping lines that are asymmetric.
[0093] FIGS. 14A-140 show four asymmetric excitation patterns
generated on the face of a trapezoidal piezoelectric material at
four different frequencies. The asymmetry of the piezoelectric
material leads to generation of asymmetric trapping lines of
particles inside the fluid, at different frequencies of excitation.
This asymmetric field of trapping lines allows for less
interference between adjacent trapping lines when continuous
gravity separation of a secondary fluid or particulate from a host
fluid is in operation. Put another way, when a non-symmetrical
piezoelectric material is placed in an acoustic chamber across from
a reflector having a non-symmetrical or another shape, the trapping
lines of the standing wave will be staggered in such a manner that
the collected secondary fluid or particles in each trapping line
interfere less with one another as they are gravitationally
separated from the host fluid, compared to those generated by a
symmetric piezoelectric material.
[0094] In accordance with the present disclosure, the particles or
secondary fluid collect at the nodes or anti-nodes of the acoustic
standing wave, depending on the particles' or secondary fluid's
acoustic contrast factor relative to the host fluid, forming
clusters/clumps/agglomerates/coalesced droplets that continuously
fall out of the acoustic standing wave when the clusters have grown
to a size large enough to overcome the holding force of the
acoustic standing wave (e.g. by coalescence or agglomeration) and
the particle/secondary fluid density is higher than the host fluid,
or to rise out of the acoustic standing wave when the
particle/secondary fluid density is less than the host fluid. The
acoustic radiation force is proportional to the particle volume
(e.g. the cube of the radius) when the particle is small relative
to the wavelength. It is proportional to frequency and the acoustic
contrast factor. It also scales with acoustic energy (e.g. the
square of the acoustic pressure amplitude). For harmonic
excitation, the sinusoidal spatial variation of the force is what
drives the particles to the stable axial positions within the
standing waves. When the acoustic radiation force exerted on the
particles is stronger than the combined effect of fluid drag force
and buoyancy and gravitational force, the particle is trapped
within the acoustic standing wave field. This results in
concentration, agglomeration and/or coalescence of the trapped
particles. The strong lateral forces create rapid clustering of
particles. Micron-sized particles, e.g., bacteria, mammalian cells,
micro-algae, metal particles, yeast, fungi, lipids, oil droplets,
red blood cells, white blood cells, platelets, etc., can thus be
separated from the host fluid through enhanced gravitational
separation. For the case of a suspension with several different
particle sizes, it is possible by tuning of the system parameters
to settle out the group of particles that are larger in size
whereas the group of particles smaller in size can be kept in
suspension. These two layers can then be harvested separately. A
repeated process can then be used to fractionate groups of
different sized particles according to size. In this regard, the
multi-dimensional acoustic standing waves generated by each
transducer can be of different frequencies.
[0095] One specific application for the acoustophoresis device is
in the processing of bioreactor materials. It is important to be
able to separate relatively larger cells and cell debris from the
expressed materials that are in the host fluid. The expressed
materials are composed of biomolecules such as recombinant proteins
or monoclonal antibodies, and are the desired product to be
recovered. Through the use of acoustophoresis, the separation of
the cells and cell debris is very efficient and leads to very
little loss of the expressed materials. This is an improvement over
current filtration processes (depth filtration, tangential flow
filtration, and the like), which show limited efficiencies at high
cell densities, so that the loss of the expressed materials in the
filter beds themselves can be up to 5% of the materials produced by
the bioreactor. The use of mammalian cell cultures including
Chinese hamster ovary (CHO), NS0 hybridoma cells, baby hamster
kidney (BHK) cells, insect cells, and human cells (e.g. T-cells,
B-cells, stem cells, red blood cells), and living/biological cells
in general has proven to be a very efficacious way of
producing/expressing the recombinant proteins and monoclonal
antibodies required of today's pharmaceuticals. The filtration of
the mammalian cells and the mammalian cell debris through
acoustophoresis aids in greatly increasing the yield of the
bioreactor. As desired, the acoustophoresis process may also be
coupled with a standard filtration process upstream or downstream,
such as depth filtration, tangential flow filtration (TFF), or
other physical filtration processes.
