Method and apparatus for dispensing foam materials

A method and apparatus for dispensing a polymer foam includes apparatus for forming a pressurized solution of intermixed polymeric material and gas. The polymeric material remains intermixed with the gas while the solution is maintained above a critical pressure. The pressurized solution is dispensed in wide band through an elongated slot. The dispensing apparatus includes an exit slot section in which the pressure of the solution drops below the critical pressure and the foam begins to form. The solution is maintained above the critical pressure until the solution enters the exit slot section so that premature foaming of the material is prevented.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
This invention relates to systems for dispensing foam polymer material, and 
more particularly to systems which maintain the polymer material under 
pressure with foaming gas in solution and which dispense the polymer/gas 
solution to form the foam. 
2. Description of the Prior Art 
The assignee of the present invention has pioneered the development and 
application of methods and apparatus for foaming and dispensing polymeric 
materials such as hot melt thermoplastic adhesives, polymeric coatings, 
paints and other thermoplastic and/or thermosetting materials. 
This technology has been used in the application of hot melt adhesives in 
which it has been found that the adhesive strength of a bond achieved with 
a given volume of selected hot melt adhesive can be appreciably improved, 
and in most instances at least doubled, if the adhesive were applied as a 
foam rather than as a conventional non-foamed adhesive. Foam adhesive 
systems encompassed by this technology are commercially available from the 
assignee of the present invention under the trademark FoamMelt.RTM.. 
A hot melt thermoplastic adhesive foam system is disclosed in U.S. Pat. No. 
4,059,466 wherein a solid mixture of hot melt thermoplastic adhesive and 
blowing agent is heated and melted in a heated reservoir at a temperature 
above the melting temperature of the adhesive but below the decomposition 
temperature of the blowing agent. The molten adhesive and solid blowing 
agent mixture is then pressurized by a gear pump and supplied under 
pressure as, for example, 300 pounds per square inch (psi) to a hot melt 
dispenser. Between the pump and the outlet of the hot melt dispenser, the 
molten adhesive and solid blowing agent mixture is further heated to a 
higher temperature at which the blowing agent decomposes and evolves as a 
gas as for example, nitrogen, which at that pressure goes into solution 
with the liquid adhesive. The pressurized liquid/gas adhesive solution is 
then supplied to a valved-type outlet at the adhesive dispenser from which 
the adhesive is dispensed at atmospheric pressure. Upon emerging from the 
outlet nozzle of the dispenser, the gas evolves from the solution in the 
form of small bubbles causing the adhesive to expand volummetrically. The 
resultant adhesive in an uncompressed state sets up as a homogeneous solid 
foam having gas cells substantially evenly distributed throughout the 
adhesive. 
In U.S. Pat. No. 4,059,714, another hot melt thermoplastic adhesive foam 
system is disclosed in which the molten adhesive is mixed with a gas and 
pressurized by either a one-step or two-step gear pump. Within the gear 
pump, the gas and molten adhesive are thoroughly mixed and the gas is 
forced under pump outlet pressure into solution with the liquid adhesive. 
The pressurized liquid/gas adhesive solution is then supplied to a 
valved-type dispensing gun from which the adhesive is dispensed at 
atmospheric pressure. Again, upon emerging from the outlet nozzle of the 
dispenser, the gas evolves from the solution in the form of small bubbles 
causing the adhesive to expand volummetrically and forming in an 
uncompressed state a homogeneous solid foam having gas cells evenly 
distributed throughout the adhesive. 
This technology has been very successful in producing foamed adhesives. The 
insulating effect of the gas bubbles adds to the open time of the 
adhesive, and reduces its working viscosity. Thus the adhesive spreads 
easier and covers more surface area, reducing consumption of the adhesive. 
Other advantages are increased bond strength, longer open times for 
product positioning, faster set times, stronger bonding to porous or 
irregular surfaces, improved bonding to conductive materials, reduced 
adhesive consumption, increased production rates, lowered labor costs and 
better product appearance. 
The extension of this technology to other polymeric materials, such as 
thermoset sealant materials presented certain problems. Whereas hot melt 
adhesives have a viscosity typically in the range of about 2,200 cps to 
20,000-35,000 cps, "high" viscosity polymeric material such as thermoset 
materials used as adhesives, seals and gasketing material have viscosities 
in the range of about 50,000 cps to about 1,000,000 cps. The low viscosity 
foaming gas is more difficult to mix successfully with the highly viscous 
sealant material so as to achieve a uniform solution without creating 
undesirable heat and other problems. Many of these difficulties were 
solved by using a bulk mixer and associated apparatus as described in U.S. 
