U.S. patent number 3,878,519 [Application Number 05/438,105] was granted by the patent office on 1975-04-15 for method and apparatus for synchronizing droplet formation in a liquid stream.
This patent grant is currently assigned to International Business Machines Corporation. Invention is credited to James H. Eaton.
United States Patent |
3,878,519 |
Eaton |
April 15, 1975 |
Method and apparatus for synchronizing droplet formation in a
liquid stream
Abstract
A source of energy is selectively applied to a liquid stream to
reduce the surface tension of the liquid and is applied before the
stream would randomly break up into droplets. Both the quantity of
energy applied and the time period that the energy is applied are
controlled to control the time to droplet breakoff and the time
between droplets by selectively reducing the surface tension of
segments of the stream. The source of energy can be high intensity
light, which is converted by the stream to heat energy, or a source
of heat (resistive or inductive) with the resistive heat being
applied to the stream by conduction and the inductive heat being
converted by the stream to heat energy. In some ink jet printing
embodiments, the droplets are selectively deflected in a direction
perpendicular to the paper motion to place the droplets on the
desired position of the paper. Where droplets are not wanted, they
are selectively deflected into a gutter to catch them before they
can impinge on the paper. In other embodiments, an array of nozzles
is used to form a droplet stream for each desired spot position on
the paper. Thus, if all droplets were to hit the paper, the paper
would be uniformly covered with ink. Printing is accomplished by
selectively removing unwanted droplets from the stream, usually by
deflecting them into a gutter. The most common means for
selectively deflecting the droplets is to selectively place an
electrical charge on the droplets and then to pass the droplets
through a uniform electric field for deflection as shown and
described in U.S. Pat. No. 3,596,275 to Sweet. The amount of
deflection for a given droplet is then proportional to the
previously selected electric charge and inversely proportional to
its mass and velocity. The charge on a droplet is determined by the
electric field on the droplet at its moment of breakoff from the
stream. The usual method of charging the droplet involves applying
a voltage to a cylinder (charging tunnel) surrounding the point of
breakoff of the droplet from the stream. Thus, it is important to
control both the time and position of the breakoff so that a given
timed voltage sequence will appropriately charge the droplets. If
the droplets do not break off at the correct time and position,
they can receive an incorrect charge and, thus, be deflected to an
undesired position. The correct time and position is determined by
synchronizing the droplets so that they pass through the cylinder
(charging tunnel) at uniform intervals of time and with the correct
phase. In addition, the disturbance causing the breakoff is
modified in amplitude to give the desired breakoff point within the
charging tunnel. Various means for obtaining synchronization of the
droplets have been previously suggested. For example, mechanical
forces have been applied to a nozzle by a piezoelectric device, for
example, at a desired frequency. When using a mechanical
arrangement for creating the breakup of the stream into droplets,
the mechanical force applied to one nozzle to produce a vibrating
frequency of the nozzle can have an effect on an adjacent nozzle of
the ink jet streams if the ink streams are disposed on five mil
centers, for example. The transmission of the mechanical vibrations
to an adjacent nozzle can alter the phase and breakoff point of the
droplets of an adjacent nozzle. The present invention
satisfactorily solves the foregoing problem by producing
synchronous formation of the droplets without any mechanical force
being applied. Thus, with the method and apparatus of the present
invention, the nozzles for more than one ink stream, if such is
required, can be placed very close to each other without the
droplet forming means for one of the ink streams having any effect
on any of the adjacent ink streams. Thus, droplet formation from
each ink stream, if more than one is required, can be effectively
controlled with the method and apparatus of the present invention.
The present invention accomplishes the foregoing through causing a
thermal change or disturbance within the ink stream prior to the
time that the stream would randomly break up into droplets. The
random breakup of a stream into droplets depends upon its surface
tension, its velocity, and its diameter with the breakup occurring
after the stream leaves a confined passage unless the passage
should be coated with a material that the liquid does not wet such
as Teflon, for example. By regulating the thermal change or
disturbance in the ink stream, the breakup of the stream into
droplets is controlled to cause synchronous formation of the
droplets and break off at the desired point. The thermal change or
disturbance in the stream is controlled through regulating a source
of energy, which produces this thermal change or disturbance, as to
the time it is applied, the length of the segment of the stream to
which it is applied, and the quantity of energy applied. By
creating the thermal change or disturbance in spaced segments of
the stream, the temperature of the spaced segments of the stream is
increased so that the surface tension of the spaced segments of the
stream is reduced to cause synchronous formation of the droplets.