[0096] Efficient separation has been demonstrated for CHO cells,
T-cells, and yeast cells with separation efficiencies in excess of
90% and more for cell concentrations from as little as 50,000 cells
per ml of fluid to 80 million cells per ml of fluid. The flow rates
of the acoustic separation devices according to the current
embodiments vary from 1 ml/min for smaller scale devices to in
excess of 50 liter/hour for larger scale devices.
[0097] In this regard, the acoustic contrast factor is a function
of the ratio of particle to fluid compressibility and particle to
fluid density. Most cell types present a higher density and lower
compressibility than the medium in which they are suspended, so
that the acoustic contrast factor between the cells and the medium
has a positive value. As a result, the axial acoustic radiation
force (ARF) drives the cells, with a positive contrast factor, to
the pressure nodal planes, whereas cells or other particles with a
negative contrast factor are driven to the pressure anti-nodal
planes. The radial or lateral component of the ARF is larger than
the combined effect of fluid drag force and gravitational force.
The radial or lateral component drives the cells/particles to
specific locations (points) within these planes where they cluster,
clump, agglomerate, or coalesce into larger groups, which will then
continuously gravity separate from the fluid.
[0098] Desirably, the ultrasonic transducer(s) generate a
three-dimensional or multi-dimensional acoustic standing wave in
the fluid that exerts a lateral force on the suspended particles to
accompany the axial force so as to increase the particle trapping
and clumping capabilities of the standing wave. Typical results
published in literature state that the lateral force is two orders
of magnitude smaller than the axial force. In contrast, the
technology disclosed in this application provides for a lateral
force to be of the same order of magnitude as the axial force (i.e.
a multi-dimensional acoustic standing wave). However, in certain
embodiments described further herein, combinations of transducers
that produce both multi-dimensional acoustic standing waves and
planar standing waves are contemplated. For purposes of this
disclosure, a standing wave where the lateral force is of the same
order of magnitude as the axial force is considered a
"multi-dimensional acoustic standing wave."
[0099] A diagrammatic representation of an acoustic chamber for
removing oil or other lighter-than-water material is shown in FIG.
15. Excitation frequencies typically in the range from hundreds of
kHz to 10s of MHz are applied by transducer 10. One or more
standing waves are created between the transducer 10 and the
reflector 11. Incoming host fluid containing a secondary phase
enters at inlet 12. Microdroplets are trapped in standing waves at
the pressure anti-nodes 14 where they agglomerate, aggregate,
clump, or coalesce, and, in the case of buoyant material, float to
the surface and are discharged via an effluent outlet 16 located
above the flow path. Clarified fluid (e.g. water) is discharged at
outlet 18. The acoustophoretic separation technology can accomplish
multi-component particle separation without any fouling at a much
reduced cost.
[0100] A diagrammatic representation of an acoustic chamber for
removing contaminants or other heavier-than-water material is shown
in FIG. 16. Excitation frequencies typically in the range from
hundreds of kHz to 10s of MHz are applied by transducer 10.
Incoming contaminated fluid enters through inlet 13. Contaminants
are trapped in standing waves at the pressure nodes 15 where they
agglomerate, aggregate, clump, or coalesce, and, in the case of
heavier material, sink to the bottom collector and are discharged
via an effluent outlet 17 located below the flow path. Clarified
fluid is discharged at outlet 18.
[0101] As previously explained, the ultrasonic transducer and
reflector are located on opposite sides of the acoustic chamber. In
this way, one or more acoustic standing waves are created between
the ultrasonic transducer and reflector.
[0102] Prior to discussing further optimization of the systems, it
is helpful to provide an explanation now of how multi-dimensional
acoustic standing waves are generated. The multi-dimensional
acoustic standing wave needed for particle collection is obtained
by driving an ultrasonic transducer at a frequency that both
generates the acoustic standing wave and excites a fundamental 3D
vibration mode of the transducer piezoelectric element. The
multi-dimensional acoustic standing wave may be generated by
distinct modes of the piezoelectric element such as a 3.times.3
mode that would generate multidimensional acoustic standing waves.
