We claim:
1. An apparatus for determining the viscosity of the circulating blood of a living being over plural shear rates using a decreasing pressure differential, said apparatus comprising:
a lumen being positioned at an angle to a horizontal reference greater than zero degrees, said lumen comprising a first end and a second end, said first end being exposed to atmospheric pressure, said lumen comprising a first known dimension;
a flow restrictor having an inlet and an outlet, said outlet being arranged to deliver any blood that passes therethrough to a collector, said flow restrictor including some known dimensions;
a valve coupled to the vascular system of the living being at a first port, said valve comprising a second port coupled to said second end and a third port coupled to said inlet;
a sensor for detecting the movement of the blood over time through said apparatus, said sensor generating data relating to the movement of the blood over time;
a processor, coupled to said valve and said sensor, said processor arranged to operate said valve to create a column of blood in said first lumen and said flow restrictor and to establish a pressure differential between said first end and said outlet, said column of blood moving through said lumen and said flow restrictor at a first shear rate caused by said pressure differential, said movement of said column of blood causing said pressure differential to decrease from said first shear rate for generating said plural shear rates; and
wherein said processor calculates the viscosity of the blood based on said data relating to the movement of the column of blood over time, said first known dimension of said lumen and said some known dimensions of said flow restrictor.
2. The apparatus of claim 1 wherein said outlet remains submerged in the blood that is being collected in said collector when said column of blood is moving.
3. The apparatus of claim 2 wherein said sensor detects the changing weight of said collector over time as the blood passes from said outlet into said collector.
4. The apparatus of claim 2 wherein said column of blood comprises a level that changes with time, said sensor detecting said changing level of fluid over time.
5. The apparatus of claim 3 wherein said flow restrictor is a capillary tube and wherein the pressure drop across said capillary tube, Pc, is given by:
14
P
c
=
4
g
R
2
m
–
m
i
–
m
(
t
)
where,
g is gravitational acceleration;
R is the diameter of said lumen;
m is the final weight of said collector after a long period of time;
mi is the initial weight of said collector before said column of blood starts moving; and
m(t) is the changing weight of the collector over time.
6. The apparatus of claim 5 wherein the viscosity, , is given by:
15
=
g
c
4
8
L
c
R
2
m
–
m
i
–
m
(
t
)
(
m
t
)
(
3
+
1
n
)
where,
is the density of the blood;
c is the diameter of said capillary tube;
Lc is the length of said capillary tube; and
16
1
n
=
ln
Q
ln
w
,
where
Q is the volumetric flow rate through said capillary tube; and
w is
17
P
c
c
4
L
c
.
7. The apparatus of claim 6 wherein the quantity
18
1
n
can be approximated by
19
1
n
where n is the exponent of a power law constitutive equation.
8. The apparatus of claim 3 wherein said sensor is a precision balance or load cell.
9. The apparatus of claim 3 wherein said collector comprises:
a container having an inner compartment in which said outlet is disposed; and
an annular compartment surrounding said inner compartment for forming an overflow chamber.
10. The apparatus of claim 4 wherein said flow restrictor is a capillary tube and wherein the pressure drop across said capillary tube, Pc, is given by:
Pcghihh(t)
where:
is the density of the blood;
g is gravitational acceleration;
hi is the initial height of said column of blood;
h is the final height of said column of blood; and
h(t) is the changing height of said column of blood over time.
11. The apparatus of claim 10 wherein the viscosity of the blood, , is given by:
20
=
g
c
4
8
L
c
R
2
(
h
i
–
h
–
h
(
t
)
h
(
t
)
t
(
3
+
1
n
)
)
where,
c is the diameter of said capillary tube;
R is the diameter of said lumen;
Lc is the length of said capillary tube; and
21
1
n
=
ln
Q
ln
w
,
where
Q is the volumetric flow rate through said capillary tube; and
w is
22
P
c
c
4
L
c
.
12. The apparatus of claim 11 wherein the quantity
23
1
n
can be approximated by
24
1
n
where n is the exponent of a power law constitutive equation.
13. The apparatus of claim 4 wherein said sensor is a column level detector.
14. The apparatus of claim 4 wherein said collector comprises:
a container having an inner compartment in which said outlet is disposed; and
an annular compartment surrounding said inner compartment for forming an overflow chamber.