Pat. No. 4,778,631, to Cobbs, Jr., et al., wherein a low energy input disc 
mixer is employed to force the low viscosity foaming gas into solution 
with the "high" viscosity polymeric material. The mixer may be driven by a 
constant speed motor, which is monitored by a torque sensor. The mixing 
apparatus may also require a bulk melter for the material that is fed to 
the mixer, a cooling system with a supply of cooling fluid, and a 
pressurized supply of foaming gas including a pump. The apparatus 
uniformly blends the foaming gas with curable sealant materials to produce 
high-performance gaskets. When the solution is released to atmosphere, a 
homogeneous foam is formed wherein the gas is released from solution and 
becomes entrapped in the polymer. 
Systems for producing foams of such "high" viscosity materials are 
commercially available from the assignee of the present invention under 
the trademark FoamMix.RTM.. The systems can produce sealants that are 
foamed in place, creating closed-cell foam seals that act as effective, 
long-lasting barriers against air, dust, vapor and fluids in various 
applications. The sealant may be any pumpable material, such as 
polyurethane, silicone or plastisol. This technology produces a foam 
without any chemical reaction, without any chemical blowing agent and 
without any volatiles. Since chemical reactions are not used in the 
foaming process, the chemical composition of the sealant material is not 
changed. Foamed sealants retain their basic physical properties such as 
temperature and chemical resistance. The gas content of the foamed 
material is typically 50% by volume, but the amount of gas in the solution 
can be adjusted to control material durometer, compression set resistance 
and flexibility. The use of this "foam-in-place" technology reduces the 
use of expensive materials such as polyurethanes and silicones and 
provides improved compressibility, improved resilience and reduced cure 
time. The technology is advantageously used to produce foam sealant which 
can be applied by robotic devices, replacing the old, labor-intensive 
manual method of applying die-cut gaskets. Automated foam-in-place 
gasketing increases production, reduces labor and material costs, and 
improves quality through accurate and consistent gasket placement. 
Whether dispensing "high" viscosity foam materials or lower viscosity foam 
adhesives, it is very important to maintain proper pressure on the 
polymer/gas solution through the dispensing process. Wide pressure 
fluctuations can result in premature formation of the foam within the 
dispenser if the pressure of the solution falls below the critical 
pressure level required to maintain the gas in solution. If the foam forms 
prematurely, the foam can shear as it leaves the dispenser, creating a 
foam layer with an uneven texture which not only is presents a rough 
appearance but also reduces the effectiveness of the foam. Conversely, if 
the pressure on the polymer/gas solution is too high within the dispenser, 
the gas will not readily leave solution when the material is dispensed. 
These problems increase when the foamed polymeric materials are dispensed 
intermittently in a production environment. When the polymeric material is 
dead-ended or stopped within the dispenser, unsatisfactory variations in 
the amount of material discharged from the dispenser can occur, and each 
opening and closing of the valves associated with the dispenser to obtain 
intermittent discharge of material can result in pressure fluctuations. 
Many of the problems associated with intermittent application of high 
viscosity polymeric materials have been addressed in U.S. Pat. No. 
5,207,352, to Porter et al. which discloses an apparatus for dispensing a 
solution of highly viscous polymeric material and a gas which comprises a 
dispenser, a pressure regulator and a swivel mount, all of which are 
interconnected to one another. The pressure regulator is adapted to be 
connected to a source of a pressurized polymer/gas solution either 
directly or through the swivel mount. The solution is transmitted through 
the pressure regulator directly into a fluid passageway formed in the 
dispenser body of the dispenser. Minimal pressure drop due to line losses 
occurs because of the close proximity of the pressure regulator and 
dispenser, and the solution is maintained under high pressure within the 
fluid passageway in the dispenser to the discharge outlet of a nozzle 
carried by the dispenser. This configuration maintains the gas in solution 
in the polymeric material within the dispenser body until it is discharged 
from the nozzle to atmosphere to form a homogeneous foam having gas cells 
substantially evenly distributed through the polymeric material. 
As indicated in U.S. Pat. No. 5,207,352, it is very important to maintain 
the proper pressure on the polymer/gas solution throughout the dispenser 
until the material emerges from the dispenser to atmospheric pressure and 
the gas can evolve from the solution to form the foam. These problems are 
magnified if the material is dispensed in a wide band instead of a small 
bead. It would be very desirable to apply hot foam adhesives in a wide 
band in the manufacture of various products. For example, in the 
manufacture of disposable diapers or training pants as shown in U.S. Pat. 