A multitude of multidimensional acoustic standing waves may also be
generated by allowing the piezoelectric element to vibrate through
many different mode shapes. Thus, the element would excite multiple
modes such as a 0.times.0 mode (i.e. a piston mode) to a 1.times.1
(the fundamental mode), to 2.times.2, 1.times.3, 3.times.1,
3.times.3, and other higher order modes and then cycle back through
the lower modes of the element (not necessarily in straight order).
This switching or dithering of the piezoelectric element between
modes allows for various multi-dimensional wave shapes, along with
a single piston mode shape, to be generated over a designated
time.
[0103] It is also possible to excite or choose a frequency of
excitation that excites multiple modes at the same time, each mode
with a varying degree of displacement amplitude. Through this
combination of multiple modes excited at the same time with varying
displacement amplitude, it is possible to generate a superposition
of multi-dimensional standing waves desirable for trapping,
clustering, and separation of a secondary fluid or particle from a
host fluid.
[0104] The scattering of the acoustic field off the particles
results in a three dimensional acoustic radiation force, which acts
as a three-dimensional trapping field. The acoustic radiation force
is proportional to the particle volume (e.g. the cube of the
radius) when the particle is small relative to the wavelength. It
is proportional to frequency and the acoustic contrast factor. It
also scales with acoustic energy (e.g. the square of the acoustic
pressure amplitude). When the acoustic radiation force exerted on
the particles is stronger than the combined effect of fluid drag
force and buoyancy and gravitational force, the particles are
trapped within the acoustic standing wave field. This results in
concentration, agglomeration and/or coalescence of the trapped
particles. Relatively large solids of one material can thus be
separated from smaller particles of a different material, the same
material, and/or the host fluid through enhanced gravitational
separation.
[0105] The multi-dimensional standing wave generates acoustic
radiation forces in both the axial direction (i.e., in the
direction of the standing wave, between the transducer and the
reflector, perpendicular to the flow direction) and the lateral
direction (i.e., in the flow direction). As the mixture flows
through the acoustic chamber, particles in suspension experience a
strong axial force component in the direction of the standing wave.
Since this acoustic force is perpendicular to the flow direction
and the drag force, it quickly moves the particles to pressure
nodal planes or anti-nodal planes, depending on the contrast factor
of the particle. The lateral acoustic radiation force then acts to
move the concentrated particles towards the center of each planar
node, resulting in agglomeration or clumping. The lateral acoustic
radiation force component has to overcome fluid drag for such
clumps of particles to continually grow and then drop out of the
mixture due to gravity. Therefore, both the drop in drag per
particle as the particle cluster increases in size, as well as the
drop in acoustic radiation force per particle as the particle
cluster grows in size, must be considered for the acoustic
separator device to work effectively. In the present disclosure,
the lateral force component and the axial force component of the
multi-dimensional acoustic standing wave are of the same order of
magnitude. In this regard, it is noted that in a multi-dimensional
acoustic standing wave, the axial force is stronger than the
lateral force, but the lateral force of a multi-dimensional
acoustic standing wave is much higher than the lateral force of a
planar standing wave, usually by two orders of magnitude or
more.
[0106] Some further explanation of the ultrasonic transducers used
in the devices, systems, and methods of the present disclosure may
be helpful as well. In this regard, the transducers use a
piezoelectric element, usually made of PZT-8 (lead zirconate
titanate). Such elements may have a 1 inch by 1 inch square shape
with a thickness of 1 mm (nominal 2 MHz resonance frequency), and
may also be of a larger size, such as a 1 inch by 3 inch shape with
a 1 mm thickness, or smaller such as 0.5 inch by 0.5 inch. The
thickness controls the resonance frequency, as the resonance
frequency is inversely proportional to thickness. Each ultrasonic
transducer module can have only one piezoelectric element, or can
have multiple elements that each act as a separate ultrasonic
transducer and are either controlled by one or multiple amplifiers.
The piezoelectric element(s) can be crystalline, semi-crystalline,
or non-crystalline. The transducer(s) is/are used to create a
pressure field that generates forces of the same order of magnitude
both orthogonal to the standing wave direction (lateral) and in the
standing wave direction (axial).