15. A method for determining the viscosity of the circulating blood of a living being over plural shear rates caused by a decreasing pressure differential, said method comprising the steps of:
(a) providing a lumen having a first end and a second end and positioned at an angle to a horizontal reference greater than zero degrees, said lumen having a first known dimension, said first end being exposed to atmospheric pressure;
(b) diverting a portion of the circulating blood into said lumen through said second end to form a column of blood therein;
(c) coupling an inlet of a flow restrictor to said second end of said lumen to establish a pressure differential between said first end and said outlet, said flow restrictor having an outlet that is arranged to deliver any blood that passes therethrough to a collector, said flow restrictor having some known dimensions;
(d) controlling said column of blood to form a continuous column of blood in said lumen and said flow restrictor, said column of blood moving through said lumen and said flow restrictor at a first shear rate caused by said pressure differential, said movement of said column of blood causing said pressure differential to decrease from said first shear rate for generating said plural shear rates;
(e) providing a sensor for detecting the movement of the column of blood over time as the column of blood moves and passes from said outlet into said collector while maintaining said outlet submerged in blood that has collected in said collector, said sensor generating data regarding said movement; and
(f) calculating the viscosity of the blood based on the generated data, said first known dimension and said some known dimensions.
16. The method of claim 15 wherein said step of providing a sensor comprises disposing said collector on a mass detector and obtaining an initial weight of said collector before said column of blood begins moving.
17. The method of claim 16 wherein said mass detector comprises a precision balance or a load cell.
18. The method of claim 15 wherein said step of providing a sensor comprises disposing a column level detector adjacent said lumen for detecting the changing position of a level of said column of blood.
19. The method of claim 16 wherein said flow restrictor is a capillary tube and wherein said step of calculating the viscosity comprises determining the pressure drop across said capillary tube, Pc, according to:
25
P
c
=
4
g
R
2
m
–
m
i
–
m
(
t
)
where,
g is gravitational acceleration;
R is the diameter of said lumen;
m final weight of said collector after a long period of time;
mi is the initial weight of said collector before said column of blood starts moving; and
m(t) is the changing weight of the collector over time.
20. The method of claim 19 wherein said step of calculating the viscosity of the blood comprises determining the viscosity, , of the blood according to:
26
=
g
c
4
8
L
c
R
2
m
–
m
i
–
m
(
t
)
(
m
t
)
(
3
+
1
n
)
where,
is the density of the blood;
c is the diameter of said capillary tube;
Lc is the length of said capillary tube; and
27
1
n
=
ln
Q
ln
w
,
where
Q is the volumetric flow rate through said capillary tube; and
w is
28
P
c
c
4
L
c
.
21. The method of claim 20 wherein the quantity
29
1
n
can be approximated by
30
1
n
where n is the exponent of a power law constitutive equation.
22. The method of claim 18 wherein said flow restrictor is a capillary tube and wherein said step of calculating the viscosity comprises determining the pressure drop across said capillary tube, Pc, according to:
Pcg(hihh(t))
where,
is the density of the fluid;
g is gravitational acceleration;
h is the final height of said column of blood after a long period of time;
hi is the initial height of said column of blood before said column of blood starts moving; and
h(t) is the changing weight of the collector over time.
23. The method of claim 22 wherein said step of calculating the viscosity of the blood comprises determining the viscosity, , of the blood according to:
31
=
g
c
4
8
L
c
R
2
(
h
i
–
h
–
h
(
t
)
h
(
t
)
t
(
3
+
1
n
)
)
where,
c is the diameter of said capillary tube;
R is the diameter of said lumen;
Lc is the length of said capillary tube; and
32
1
n
=
ln
Q
ln
w
,
where
Q is the volumetric flow rate through said capillary tube; and
33
w
is
P
c
c
4
L
c
.
24. The method of claim 23 wherein the quantity
34
1
n
can be approximated by
35
1
n
where n is the exponent of a power law constitutive equation.