Since the surface tension of the stream decreases as the
temperature of the stream increases, the source of energy, which
creates the thermal change or disturbance in the spaced segments of
the stream, results in a lowering of the surface tension of the
spaced segments of the stream to cause breakup of the stream into
droplets in the desired relation. The period between successive
applications of a quantity of energy and the stream velocity
control the spacing between the droplets. The breakoff point is
determined primarily by the energy applied in each pulse. The
surface tension of a stream is directly proportional to the
internal pressure within the stream so that the decrease in the
surface tension in a segment of the stream causes a reduction in
the internal pressure in that segment of the stream. This decrease
in the internal pressure has the same effect as an increase in the
diameter of the segment of the stream since the internal pressure
of the stream is inversely proportional to the diameter of the
stream. By reducing the internal pressure of a first segment of the
stream, a second and adjacent segment has an increase in its
internal pressure relative to the first segment to force the liquid
in the second segment to the first segment of the stream. This
results in a further reduction in the pressure in the already
lowered internal pressure of the first segment of the stream since
it increases the diameter of the first segment of the stream to
accommodate the larger volume so that a positive feedback is
provided to cause the stream to break up into droplets. By
selecting the segments or sections in which the source of energy
creates a thermal change or disturbance so that the segments or
sections defined by the selected application of the source of
energy are normally no greater than the average length of the
droplets when they break up randomly, synchronization of the
formation of the droplets from the stream can be obtained. Thus,
the small changes in surface tension in the spaced segments of the
stream trigger a positive feedback and lead to controlled droplet
formation. The breakoff point is determined primarily by the
amplitude of the thermal changes since an increase in amplitude
causes the breakoff to occur closer to the nozzle. The present
invention contemplates using a modulated heat or high intensity
light source as the source of energy. When a resistive heat source
is employed, the heat is supplied to the ink stream by conduction
to cause the thermal change or disturbance in the stream. When the
heat source is inductive, heat conversion occurs within the stream
to produce the thermal change or disturbance in the stream. When
modulated light from a high intensity light source is the source of
energy to cause the thermal change or disturbance of the stream,
heat conversion occurs within the stream. Of course, the stream
must not be transparent to the light for there to be the conversion
of the light to heat within the stream. An object of this invention
is to synchronously form droplets from a liquid stream by the
intermittent application of a source of energy directly to the
stream. Another object of this invention is to selectively alter
the surface tension of segments of a liquid stream to synchronously
form droplets from the stream. A further object of this invention
is to produce a thermal change in a liquid stream before random
breakup of the liquid stream would occur. The foregoing and other
objects, features, and advantages of the invention will be apparent
from the following more particular description of preferred
embodiments of the invention as illustrated in the accompanying
drawings.
Inventors: |
Eaton; James H. (Armonk,
NY) |
Assignee: |
International Business Machines
Corporation (Armonk, NY)
|
Family
ID: |
23739239 |
Appl.
No.: |
05/438,105 |
Filed: |
January 31, 1974 |
Current U.S.
Class: |
347/75; 239/13;
347/51; 239/133 |
Current CPC
Class: |
B41J
2/02 (20130101); B41J 2202/16 (20130101) |
Current International
Class: |
B41J
2/015 (20060101); B41J 2/02 (20060101); G01d
015/18 () |
Field of
Search: |
;346/75,140,1
;239/133,134,135,13 ;118/620,641,302 |
References Cited
[Referenced By]
U.S. Patent Documents
Primary Examiner: Hartary; Joseph W.
Attorney, Agent or Firm: Leach, Jr.; Frank C.
Claims
What is claimed is:
1. A method of forming droplets at a substantially constant
breakoff point and with substantially uniform distances from each
other from a liquid stream exiting from an opening or the like
including:
selectively altering the surface tension of spaced segments of the
stream by initially reducing the surface tension of each of the
spaced segments of the stream as it passes a predetermined portion
of its path and before random break up of the stream into droplets
would occur after the stream leaves the opening;
and controlling the amount of initial reduction of the surface
tension of each of the spaced segments of the stream to control the
breakoff point of the droplets from the stream at a substantially
constant breakoff point and with substantially uniform distances
from each other.