No. 5,246,433, a hot melt adhesive is applied to a flap member using a 
melt blown application system. However, heretofore it has not been 
possible to dispense a pressurized polymer/gas solution to provide a wide 
band of foam material. The addition of another dimension to the dispensing 
profile greatly complicates the task of maintaining the proper pressure on 
the polymer/gas solution within the dispenser. 
In order to dispense the solution in a wide band, a slot-type dispenser 
must be used, and many inherent problems arise in attempting to dispense 
solution through a slot dispenser. The material must be uniformly 
distributed across the width of the slot. In addition, as the material is 
distributed across the width of the slot, the pressure must be maintained 
on the solution to prevent premature foaming of the material. If the 
material begins to foam before it has left the dispenser, the foam shears 
as it leaves the dispenser, and as it is applied to the substrate. This 
premature shearing of the finished foam produces a layer of material 
having a unacceptably rough texture and reduces the effectiveness of the 
foam. In addition, the flowrate of the material leaving the dispenser must 
match the rate at which the substrate passes beneath the dispenser. The 
configuration of the slot and of the distribution manifold leading to the 
slot must be capable of being used with different materials having 
different viscosities and at various flowrates, so that the dispenser can 
be used over a range of production rates. 
SUMMARY OF THE INVENTION 
The present invention provides a method and apparatus for dispensing a 
pressurized polymer/gas solution through an elongated slot to produce a 
foam material. In accordance with the present invention, the polymer/gas 
solution is maintained above the critical pressure until the material 
reaches the exit section of the slot so that premature foaming of the 
material is prevented. 
The dispensing apparatus of this invention is designed with a slot having 
an elongated exit slot section of substantially constant width and 
substantially constant thickness. The material is above the critical 
pressure at the inlet to the exit slot section and, the material is at 
atmospheric pressure at the outlet to the exit slot section where the 
foams begins to form. The exit slot section is designed so as to minimize 
the residence time of the material where the material is below the 
critical pressure and thus minimize premature foaming. 
Upstream of the exit slot section is a converging slot section which 
provides a transition from a enlarged slot section to the smaller exit 
slot section. The converging slot section is configured with a 
substantially constant width, but with a gradually decreasing thickness in 
the downstream direction. The pressure drop of the material through the 
converging slot section is compensated for by increasing the supply 
pressure of the material so that the material is maintained at the 
critical pressure until it reaches the inlet of the exit slot section. 
The method and apparatus of the present invention includes a distribution 
manifold upstream of the exit slot to distribute the polymer/gas solution 
across with the width of the slot to produce a smooth, even band of foam 
material. The distribution manifold may be configured so as to maintain a 
substantially even shear rate throughout the distribution manifold. 
Although the shear rate varies with flowrate, the material remains at a 
even shear rate for a given flow rate, and since viscosity is a function 
of shear rate, the effectiveness of the distribution manifold is 
essentially independent of the viscosity of the material. This allows the 
design of the distribution manifold to work for a wide range of flow 
rates. Although any suitable design of distribution manifold may be used, 
a coathanger-type distribution manifold is preferred. 
These and other advantages are provided by the present invention of 
apparatus for dispensing a polymer foam which comprises means for forming 
a pressurized solution of intermixed polymeric material and gas. The 
polymeric material remains intermixed with the gas while the solution is 
maintained above a critical pressure. The apparatus also comprises means 
for dispensing the pressurized solution in wide band through an elongated 
slot. The solution is maintained above the critical pressure until just 
before the solution emerges from the elongated slot.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
Referring more particularly to the drawings and initially to FIG. 1, there 
is shown a dispensing apparatus including a dispensing gun 10 connected to 
a source of a polymer/gas solution. One method and apparatus of producing 
a solution of polymeric material and gas in preparation for application 
and foaming by the dispensing gun 10 is disclosed in U.S. Pat. No. 
4,778,631 to Cobbs, Jr. et al., owned by the assignee of this invention, 
the disclosure of which is incorporated by reference in its entirety 
herein. Although the pressurizing, mixing and delivery system described in 
the aforesaid patent may be used, it is preferred to use one of a system 
that is presently commercially available, such as the FoamMix.RTM. system 
sold by Nordson Corporation of Westlake, Ohio. 
The pressurizing, mixing and delivery apparatus is schematically 
illustrated in FIG. 1 as it is connected to the dispensing gun 10. The 
apparatus employs a bulk source of polymeric material such as a bulk 
melter 13 containing a heating means for liquefying a solid or semi-solid 
polymer material and pumping it from a tank. An example of a bulk melter 
is shown in U.S. Pat. No. 4,073,409, assigned to the assignee of this 
invention, the disclosure of which is incorporated by reference in its 
entirety herein. The pump associated with the bulk melter 13 is a 
cartridge-type gear pump, however, any pump capable of providing 
sufficient pressure to pump the material from the bulk melter is suitable. 