25. An apparatus for determining the viscosity of the circulating blood of a living being over plural shear rates using a decreasing pressure differential, said apparatus comprising:
a lumen being positioned at an angle to a horizontal reference greater than zero degrees, said lumen comprising a first end and a second end, said lumen comprising a first known dimension;
a flow restrictor having an inlet and an outlet, said outlet being arranged to deliver any blood that passes therethrough to a collector, said inlet being coupled to said second end, said flow restrictor including some known dimensions;
a valve coupled to the vascular system of the living being at a first port, said valve comprising a second port coupled to said first end;
a sensor for detecting the movement of the blood over time through said apparatus, said sensor generating data relating to the movement of the blood over time;
a processor, coupled to said valve and said sensor, said processor arranged to operate said valve to create a column of blood in said first lumen and said flow restrictor and to establish a pressure differential between said first end and said outlet, said column of blood moving through said lumen and said flow restrictor at a first shear rate caused by said pressure differential, said movement of said column of blood causing said pressure differential to decrease from said first shear rate for generating said plural shear rates; and
wherein said processor calculates the viscosity of the blood based on said data relating to the movement of the column of blood over time, said first known dimension of said lumen and said some known dimensions of said flow restrictor.
26. The apparatus of claim 25 wherein said outlet remains submerged in the blood that is being collected in said collector when said column of blood is moving.
27. The apparatus of claim 26 wherein said sensor detects the changing weight of said collector over time as the blood passes from said outlet into said collector.
28. The apparatus of claim 26 wherein said column of blood comprises a level that changes with time, said sensor detecting said changing level of fluid over time.
29. The apparatus of claim 27 wherein said flow restrictor is a capillary tube and wherein the pressure drop across said capillary tube, Pc, is given by:
36
P
c
=
4
g
R
2
m
–
m
i
–
m
(
t
)
where,
g is gravitational acceleration;
R is the diameter of said lumen;
m is the final weight of said collector after a long period of time;
mi is the initial weight of said collector before said column of blood starts moving; and
m(t) is the changing weight of the collector over time.
30. The apparatus of claim 29 wherein the viscosity, , is given by:
37
=
g
c
4
8
L
c
R
2
m
–
m
i
–
m
(
t
)
(
m
t
)
(
3
+
1
n
)
where,
is the density of the blood;
c is the diameter of said capillary tube;
Lc is the length of said capillary tube; and
38
1
n
=
ln
Q
ln
w
,
where
Q is the volumetric flow rate through said capillary tube; and
w is
39
P
c
c
4
L
c
.
31. The apparatus of claim 30 wherein the quantity
40
1
n
can be approximated by
41
1
n
where n is the exponent of a power law constitutive equation.
32. The apparatus of claim 27 wherein said sensor is a precision balance or load cell.
33. The apparatus of claim 27 wherein said collector comprises:
a container having an inner compartment in which said outlet is disposed; and
an annular compartment surrounding said inner compartment for forming an overflow chamber.
34. The apparatus of claim 29 wherein said flow restrictor is a capillary tube and wherein the pressure drop across said capillary tube, Pc, is given by:
Pcghihh(t)
where:
is the density of the blood;
g is gravitational acceleration;
hi is the initial height of said column of blood;
h is the final height of said column of blood; and
h(t) is the changing height of said column of blood over time.
35. The apparatus of claim 34 wherein the viscosity of the blood, , is given by:
42
=
g
c
4
8
L
c
R
2
(
h
i
–
h
–
h
(
t
)
h
(
t
)
t
(
3
+
1
n
)
)
where,
c is the diameter of said capillary tube;
R is the diameter of said lumen;
Lc is the length of said capillary tube; and
43
1
n
=
ln
Q
ln
w
,
where
Q is the volumetric flow rate through said capillary tube; and
44
w
is
P
c
c
4
L
c
.
36. The apparatus of claim 35 wherein the quantity
45
1
n
can be approximated by
46
1
n
where n is the exponent of a power law constitutive equation.
37. The apparatus of claim 28 wherein said sensor is a column level detector.
38. The apparatus of claim 28 wherein said collector comprises:
a container having an inner compartment in which said outlet is disposed; and
an annular compartment surrounding said inner compartment for forming an overflow chamber.