2. The method according to claim 1 including:
applying a source of energy directly to each of the spaced segments
of the liquid stream to produce a thermal change in the spaced
segments of the stream before random break up of the stream into
droplets would occur after the stream leaves the opening;
periodically applying the source of energy to each of the spaced
segments of the stream as it passes the predetermined portion of
its path for a constant period of time to initially reduce the
surface tension of the stream in the spaced segments of the stream
to form droplets at substantially uniform distances from each
other;
and controlling the quantity of energy applied from the source of
energy during each constant period of time to control the breakoff
point.
3. The method according to claim 2 including applying the source of
energy to the spaced segments of the stream after the stream leaves
the opening.
4. The method according to claim 3 including applying light from a
high intensity light source as the source of energy to produce the
thermal change in the stream.
5. The method according to claim 2 including controlling the
quantity of energy applied during the constant period of time and
controlling the time period of the constant period of time to
obtain the desired synchronization and breakoff point of the
droplets from the stream.
6. The method according to claim 2 including applying the source of
energy to the spaced segments of the stream just before the stream
exits from the opening.
7. The method according to claim 6 including applying the source of
energy to the spaced segments of the stream around the entire
periphery of the stream.
8. The method according to claim 7 including applying heat to the
spaced segments of the stream as the source of energy.
9. The method according to claim 6 including applying the source of
energy to the spaced segments of the stream around only a portion
of the periphery of the stream.
10. The method according to claim 9 including applying heat to the
spaced segments of the stream as the source of energy.
11. An apparatus for forming droplets at a substantially constant
breakoff point and with substantially uniform distances from each
other from a liquid stream including:
means to supply the liquid stream through an opening or the
like;
and means to selectively alter the surface tension of spaced
segments of the stream to form droplets at substantially uniform
distances from each other and of substantially uniform size, said
selectively altering means being applied to each of the spaced
segments of the stream as it passes a predetermined portion of its
path to initially reduce the surface tension of each of the spaced
segments before random break up of the stream into droplets would
occur after the stream exits from the opening.
12. The apparatus according to claim 11 in which said selectively
altering means includes means to periodically apply a source of
energy directly to each of the spaced segments of the liquid stream
for a constant period of time at the predetermined portion of its
path to produce a thermal change in the stream to reduce the
surface tension of each of the spaced segments of the stream to
which the energy is applied.
13. The apparatus according to claim 12 in which said applying
means comprises energy supply means disposed exterior of the
opening to apply energy to the spaced segments of the stream before
random break up of the liquid stream into droplets would occur.
14. The apparatus according to claim 13 in which:
said energy supply means includes:
a high intensity light source;
and means to modulate said high intensity light source to apply the
light of said high intensity light source periodically for the
constant period of time.
15. The apparatus according to claim 14 in which said high
intensity light source is a continuous light source.
16. The apparatus according to claim 12 in which said applying
means includes heating means disposed within the opening.
17. The apparatus according to claim 16 in which said heating means
is disposed adjacent the exit of the opening.
18. The apparatus according to claim 16 in which said heating means
completely surrounds the liquid stream to apply heat to the entire
periphery of each of the spaced segments of the liquid stream.
19. The apparatus according to claim 16 in which said heating means
only partially surrounds the liquid stream to apply heat to only
the surrounded portion of the periphery of each of the spaced
segments of the liquid stream.
Description
In the drawings:
FIG. 1 is a schematic view showing a source of energy being applied
to a liquid stream to cause synchronous formation of droplets
therefrom and the droplets producing printing on a recording
surface.
FIG. 2 is a schematic view of another form of the source of energy
being applied to the liquid stream to cause synchronous formation
of droplets therefrom.
FIG. 3 is a fragmentary sectional view of a portion of a nozzle and
showing a modification of the present invention in which an
electric heater is the source of energy to a liquid stream and
taken along line 3--3 of FIG. 4.