The polymeric material is conveyed through a line which may be a hose 
capable of conveying heated material under pressure to the upstream end of 
a mixer 14 where the material is injected into the mixer. Foaming gas is 
supplied to the disk mixer 14 from a pressurized gas supply 15 through a 
gas line. A pressure regulator 16 and a flow meter 17 are connected in the 
gas line and permit control of gas pressure and flow rate, respectively, 
to the mixer 14. As schematically illustrated in FIG. 1, the gas is 
supplied from the gas supply 15 to the mixer 14 directly through the gas 
line. 
As described in detail in U.S. Pats. Nos. 4,778,631 and 5,207,352, and as 
used herein, the term "polymer/gas" solution is meant to refer to a 
combination of thermoplastic or thermosetting polymeric material and gases 
such as air, nitrogen, oxygen, carbon dioxide and a variety of other gases 
or mixtures thereof. The term "solution" is used to describe a pressurized 
mixture of liquid polymer and dissolved gas which remains as a mixture 
only so long as the mixture is maintained at or above a critical pressure 
and which, when subjected to atmospheric pressure, forms a foam in which 
the gas evolves from solution in the form of small bubbles which enlarge 
and cause the polymer material to expand volummetrically. The foam is 
formed without a chemical reaction by the mechanical process of allowing 
the gas in the pressurized solution to evolve from the solution when the 
pressure is reduced. The "critical pressure" is defined as the pressure 
above which the polymeric material and gas remain intermixed and below 
which the gas begins to evolve from solution to form the foam. As used in 
the specification and claims, the "solution" of polymeric material and gas 
is intended to define and encompass the broader generic definition of 
solution which is a homogeneous mixture of a gas and molten or liquid 
polymer, whether or not the gas molecules are in fact dissolved or 
dispersed among the polymer molecules. 
Referring again to FIG. 1 the dispensing gun 10 comprises a body 20 which 
can be adjustability mounted to a frame by means of a mounting block 21 
attached to the top of the body. The mounting block 21 has mounting holes 
22 lined with sliding sleeves through which portions of the frame may 
extend. Once positioned on the frame, the mounting block 21 is secured in 
position by means of a set screw 23 or other suitable means. 
A control module 26 is attached to the front of the body 20. A dispensing 
nozzle assembly 27 is attached to the bottom of the control module 26. A 
hose connector 28 extends from the rear of the control module 26 and is 
adapted to be connected to hose connected to the mixer 14 providing the 
pressurized supply of the polymer/gas solution. An elbow connector 29 
extends from the body 20 near the mounting block and is used to connect 
the gun to a pneumatic control line. Pressurized control air is supplied 
to the gun from a pressurized air source 30, and the supply of the air is 
operated by a controller 31 as shown schematically in FIG. 1. Extending 
from one side of the body 20 is a connecting cord 32 for attachment to an 
electric heater 33 and a thermocouple 34. The heater 33 is used to heat 
the body 20 and the control module to maintain the temperature of the 
polymer/gas solution during the dispensing operation. The thermocouple 34 
measures the temperature of the body 20 to assure that the polymer/gas 
solution is within an acceptable temperature range when it is applied. An 
insulating layer 35 is provided between the body 20 and the mounting block 
21 to avoid heating the mounting block and the frame. 
The interior of the dispensing gun 10 shown in FIG. 1 is depicted in FIG. 
2. A pneumatic control passage 40 extends from the elbow connector 29 
through the body 20 and into the module 26. The portion of the passage 40 
near the mounting block 21 is closed by a plug 41. A suitable sealing ring 
42 may be supplied between the body 20 and the module 26 where the passage 
40 passes therebetween. The polymer/gas solution is supplied to the body 
20 from the hose connector 28 through a passage 43 extending across the 
body 20 and into the module 26 to a chamber 44 located in the module. A 
suitable sealing ring 45 may be supplied between the body 20 and the 
module 26 where the passage 43 passes therebetween. The interior of the 
module 26 also includes a pneumatic cylinder 46 connected to the passage 
40. A piston 47 is disposed within the cylinder 46. Within the cylinder 46 
above the piston 47 is a spring 48 which urges the piston downwardly. The 
top of the cylinder 46 is covered by a cover 49 secured by screws 50. The 
pneumatic flow from the passage 40 is connected to the cylinder 46 below 
the piston 47, so that the pneumatic pressure moves the piston 47 upwardly 
in opposition to the spring 48. A rod 51 is connected to the piston 47 and 
extends from the cylinder 46 downwardly into the chamber 44. The rod 51 
actuates a suitable valving mechanism, such as a ball valve member 52 
mounted on the bottom of the rod which engages a valve seat 53 located in 
the chamber 44. Thus, actuation of the pneumatic flow controls the flow of 
the polymer/gas solution through the gun. 