39. A method for determining the viscosity of the circulating blood of a living being over plural shear rates caused by a decreasing pressure differential, said method comprising the steps of:
(a) providing a lumen having a first end and a second end and positioned at an angle to a horizontal reference greater than zero degrees, said lumen having a first known dimension;
(b) coupling an inlet of a flow restrictor to said second end and arranging an outlet of said flow restrictor to deliver any blood that passes therethrough to a collector, said flow restrictor having some known dimensions;
(c) diverting a portion of the circulating blood into said lumen through said first end to form a column of blood in said lumen and said flow restrictor and to establish a pressure differential between said first end and said outlet;
(c) exposing said first end to atmospheric pressure to cause said column of blood to move through said lumen and said flow restrictor, said movement of said column of blood causing said pressure differential to decrease from said first shear rate for generating said plural shear rates;
(d) providing a sensor for detecting the movement of the column of blood over time as the column of blood moves and passes from said outlet into said collector while maintaining said outlet submerged in blood that has collected in said collector, said sensor generating data regarding said movement; and
(e) calculating the viscosity of the blood based on the generated data, said first known dimension and said some known dimensions.
40. The method of claim 39 wherein said step of providing a sensor comprises disposing said collector on a mass detector and obtaining an initial weight of said collector before said column of blood begins moving.
41. The method of claim 40 wherein said mass detector comprises a precision balance or a load cell.
42. The method of claim 39 wherein said step of providing a sensor comprises disposing a column level detector adjacent said lumen for detecting the changing position of a level of said column of blood.
43. The method of claim 40 wherein said flow restrictor is a capillary tube and wherein said step of calculating the viscosity comprises determining the pressure drop across said capillary tube, Pc, according to:
47
P
c
=
4
g
R
2
m
–
m
i
–
m
(
t
)
where,
g is gravitational acceleration;
R is the diameter of said lumen;
m is the final weight of said collector after a long period of time;
mi is the initial weight of said collector before said column of blood starts moving; and
m(t) is the changing weight of the collector over time.
44. The method of claim 43 wherein said step of calculating the viscosity of the blood comprises determining the viscosity, , of the blood according to:
48
=
g
c
4
8
L
c
R
2
m
–
m
i
–
m
(
t
)
(
m
t
)
(
3
+
1
n
)
where,
is the density of the blood;
c is the diameter of said capillary tube;
Lc is the length of said capillary tube; and
49
1
n
=
ln
Q
ln
w
,
where
Q is the volumetric flow rate through said capillary tube; and
w is
50
P
c
c
4
L
c
.
45. The method of claim 44 wherein the quantity
51
1
n
can be approximated by
52
1
n
where n is the exponent of a power law constitutive equation.
46. The method of claim 42 wherein said flow restrictor is a capillary tube and wherein said step of calculating the viscosity comprises determining the pressure drop across said capillary tube, Pc, according to:
Pcg(hihh(t))
where,
is the density of the fluid;
g is gravitational acceleration;
h is the final height of said column of blood after a long period of time;
hi is the initial height of said column of blood before said column of blood starts moving; and
h(t) is the changing weight of the collector over time.
47. The method of claim 46 wherein said step of calculating the viscosity of the blood comprises determining the viscosity, , of the blood according to:
53
=
g
c
4
8
L
c
R
2
(
h
i
–
h
–
h
(
t
)
h
(
t
)
t
(
3
+
1
n
)
)
where,
c is the diameter of said capillary tube;
R is the diameter of said lumen;
Lc is the length of said capillary tube; and
54
1
n
=
ln
Q
ln
w
,
where
Q is the volumetric flow rate through said capillary tube; and
w is
55
P
c
c
4
L
c
.
48. The method of claim 47 wherein the quantity
56
1
n
can be approximated by
57
1
n
where n is the exponent of a power law constitutive equation.
49. An apparatus for determining the viscosity of the circulating blood of a living being over plural shear rates using a decreasing pressure differential, said apparatus comprising:
a first lumen being positioned at an angle to a horizontal reference greater than zero degrees, said lumen comprising a first end and a second end, said first end being exposed to atmospheric pressure, said lumen comprising a first known dimension;
a flow restrictor having an inlet and an outlet, said inlet coupled to said second end, said flow restrictor including some known dimensions;
a valve coupled to the vascular system of the living being at a first port, said valve comprising a second port coupled to said outlet and a third port coupled to an input of a second lumen arranged to deliver any blood that passes therethrough to a collector through an output of said second lumen;
a sensor for detecting the movement of the blood over time through said apparatus, said sensor generating data relating to the movement of the blood over time;
a processor, coupled to said valve and said sensor, said processor arranged to operate said valve to create a column of blood in said first lumen and said flow restrictor and to establish a pressure differential between said first end and said output, said column of blood moving through said lumen and said flow restrictor at a first shear rate caused by said pressure differential, said movement of said column of blood causing said pressure differential to decrease from said first shear rate for generating said plural shear rates; and
wherein said processor calculates the viscosity of the blood based on said data relating to the movement of the column of blood over time, said first known dimension of said first lumen and said some known dimensions of said flow restrictor.