[0107] FIG. 17 is a cross-sectional diagram of a conventional
ultrasonic transducer. This transducer has a wear plate 50 at a
bottom end, epoxy layer 52, piezoelectric element 54 (e.g. a
ceramic crystal made of, e.g. PZT), an epoxy layer 56, and a
backing layer 58. On either side of the piezoelectric element,
there is an electrode: a positive electrode 61 and a negative
electrode 63, each being connected with an electrical connection
65. The epoxy layer 56 attaches backing layer 58 to the
piezoelectric element 54. The entire assembly is contained in a
housing 60 which may be made out of, for example, aluminum. An
electrical adapter 62 provides connection for wires to pass through
the housing and connect to leads (not shown) which attach to the
piezoelectric element 54. Typically, backing layers are designed to
add damping and to create a broadband transducer with uniform
displacement across a wide range of frequency and are designed to
suppress excitation at particular vibrational eigen-modes. Wear
plates are usually designed as impedance transformers to better
match the characteristic impedance of the medium into which the
transducer radiates.
[0108] FIG. 18 is a cross-sectional view of an ultrasonic
transducer 81 of the present disclosure. Transducer 81 is shaped as
a disc or a plate, and has an aluminum housing 82. The
piezoelectric element can be, e.g., a mass of perovskite ceramic
crystals, each consisting of a small, tetravalent metal ion,
usually titanium or zirconium, in a lattice of larger, divalent
metal ions, usually lead or barium, and O2- ions. As an example, in
the embodiment shown in FIG. 18, a PZT (lead zirconate titanate)
crystal 86 defines the bottom end of the transducer, and is exposed
from the exterior of the housing. The crystal is supported on its
perimeter by a small elastic layer 98, e.g. silicone or similar
material, located between the crystal and the housing. Put another
way, no wear layer is present. In particular embodiments, the
crystal is an irregular polygon, and in further embodiments is an
asymmetrical irregular polygon.
[0109] Screws 88 attach an aluminum top plate 82a of the housing to
the body 82b of the housing via threads. The top plate includes a
connector 84 for powering the transducer. The top surface of the
PZT crystal 86 is connected to a positive electrode 90 and a
negative electrode 92, which are separated by an insulating
material 94. The electrodes can be made from any conductive
material, such as silver or nickel. Electrical power is provided to
the PZT crystal 86 through the electrodes on the crystal. Note that
the crystal 86 has no backing layer or epoxy layer. Put another
way, there is an air gap 87 in the transducer between aluminum top
plate 82a and the crystal 86 (i.e. the air gap is completely
empty). A minimal backing 58 and/or wear plate 50 may be provided
in some embodiments, as seen in FIG. 19.
[0110] The transducer design can affect performance of the system.
A typical transducer is a layered structure with the piezoelectric
element bonded to a backing layer and a wear plate. Because the
transducer is loaded with the high mechanical impedance presented
by the standing wave, the traditional design guidelines for wear
plates, e.g., half wavelength thickness for standing wave
applications or quarter wavelength thickness for radiation
applications, and manufacturing methods may not be appropriate.
Rather, in one embodiment of the present disclosure the
transducers, there is no wear plate or backing, allowing the
piezoelectric element to vibrate in one of its eigenmodes (i.e.
near eigenfrequency) with a high Q-factor. The vibrating
piezoelectric element, such as, e.g., a ceramic crystal/disk, is
directly exposed to the fluid flowing through the acoustic
chamber.
[0111] Removing the backing (e.g. making the piezoelectric element
air backed) also permits the element to vibrate at higher order
modes of vibration with little damping (e.g. higher order modal
displacement). In a transducer having a piezoelectric element with
a backing, the element vibrates with a more uniform displacement,
like a piston. Removing the backing allows the element to vibrate
in a non-uniform displacement mode. The higher order the mode shape
of the piezoelectric element, the more nodal lines the element has.
The higher order modal displacement of the element creates more
trapping lines, although the correlation of trapping line to node
is not necessarily one to one, and driving the element at a higher
frequency will not necessarily produce more trapping lines.