The dispensing nozzle assembly 27 is shown in more detail in FIGS. 3, 4 and 
5. The nozzle assembly 27 comprises a mounting member 60 attached to the 
bottom of the module 26. A main nozzle member 61 is attached to the bottom 
of the mounting member 60 and receives the polymer/gas solution from the 
chamber 44 in the module 26. A shim member 62 is attached to the front of 
the nozzle member 61 by means of a shim clamp member 63 and a plurality of 
fasteners, such as cap screws 64. 
When the ball valve member 52 is spaced from the valve seat 53, the valve 
is open and the pressurized polymer/gas solution enters the nozzle 
assembly 27 through a vertical passage 66 extending through the valve seat 
53 and into the main nozzle member 61. From the passage 66, the 
pressurized solution travels into a transverse passage 67 extending from 
the bottom of the vertical passage 66 to the shim member 62. A 
distribution manifold 68 is located at the outlet of the transverse 
passage 67 along the front of the nozzle member 61 adjacent to the shim 
member 62. The distribution manifold 68 serves to distribute the 
polymer/gas solution across the width of the dispensing nozzle assembly 
27. Preferably, the distribution manifold 68 is a "coathanger" type 
manifold which may be designed in accordance with known techniques of 
design of such manifolds. However, any other type of distribution manifold 
may be used to distribute the pressurized polymer/gas solution across the 
width of the nozzle assembly. A typical width for the application of 
polymer/gas solution using this invention is 1.5 inches, although any 
desired width can be used. 
From the distribution manifold 68, the pressurized polymer/gas solution 
proceeds through the slot from which it is dispensed from the nozzle. The 
slot comprises three sections, an enlarged slot section 71, a converging 
slot section 72, and an exit slot section 73. As used in this description 
and in the claims, the "width" of the slot and the slot sections refers to 
the wide dimension generally perpendicular to the direction of flow of the 
polymer/gas solution through the slot, or the dimension shown extending 
from left to right in FIGS. 4 and 5; the thickness of the slot and the 
slot sections refers to the narrow dimension generally perpendicular to 
the direction of flow of the polymer/gas solution through the slot, or the 
dimension shown extending from left to right in FIG. 3 and from top to 
bottom in FIG. 5; the length of the slot section is the dimension 
generally parallel to the direction of flow of the polymer/gas solution, 
or the dimension shown extending from top to bottom in FIGS. 3 and 4. 
The pressurized polymer/gas solution first enters the enlarged slot section 
71 which is formed in the shim member 62 and extends into an adjacent 
portion of the shim clamp member 63. The enlarged slot section 71 is 
formed in part by the outlet or "land" portion of the coathanger-type 
distribution manifold 68. The enlarged slot section 71 provides a chamber 
containing a pressurized supply of solution for the downstream slot 
sections. Extending from the enlarged slot section 71 is a passage 76 
extending to the thermocouple 34 so that the thermocouple measures the 
temperature of the polymer/gas solution in the enlarged slot section. 
At the outlet of the enlarged slot section 71 is the converging slot 
section 72 having a substantially constant width and having a thickness 
which gradually decreases in the downstream direction. The converging slot 
section 72 reduces the thickness of the slot from the enlarged thickness 
needed to provide the supply chamber of the enlarged slot section 71 to 
the much smaller thickness required to dispense the foam. The converging 
slot section 72 should be designed such that fully developed flow is 
maintained throughout this section. In addition, the converging slot 
section 72 has a constantly decreasing thickness in order to facilitate 
estimation of pressure drops through the section. 
At the bottom of the converging slot section 72 is the exit slot section 73 
formed in the shim member 62. The exit slot section 73 has a substantially 
constant thickness and a substantially constant width. The pressure of the 
polymer/gas solution at the inlet to the exit slot section 73 should be 
above the critical pressure of the solution. By the time the solution 
reaches the outlet of the exit slot section 73, the pressure of the 
solution will have dropped to atmospheric pressure. The dimensions of the 
exit slot section 73 thus minimize the residence time of the solution flow 
near or below the critical pressure. A typical thickness for the exit slot 
is 0.016 inches. Thus the dispensing gun produces a wide ribbon of the 
foam material, with a typical dimension of 1.5 inches wide and 0.030 
inches thick or greater depending upon the foam density ratio. Of course, 
the actual dimensions can be varied as desired depending upon the 
application of the material. 