FIG. 4 is a schematic end elevational view of the nozzle of FIG. 3
with the electric heater and its control.
FIG. 5 is a fragmentary sectional view of another embodiment for
disposing an electric heater within a nozzle and taken along line
5--5 of FIG. 6.
FIG. 6 is a schematic end elevational view of the nozzle of FIG. 5
with the electric heater and its control.
Referring to the drawings and particularly FIG. 1, there is shown
an ink supply 10. Ink, which can be magnetic or non-magnetic, is
supplied under pressure from the ink supply to a nozzle 11.
A pressurized ink stream 12 passes from the nozzle 11 through an
opening 14 thereof. As the pressurized ink stream 12 exits from the
opening 14 of the nozzle 11, it is subjected to a modulated light
beam 15, which is supplied from a high intensity light source 16.
The high intensity light source 16 can be a gas laser such as a
helium-neon gas laser, for example. The laser is continuous since
it cannot be turned on and off at the desired frequency such as 100
kiloHertz, for example.
To intermittently supply the light beam 15 from the high intensity
light source 16 to the stream 12, a modulator 17 is disposed
between the high intensity light source 16 and the ink stream 12.
The modulator 17 can be any suitable type in which a control 18 can
effectively start and stop the application of the light beam 15 to
the ink stream 12.
The modulator 17 could include, for example, a glass with a chrome
mask having a slit through which light could pass. The modulator 17
could include an accoustic deflector, for example, which would
shift the light in response to the control 18 so that a focusing
lens, for example, within the modulator 17 would not focus the beam
at the slit in the chrome mask. When the accoustic deflector is
inactivated by the control 18, the beam is focused at the slit so
that the beam passes through the slit and another lens from which
it exits from the modulator 17.
Each time that the light beam 15 is applied to a segment of the ink
stream 12, which must not be transparent to the light beam 15, the
light is converted to heat within the segment of the ink stream 12.
This conversion of the light to heat increases the temperature of
the segment of the ink stream 12 to reduce its surface tension
since the surface tension of the ink stream 12 is inversely
proportional to the temperature of the ink stream 12.
Each time that the light beam 15 is applied to a segment of the ink
stream 12 for a predetermined period of time, the surface tension
of the stream 12 is reduced in the segment of the ink stream 12
subjected to the light beam 15. The velocity of the ink stream 12
determines the segment subjected to the light beam 15 during the
predetermined period of time. As a result of the reduction of the
surface tension of the spaced segments of the ink stream 12, the
ink stream 12 breaks into droplets 19 of substantially uniform size
with the droplets 19 having substantially uniform spacing
therebetween.
Prior to the droplets 19 being formed, the stream 12 enters a
deflection means 20, which is connected to a deflection signal
source 21, in which the droplets 19 are charged at the moment of
breakoff in the manner more particularly shown and described in the
aforesaid Sweet patent. The deflection signal source 21 applies a
signal to the deflection means 20 to determine whether each of the
droplets 19 falls into a gutter 22 from which the droplet can be
returned to the reservoir of the ink supply 10 or strikes a
recording surface such as a moving paper 23, which would be moving
horizontally in a plane perpendicular to the drawing. The position
on the paper 23 at which each of the droplets 19 strikes the paper
23 also can be determined by the strength of the signal to the
deflection means 20 from the deflection signal source 21. Of
course, if a plurality of the ink streams 12 were used, then the
deflection means 20 would either cause the droplet 19 to fall into
the gutter 22 or to strike the same position on the paper 23 each
time. In this case, the paper 23 would be moving vertically with
the plurality of nozzles disposed in a horizontal plane.
It should be understood that the control 18 for the modulator 17
and the deflection signal source 21 must be synchronized so that
the deflection signal source 21 provides the desired charge to the
droplet 19 when it is within the deflection means 20. This desired
charge results in the desired deflection of the droplet 19.
Referring to FIG. 2, there is shown another embodiment in which the
ink stream 12 is subjected to a light beam 30 from a high intensity
light source 31 such as a light emitting diode or an injection
laser, which is a solid state laser, for example. The light beam 30
from the high intensity light source 31 is modulated by a control
32, which is connected to the high intensity light source 31. Thus,
the control 32 controls the period of time that the high intensity
light source 31 applies the light beam 30 to a segment of the ink
stream 12, which cannot be transparent to the light beam 30.