[0112] In some embodiments, the piezoelectric element may have a
backing that minimally affects the Q-factor of the crystal (e.g.
less than 5%). The backing may be made of a substantially
acoustically transparent material such as balsa wood, foam, or cork
which allows the element to vibrate in a higher order mode shape
and maintains a high Q-factor while still providing some mechanical
support for the element. The backing layer may be a solid, or may
be a lattice having holes through the layer, such that the lattice
follows the nodes of the vibrating element in a particular higher
order vibration mode, providing support at node locations while
allowing the rest of the element to vibrate freely. The goal of the
lattice work or acoustically transparent material is to provide
support without lowering the Q-factor of the piezoelectric element
or interfering with the excitation of a particular mode shape.
[0113] Placing the piezoelectric element in direct contact with the
fluid also contributes to the high Q-factor by avoiding the
dampening and energy absorption effects of the epoxy layer and the
wear plate. Other embodiments may have wear plates or a wear
surface to prevent the PZT, which contains lead, contacting the
host fluid. This may be desirable in, for example, biological
applications such as separating blood. Such applications might use
a wear layer such as chrome, electrolytic nickel, or electroless
nickel. Chemical vapor deposition could also be used to apply a
layer of poly(p-xylylene) (e.g. Parylene) or other polymers or
polymer films. Organic and biocompatible coatings such as silicone
or polyurethane are also usable as a wear surface.
[0114] The lateral force of the total acoustic radiation force
(ARF) generated by the ultrasonic transducers of the present
disclosure is significant and is sufficient to overcome the fluid
drag force at high linear velocities up to 1 cm/s and beyond. For
example, linear velocities through the devices of the present
disclosure can be a minimum of 4 cm/min for separation of
cells/particles, and can be as high as 1 cm/sec for separation of
oil/water phases.
[0115] The lateral force of the acoustic radiation force generated
by the transducer can be increased by driving the transducer in
higher order mode shapes, as opposed to a form of vibration where
the piezoelectric element effectively moves as a piston having a
uniform displacement. The acoustic pressure is proportional to the
driving voltage of the transducer. The electrical power is
proportional to the square of the voltage. The voltage signal can
have a sinusoidal, triangular, pulsed, or similar waveform and can
have a frequency of from about 100 kHz to about 20 MHz. The
transducer is typically a thin piezoelectric plate, with electric
field in the z-axis and primary displacement in the z-axis. The
transducer is typically coupled on one side by air (i.e., the air
gap within the transducer) and on the other side by the fluid
mixture of the cell culture media. The types of waves generated in
the plate are known as composite waves. A subset of composite waves
in the piezoelectric plate is similar to leaky symmetric (also
referred to as compressional or extensional) Lamb waves. The
piezoelectric nature of the plate typically results in the
excitation of symmetric Lamb waves. The waves are leaky because
they radiate into the water layer, which result in the generation
of the acoustic standing waves in the water layer. Lamb waves exist
in thin plates of infinite extent with stress free conditions on
its surfaces. Because the transducers of this embodiment are finite
in nature, the actual modal displacements are more complicated.
[0116] Generally, the transducers of the present disclosure are
used to create a pressure field that generates acoustic radiation
forces of the same order of magnitude both orthogonal to the
standing wave direction and in the standing wave direction. When
the forces are roughly the same order of magnitude, particles of
size 0.1 microns to 300 microns will be moved more effectively
towards "trapping lines," so that the particles will not pass
through the pressure field. Instead, the particles will remain
within the acoustic chamber, from which they can advantageously be
collected via specified outlets of the acoustophoretic device or
otherwise recycled back to an associated bioreactor.
[0117] The acoustophoretic devices and methods described herein are
useful for separating a second fluid or particulate from a host
fluid. In this regard, the devices and methods of the present
disclosure utilize higher order modal displacement of a
piezoelectric material having a non-planar face, such that the
piezoelectric material may be perturbed by a single excitation, yet
still generate multi-dimensional acoustic standing waves.
[0118] The present disclosure has been described with reference to
exemplary embodiments. Obviously, modifications and alterations
will occur to others upon reading and understanding the preceding
detailed description. It is intended that the present disclosure be
construed as including all such modifications and alterations
insofar as they come within the scope of the appended claims or the
equivalents thereof.
* * * * *