The converging slot section 72 and the exit slot section 73 are designed so 
that a proper pressure drop of the polymer/gas solution is achieved and 
the pressure of the polymer/gas solution is maintained above the critical 
pressure until the polymer/gas solution exits from the slot. The 
polymer/gas solution thus reaches the critical pressure so that gas 
evolves from the solution in the form of small bubbles causing the 
material to expand volummetrically and foam just as it exits the nozzle. 
The residence time of the material at pressures below the critical 
pressure is minimized or eliminated. 
The pressure of the polymer/gas solution at the inlet to the exit slot 
section 73 should be above the critical pressure of the solution. If, 
however, a polymer/gas solution flows at a rate significantly slower than 
the rate for which the nozzle is designed, the point at which the solution 
drops below the critical pressure may move slowly into the converging slot 
section 72. Since the converging slot section 72 is designed with a small 
converging angle, reasonable foam quality is maintained. 
As shown in FIG. 1, a substrate 78 is moved beneath the nozzle assembly 27 
at a predetermined production rate and the polymer/gas solution exiting 
the slot is applied to the substrate as it moves beneath the nozzle 
assembly. The flow of the polymer/gas solution through the nozzle assembly 
must be such that the exit velocity of the solution matches the velocity 
of the substrate as it passes beneath the nozzle, so that a smooth even 
layer of the foam is dispensed onto the substrate. The substrate velocity 
will typically vary in most production environments, so the design of the 
slot must be such that the flow of the polymer/gas solution is capable of 
being varied to match changes in the substrate speed. 
Example 
The dimensions of the distribution nozzle can be calculated in accordance 
with this invention for a specific example. The starting parameters are 
the line speed, or the speed at which the substrate 78 passes beneath the 
dispensing gun 10, 
the width W of the slot, or the applied width of the band of foam, 
the loft of the applied material, or thickness of the foam material above 
the substrate after it has been applied, 
the "add-on" or the weight of material applied per unit area of substrate, 
and 
the density reduction or percent by which the density of the polymer/gas 
solution decreases after it is released from its pressurized state and the 
material fully foamed. 
For this example, the following values are used: 
the line speed is 1,000 ft/min, 
the width W is 1.5 inches, 
the loft of the applied material is 0.040 inches, 
the add-on is 0.15 g/in.sup.2, and 
the density reduction is 77%. 
Based upon the above values, the flowrate of the unfoamed pressurized 
polymer/gas solution can be calculated. From these values, the flowrate of 
the polymer/gas solution is 2.802 in.sup.3 /sec. 
The dimensions of the slot can then be determined. The dimensions of the 
slot are shown schematically in FIG. 6. Based upon the above given values, 
the thickness H.sub.2 of the exit slot section 73 is calculated. The exit 
thickness H.sub.2 is essentially the unfoamed thickness of the polymer/gas 
solution. In other words, H.sub.2 matches the unfoamed polymer/gas 
solution height needed to produce the desired loft based upon the given 
density reduction. In this example the exit thickness H.sub.2 is 0.016 
inches. 
In this example, the material being applied in a pressurized polymer/gas 
solution is a typical adhesive having a density of 0.98 g/cm.sup.3. The 
viscosity of the material is calculated using the following formula: 
##EQU1## 
where V.sub.0 is 0.004291 lb/in.sup.2- sec, T is 1.155278 lb/in.sup.2, and 
a is 2.2077 for the adhesive polymer of this example. 
From the desired exit thickness H.sub.2 of 0.016 inches, the length L.sub.3 
of the exit slot section 73 is calculated. Along the length L.sub.3 the 
pressure of the polymer/gas solution must drop from the critical pressure 
to atmosphere, so L.sub.3 must be long enough so that the critical 
pressure is maintained at the entrance to L.sub.3, and L.sub.3 is chosen 
so that the pressure drop along L.sub.3 is greater than the critical 
pressure. Using the values in this example the length L.sub.3 is chosen as 
0.1 inches. 
If the length of L.sub.3 is such that the volume of material in the exit 
slot section 73 results in a residence time that is more than a small 
fraction of a second at the operative flowrate, a short diverging section 
73a should be added as shown in FIG. 6a. This increases the exit thickness 
from H.sub.2 to H.sub.3 so that the material flows through the L.sub.3 
region faster but has the proper exit velocity. If such a diverging 
section 73a is added the thickness H.sub.2 is decreased, and H.sub.3 
becomes the exit thickness which is essentially the unfoamed thickness of 
the polymer/gas solution. 