Accordingly, the high intensity light source 31 is a source of
energy for creating a thermal disturbance or change in segments of
the ink stream 12. This conversion of the energy of the light beam
30 to heat in the ink stream 12 produces the desired increase in
temperature in spaced segments of the ink stream 12 to decrease the
surface tension of the spaced segments of the stream 12 so that
synchronous formation of the droplets 19 again occurs. The
remainder of the operation is the same as described when the high
intensity light source 16 of FIG. 1 is employed including
synchronization of the control 32 with the deflection signal source
21.
Because the high intensity light source 31 can be relatively small
and does not require a modulator between it and the ink stream 12
but uses only the control 32 to regulate it, the high intensity
light source 31 can be placed fairly close to the ink stream 12
such as about one diameter of the ink stream 12 from the ink stream
12. As a result, there is no need for any lens with the high
intensity light source 31 as is necessary with the high intensity
light source 16.
Referring to FIGS. 3 and 4, there is shown another form of the
invention in which an electric heater 35 such as a thin film
resistive heater or an inductive heater, is employed. The heater 35
is disposed within an opening or passage 36 of a nozzle 37, which
is connected to the ink supply 10 in the same manner as the nozzle
11, and adjacent the exit of the opening 36.
Electrical energy is supplied to the heater 35 through contacts 38
and 39, which are connected to a control 40. The control 40
regulates when the heater 35 is turned on and off to control for
how long the heat is applied to the segment of the ink stream
12.
When the heater 35 is a thin film resistive heater, the heat
transfer to the ink stream 12 via conduction results in the surface
of the segment of the ink stream 12 becoming hotter than the
interior of the ink stream 12 in the segment to which heat is
applied. Since the heat is applied to the surface of the ink stream
12, this aids in reducing the surface tension of the segment of the
ink stream 12.
When the heater 35 is formed of a thin film of resistive material,
it is formed of any suitable material. For example, it could be
formed of copper or Nichrome.
When the heater 35 is an inductive heater, the heat transfer to the
ink stream 12 is by induction. As a result, the thermal disturbance
or change in the segment of the ink stream 12 to which the
inductive heat is applied is produced by conversion in the same
manner as when light is applied.
The nozzle 37 is preferably formed of an electrically insulating
material such as quartz, for example. If the nozzle 37 is formed of
metal, then the heater 35 must be electrically insulated from the
nozzle 37. In such an arrangement, a layer of insulating material
such as silicon dioxide, for example, would be disposed around the
portions of the heater 35 and the contacts 38 and 39 in engagement
with the nozzle 37.
The ink stream 12 can be transparent when used with this
modification. The remainder of the operation of this modification
is the same as that described with respect to FIG. 1 including the
synchronization of the control 40 with the deflection signal source
21.
Referring to FIGS. 5 and 6, there is shown a modification of the
structure of FIGS. 3 and 4 in that a heater 45, which can be a thin
film resistive heater or an inductive heater, does not completely
surround an opening or passage 46 of a nozzle 47 but only partially
surrounds it. Furthermore, the heater 45 is disposed within the
nozzle 47 to form a streamline with the surface of the opening 46
as shown in FIG. 5.
The heater 45 is connected through contacts 48 and 49 to a control
50. The nozzle 47 is preferably formed of an electrically
insulating material such as quartz, for example. If the nozzle 47
is formed of metal, then a layer of insulating material such as
silicon dioxide, for example, must be used to electrically insulate
the heater 45 and the contacts 48 and 49 from the nozzle 47.
The control 50 functions in the same manner as the control 40 to
determine when the heater 45 is on and off. The control 50 is
synchronized with the deflection signal source 21. The remainder of
the operation of this modification is the same as described with
respect to FIG. 1.
The heater 45 requires a smaller quantity of power than that
required when the heater 35 is employed. By heating a portion of
the surface of the segment of the ink stream 12 when the heater 45
is a thin film resistive heater, the temperature of the portion of
the segment of the ink stream 12 to which the heat is applied is
increased sufficiently to decrease the surface tension of the
segment of the ink stream 12.
While the heater 45, which only partially surrounds the stream 12,
has been shown as being disposed to form a streamline with the
surface of the opening 46, it should be understood that the heater
45 could be disposed within the opening 46 in the nozzle 47 as the
heater 35 of FIGS. 3 and 4. Similarly, while the heater 35 has been
shown as being disposed within the opening 36, it should be
understood that the heater 35 could be disposed to form a
streamline with the opening 36 as the heater 45 of FIGS. 5 and
6.
Instead of disposing the heater 45 within the nozzle 47 to form a
streamline with the surface of the opening 46, it should be
understood that the high intensity light source 31 could be
disposed within the nozzle 47 rather than the heater 45. Thus, it
is not necessary for the high intensity light source 31 to be
exterior of the nozzle as shown in FIG. 2.
To show how the reduction in surface tension of a liquid stream can
form droplets with substantially uniform spacing and of
substantially uniform size, a stream of water to which a thin film
resistive heater of 80% nickel and 20% chrome (Nichrome) applies
heat will be considered as an example. When the temperature of
water is heated from 20.degree. C. to 30.degree. C., its surface
tension decreases from 72.75 dynes/cm. to 71.18 dynes/cm. for a
decrease of 2.4%. Since the internal pressure of a jet stream of
liquid is directly proportional to the surface tension of the
stream and inversely proportional to the diameter of the stream, a
temperature rise of 10.degree. C. at the surface of the water
stream has the same effect on internal pressure as an increase in
the diameter of the stream of 2.4%.
If the stream is assumed to have a diameter of 1 mil, a 2.4%
variation in the surface tension of a 1 mil section or segment at 4
mil intervals produces a diameter increase of 2.4% within
approximately 5 microseconds since it is known, as explained
hereinafter, that the time constant of the stream instability
causes a disturbance to double in magnitude in about 5 microseconds
and since the initial 2.4% reduction in surface tension is
equivalent to an initial diameter increase of 2.4%.
As explained in "Breakup of a Laminal Capillary Jet of a
Viscoelastic Fluid" by M. Goldin et al. on pages 689-711 of Vol.
38, Part 4 of the Journal of Fluid Mechanics (1969), the growth
rate of a diameter disturbance is given by d (t) = d.sub.o
e.sup..alpha..sbsp.o .sup.t where d.sub.o is the size of the
disturbance when the time t = 0 and d (t) is the size of the
disturbance when time is equal to or greater than 0. Ignoring
viscosity, the coefficient .alpha..sub.o * is given in equation
(19) on page 693 of the aforesaid article by
.alpha..sub.o * = (.sigma./2 .rho. a.sup.3).sup.1/2
where .sigma. is the surface tension and is approximately 70 dyne
cm.sup.-.sup.1 for water, .rho. is the density and is 1 gm
cm.sup.-.sup.3 for water, and a is the radius of the stream. For a
jet diameter of 1 mil, a = 0.5 mil = 12.5 .times. 10.sup.-.sup.4
cm. Thus,
.alpha..sub.o * = (70/2 (12.5 .times. 10.sup.-.sup.4).sup.
3).sup.1/2 = 0.134 .times. 10.sup.6.
A disturbance of size d.sub.o doubles when e.sup..alpha..sbsp.o
.sup. t = 2. Accordingly, .alpha..sub.o *t = 1n 2 so that t = 1n
2/.alpha..sub.o *. With .alpha..sub.. * = 0.134 .times. 10.sup.6 ,
t = 5.17 .times. 10.sup.-.sup.6 sec. Thus, for a 1 mil diameter jet
of water, a diameter disturbance doubles in size in about 5 .times.
10.sup.-.sup.6 sec.
Since the random breakup of a jet stream until it has droplet
formation is about 100 microseconds after leaving a nozzle, it is
necessary that the breakup of the stream into the controlled
droplet formation occur before this time. Therefore, if the
disturbance in the diameter of the stream were to be reduced from
the point of droplet formation back to its exit from the nozzle by
one-half every 5 microseconds since this is the opposite of
doubling the disturbance every 5 microseconds from the nozzle to
the point of droplet formation, the reduction of the diameter of
the stream adjacent the outlet of the nozzle to obtain controlled
droplet formation in 100 microseconds can be ascertained. Thus,
1/2.sup.100/5 = 10.sup.-.sup.6 stream diameters so that a
perturbation of 10.sup.-.sup.6 mil in a stream having a diameter of
1 mil is adequate to produce droplets of uniform spacing in 100
microseconds from this perturbation. Accordingly, a 3 .times.