After determining the dimensions of the exit slot section 73, the 
dimensions of the converging section 72 of the slot are determined. The 
dimensions of the converging slot section 72 depend upon the converging 
angle or taper angle A of the converging section and the length L.sub.2 of 
the converging section. A shallow converging angle A which is chosen must 
be small enough to maintain fully developed flow throughout the converging 
section. For a given angle A and length L.sub.2, the pressure drop and 
shear rate can be calculated at spaced positions along the length of the 
converging section using an Ellis model. Table 1 shows such a calculation 
using an angle A of 5.6.degree., and a length L.sub.2 of 0.3 inches, and 
includes a calculation of the pressure drop along the length L.sub.3 and 
along the length L.sub.1 of the slot section leading to the converging 
section. Table 1 also includes a calculation of the pressure drop in the 
feed line leading to the slot, in which the feed line is assumed to be a 
cylindrical line having a constant circular cross section of 0.625 inches 
and a length of 120 inches. 
The pressure drops in Table 1 are calculated using an equation from 
Principles of Polymer Processing, by Tadmor and Gogos, 1979, published by 
John Wiley & Sons of New York, page 568. For an infinitely wide slit this 
gives the following equation for flow Q as a function of pressure P for an 
Ellis fluid: 
##EQU2## 
Since it is not possible to solve this algebraically for pressure, an 
iterative solver, such as Newton's method, is used to adjust the pressure 
P to obtain the specified flow of 2.802 in.sup.3 /sec. 
TABLE 1 
______________________________________ 
Position Calculated 
Number, 
Length, Width, Thickness, 
Shear Pressure 
n (See L.sub.n W H.sub.n Rate Drop (psi) 
FIG. 6) 
(in) (in) (in) (l/sec) 
Ellis model) 
______________________________________ 
Line 120 0.625 0.625 15 23.6 
L.sub.1 
0 0.6 1.5 0.075 1,993 44.6 
L.sub.2 
1 0.03 1.5 0.070 2,311 2.6 
2 0.03 1.5 0.064 2,713 3.1 
3 0.03 1.5 0.059 3,230 3.7 
4 0.03 1.5 0.054 3,909 4.5 
5 0.03 1.5 0.048 4,828 5.6 
6 0.03 1.5 0.043 6,113 7.0 
7 0.03 1.5 0.037 7,990 9.2 
8 0.03 1.5 0.032 10,884 
12.5 
9 0.03 1.5 0.027 15,690 
18.0 
10 0.03 1.5 0.021 24,558 
27.9 
L.sub.3 
11 0.1 1.5 0.016 43,783 
163.5 
SLOT 1.0 -- -- -- 302.2 
(L.sub.1 + 
L.sub.2 + L.sub.3) 
______________________________________ 
The total pressure drop must not be so great as to allow the polymer/gas 
solution to drop below the critical pressure level; otherwise, premature 
foaming will occur. Assuming that the critical foaming pressure of the 
material is 150 psi, the 163.5 psi pressure drop calculated for length 
L.sub.3 is sufficient to avoid formation of foam upstream of L.sub.3. 
Based upon the calculations in Table 1, a pressure of 302 psi will be 
required to feed the slot at this flow rate. 
The analysis in Table 1 as schematically depicted in FIG. 6, provides a 
suitable two dimensional configuration for the slot, including the 
dimensions of the converging section 72. Within the L.sub.2 region it is 
necessary to provide the distribution manifold 68 to provide uniform flow 
across the width W of the slot. As discussed above, a suitable 
distribution manifold is a coathanger-type manifold, the design of which 
is well known in the art. Alternatively, other known manifold designs can 
be used. The configuration of the distribution manifold must assure that 
the pressure drop does not exceed acceptable limits as the polymer/gas 
solution is being distributed across the width of the slot. In addition, 
the distribution manifold should be configured so that similar shear rates 
occur throughout the manifold. With polymer materials such as those used 
in this example, viscosity varies with shear rate. By selecting a geometry 
to maintain a constant shear rate, the effectiveness of the distribution 
manifold is essentially independent of the viscosity of the material. This 
allows the design of the distribution manifold to work for a wide range of 
flow rates. With these goals, a suitable coathanger-type distribution 
manifold can be designed using known analysis, such as that set forth in 
Extrusion Dies for Plastics and Rubber, by Walter Michaeli, second revised 
edition, 1992, published by Hanser Publications of Munich and New York and 
distributed in the U.S. and Canada by Oxford University Press, 
particularly pages 134-150. Such an analysis for this example is set forth 
in Table 2 below. 