10.sup.-.sup.5 mil perturbation would completely dominate random
disturbances and cause droplet formation in about 75
microseconds.
To ascertain if there will be sufficient heat flow in the water
within this period of time, the 1 mil diameter nozzle, which
supplies the jet stream of 1 mil diameter, is approximated by two
plates being 1 mil apart and utilizing the temperature distribution
in a plate as shown in FIG. 104 on page 30 of Mathematical and
Physical Principles of Engineering Analysis by Walter C. Johnson
(First Edition, fourth impression). FIG. 104 shows the temperature
distribution in a plate as a function of time starting with a
uniform temperature in the plate and maintaining the surfaces of
the plate thereafter at a constant temperature, which is different
from the initial uniform temperature. There is a plurality of
curves shown with each being for a different value of Bt in which B
is a constant and t is the time with B = .pi..sup.2 k/L.sup.2 c p .
In this equation, k is the thermal conductivity and is 6.04 .times.
10.sup.-.sup.3 watt cm..sup.-.sup.1 .degree.K.sup.-.sup.1 at
20.degree. C. for water, L is the spacing between the plates so it
is 1 mil, c represents the specific heat and is 4.18 watt sec
gm.sup.-.sup.1 .degree.C..sup.-.sup.1 for water, and p is the
density and is equal to 1 gm cm..sup.-.sup.3 for water. Thus, for
water at 20.degree. C., B equals 2.3 .times. 10.sup.3
sec.sup.-.sup.1 . When Bt = 10.sup.-.sup.2, the temperature from
FIG. 104 of Mathematical Physical Principles of Engineering
Analysis may be approximated by a straight line connecting the
surface temperature .theta. at 0.degree. and x/L = 0.1. Thus, with
Bt = 10.sup.-.sup.2 , t =4.35 .times. 10.sup.-.sup.6 sec.
If the surface temperature of the water is raised 20.degree. C.
above the interior, the heat energy put into a 1 mil length of a
water stream, which has a diameter of 1 mil with the heat being
applied to only the outer layer of the stream with a thickness of
0.1 mil, is the product of (20.degree.C .times. 0.5 ), (2.5 .times.
10.sup.-.sup.4 cm), (.pi. .times. 2.5 .times. 10.sup.-.sup.3 cm),
(2.5 .times. 10.sup.-.sup.3 cm), and (4.18 watt sec gm.sup.-.sup.1
.degree.C.sup.-.sup.1) with (20.degree.C .times. 0.5 ) being the
average temperature in the 0.1 mil layer of water, (2.5 .times.
10.sup.-.sup.4 cm) being the thickness of the outer layer of the
water to which the heat is applied, (.pi. .times. 2.5 .times.
10.sup.-.sup.3 cm) being the width of the stream of water and is
its circumference, (2.5 .times. 10.sup.-.sup.3 cm) being the 1 mil
length of the stream of water to which the heat is applied, and
(4.18 watt sec gm.sup.-.sup.1 .degree.C.sup.-.sup.1) being the
specific heat of water. This produces a heat energy of 2.05 .times.
10.sup.-.sup.7 watt sec. With this heat energy of 2.05 .times.
10.sup.-.sup.7 watt sec being applied for 4.35 .times.
10.sup.-.sup.6 seconds, the power input to the water during this
time period is approximately 0.05 watt. with a 50% duty cycle and
50% efficiency in transferring heat from a thin film resistive
heater to the water, a power input of 0.05 watt to the stream seems
adequate.
Thus, sufficient heat energy can be supplied to the water stream to
reduce its surface tension 2.4% within the necessary time. If a
thin film of Nichrome (80% nickel, 20% chrome) with a thickness of
1 micron is used as the heater, 70% of the heat therein is removed
when Bt equals 1.0 according to FIG. 104 of the Mathematical and
Physical Principles of Engineering Analysis by Johnson. For
Nichrome, B is approximately 0.3 .times. 10.sup.-.sup.9 since k is
equal to 0.12 watt cm..sup.-.sup.1 .degree.K.sup.-.sup.1, L is
equal to 10.sup.-.sup.4 cm. (1 micron), and cp is equal to
approximately 4 watt sec cm..sup.-.sup.3. With B .times. 0.3
.times. 10.sup.9 , t is 33 .times. 10.sup.-.sup.9 sec. so that 70%
of the heat would be removed from a 1 micron thick heater of
Nichrome in 33 nanoseconds.
The resistance of the thin film resistive heater is obtained from
the equation of R = rl/A. In the equation, r is the resistivity of
Nichrome and is 100 .times. 10.sup.-.sup.8 ohm/meter, 1 is the
length of the heater, and A is the area of the resistive heating
element of the heater.
The resistive heater 35 in FIG. 4 can be considered as two
resistive heaters of length .pi. d/2 electrically in parallel where
d is the diameter of the nozzle. The nozzle diameter is 1 mil or 25
microns since it surrounds the stream of 1 mil diameter. Thus, each
heater is about 37.5 microns long.
Since the heater should extend for the length of the segment of the
stream to which the heat is applied, it would be 1 mil or 25
microns, and this is considered to be its width insofar as
determining its resistance. The thickness of the heater is 1 micron
since this is the thickness utilized in calculating B in Bt for
Nichrome. Thus, from R = rl/A, the resistance R of each half of the
thin film resistive heater would be 1.5 ohms.
Accordingly, the thin film resistive heater is capable of supplying
sufficient heat in 33 nanoseconds to reduce the surface tension of
the water stream 2.4%. Since this is a very small portion of time
in comparison with the available period of 5 microseconds to reduce
the surface tension of the water stream 2.4%, the thin film
resistive heater can be utilized effectively through modulating its
supply of heat.
Additionally, with the resistance of 0.75 ohm of the heater 35 of
FIG. 4, an application of voltage of about 0.2 volt could be used
and require only 267 milliamps to produce the necessary heat energy
of 0.05 watt. Thus, no large current or voltage is required.
It should be understood that the calculations of the foregoing
example are an approximation and could be an order of magnitude
different. Thus, the heat required could be an order of magnitude
different from that calculated but this still would not require a
large current or voltage.
While the foregoing has discussed the stream as being formed of
water, it should be understood that an ink stream could have a
different surface tension. However, the same type of calculations
would be made to obtain the necessary size of a thin film resistive
heater such as the heater 35, for example.
While the period of time for applying a source of heat or light to
the stream can be for the same period of time as it is not applied,
it should be understood that such is not a requisite for
satisfactory operation. Thus, the period of time during which the
energy is applied could be shorter or longer than the period of
time during which the energy is not applied to the stream. It is
only necessary that the formation of the droplets occur
substantially before random break up of the droplets would occur
and that the disturbance produced be greater than any natural
disturbance of the stream.
The diameter of each formed droplet is a function of both the
velocity and the diameter of the stream and the frequency with
which the energy is applied to the stream. However, the quantity of
energy does not affect the diameter of the droplet.
The quantity of the energy only determines the breakoff point of
the droplet from the stream. That is, as the quantity of the energy
is increased, the breakoff point of the droplet occurs closer to
the opening of the nozzle. Of course, the quantity of energy must
be sufficient to produce synchronization of droplet formation.
It should be understood that the wave form of the modulated power
applied to the stream can be of varying shapes such as a square
wave pulse or a sine wave, for example. The specific shape of the
power applied to the stream influences the formation of the
droplet, and a particular power wave form can be chosen to minimize
satellites during droplet formation.
An advantage of this invention is that substantially uniform
spacing and breakoff of the droplets of an ink stream is obtained
so that each droplet can be controlled as to whether it is applied
to a recording surface and the area to which it is applied. Another
advantage of this invention is that it has no effect on the jet
stream of any adjacent nozzle whereby a plurality of ink streams
can be disposed close to each other.
While the invention has been particularly shown and described with
reference to preferred embodiments thereof, it will be understood
by those skilled in the art that the foregoing and other changes in
form and details may be made therein without departing from the
spirit and scope of the invention.
* * * * *