As shown generally in FIGS. 7 and 8, the distribution manifold comprises 
two parts, a curved channel 81 having the "coathanger" shape, and a thin 
slot or "land" 82 extending downstream from the channel. As shown in FIGS. 
7 and 8 and as given in Table 2, x is the position of a coordinate 
measured from the centerline of the manifold, W is the width of the 
channel (which in this example is approximately 0.15 inches throughout the 
manifold), H is the depth of the channel (which varies for each position 
of x), and L is the flow distance of the fluid through the channel for 
each incremental increase in x. A graph showing the channel depth H as a 
function of x is presented in FIG. 9. From the dimensions H, W and x, the 
shape of the distribution manifold can be calculated. Also as shown in 
FIGS. 7 and 8, the distance from the exit of the distribution manifold to 
a particular point is y. FIG. 10 presents a graph showing the specific 
shape of the coathanger-type distribution manifold in which the distance 
from the outer edge of the slot is shown against the distance y from the 
exit of the coathanger. 
For the specific dimensions of the distribution manifold in this example, 
the flowrate, shear rate and pressure drop can be calculated for each 
incremental position of x, and Table 2 presents these calculations. Table 
2 includes a presentation of the pressure drop in the channel and along 
the land of the manifold. The calculations of table assume that the total 
flowrate of the fluid at the exit of the distribution manifold is 2.802 
in.sup.3 /sec, as calculated above, the polymer/gas solution has the same 
density 0.98 g/cm.sup.3 as given above, and that the viscosity of the 
polymer/gas solution is as calculated above for Table 1. 
The pressure drops in Table 2 are calculated using the same equation from 
Principles of Polymer Processing, by Tadmor and Gogos, discussed above. 
Since the channel in Table 2 is nearly a square channel, not an infinitely 
wide slit, it is necessary to correct this equation for aspect ratio. This 
is done by multiplying the result of the above equation by F.sub.p as 
shown in the graph on page 573 of Tadmor and Gogos. H/W is then calculated 
and the flow Q is reduced by the fraction F.sub.p. The following curve fit 
is used to approximate this graph: 
##EQU3## 
TABLE 2 
______________________________________ 
Calculated 
Pressure Drop 
Flow- Shear 
X W H L (psi) rate Rate 
(in) (in) (in) (in) Land Channel 
(in.sup.3 /sec) 
(l/sec) 
______________________________________ 
0.00 0.15 0.237 0.056 1.9 1.9 1.401 994 
0.05 0.15 0.225 0.057 2.0 2.0 1.308 1,032 
0.10 0.15 0.213 0.057 2.1 2.1 1.214 1,074 
0.15 0.15 0.200 0.058 2.2 2.2 1.121 1,120 
0.20 0.15 0.187 0.059 2.4 2.4 1.027 1,170 
0.25 0.15 0.175 0.060 2.6 2.6 0.934 1,223 
0.30 0.15 0.162 0.062 2.8 2.8 0.841 1,280 
0.35 0.15 0.149 0.065 3.1 3.1 0.747 1,341 
0.40 0.15 0.136 0.068 3.5 3.5 0.654 1,406 
0.45 0.15 0.123 0.074 4.2 4.2 0.560 1,479 
0.50 0.15 0.109 0.087 5.4 5.4 0.467 1,563 
0.55 0.15 0.093 0.180 13.1 13.1 0.374 1,719 
0.60 0.15 0.075 0.050 1,993 
0.65 0.15 0.075 0.050 1,328 
0.70 0.15 0.075 0.050 664 
0.75 0.15 0.075 
Distribution Manifold Total 
45.3 45.3 
______________________________________ 
The dimensions of the distribution manifold shown in Table 2 have been 
adjusted so that the shear rate remains relatively constant throughout the 
manifold. This allows the manifold to operate effectively for various 
viscosities and for the design to be essentially independent of material 
viscosity. 
Other variations and modifications of the specific embodiments herein shown 
and described will be apparent to those skilled in the art, all within the 
intended spirit and scope of the invention. While the invention has been 
shown and described with respect to particular embodiments thereof, these 
are for the purpose of illustration rather than limitation. Accordingly, 
the patent is not to be limited in scope and effect to the specific 
embodiments herein shown and described nor in any other way this is 
inconsistent with the extent to which the progress in the art has been 
advanced by the invention.