50. The apparatus of claim 49 wherein said inlet of said flow restrictor is positioned at an elevation that is lower than the elevation of said output of said second lumen.
51. The apparatus of claim 50 wherein said outlet remains submerged in the blood that is being collected in said collector when said column of blood is moving.
52. The apparatus of claim 51 wherein said sensor detects the changing weight of said collector over time as the blood passes from said outlet into said collector.
53. The apparatus of claim 51 wherein said column of blood comprises a level that changes with time, said sensor detecting said changing level of fluid over time.
54. The apparatus of claim 52 wherein said flow restrictor is a capillary tube and wherein the pressure drop across said capillary tube, Pc, is given by:
58
P
c
=
4
g
R
2
m
–
m
(
t
)
where,
g is gravitational acceleration;
R is the diameter of said lumen;
m is the final weight of said collector after a long period of time;
mi is the initial weight of said collector before said column of blood starts moving; and
m(t) is the changing weight of the collector over time.
55. The apparatus of claim 54 wherein the viscosity, , is given by:
59
=
g
c
4
8
L
c
R
2
m
–
m
i
–
m
(
t
)
(
m
t
)
(
3
+
1
n
)
where,
is the density of the blood;
c is the diameter of said capillary tube;
Lc is the length of said capillary tube; and
60
1
n
=
ln
Q
ln
w
,
where
Q is the volumetric flow rate through said capillary tube; and
w is
61
P
c
c
4
L
c
.
56. The apparatus of claim 55 wherein the quantity
62
1
n
can be approximated by
63
1
n
where n is the exponent of a power law constitutive equation.
57. The apparatus of claim 52 wherein said sensor is a precision balance or load cell.
58. The apparatus of claim 52 wherein said collector comprises:
a container having an inner compartment in which said outlet is disposed; and
an annular compartment surrounding said inner compartment for forming an overflow chamber.
59. The apparatus of claim 53 wherein said flow restrictor is a capillary tube and wherein the pressure drop across said capillary tube, Pc, is given by:
Pcghihh(t)
where:
is the density of the blood;
g is gravitational acceleration;
hi is the initial height of said column of blood;
h is the final height of said column of blood; and
h(t) is the changing height of said column of blood over time.
60. The apparatus of claim 59 wherein the viscosity of the blood, , is given by:
64
=
g
c
4
8
L
c
R
2
(
h
i
–
h
–
h
(
t
)
h
(
t
)
t
(
3
+
1
n
)
)
where,
c is the diameter of said capillary tube;
R is the diameter of said lumen;
Lc is the length of said capillary tube; and
65
1
n
=
ln
Q
ln
w
,
where
Q is the volumetric flow rate through said capillary tube; and
w is
66
P
c
c
4
L
c
,
61. The apparatus of claim 60 wherein the quantity
67
1
n
can be approximated by
68
1
n
where n is the exponent of a power law constitutive equation.
62. The apparatus of claim 53 wherein said sensor is a column level detector.
63. The apparatus of claim 53 wherein said collector comprises:
a container having an inner compartment in which said outlet is disposed; and
an annular compartment surrounding said inner compartment for forming an overflow chamber.
The claims below are in addition to those above.
All refrences to claim(s) which appear below refer to the numbering after this setence.
1. A system for fusing an unfixed toner image to a substrate passing through said system in a process direction, said system comprising:
a rotatable hot fusing roll;
a backup belt assembly comprising a backup belt and a housing structure including a nip forming pressure roll, said backup belt being wrapped about said housing structure including said nip forming pressure roll, said pressure roll comprising a crown shape having a larger diameter at a central portion of said pressure roll than at the ends of said pressure roll; and
said housing structure including structure engaging said belt to create a generally equal belt tension along substantially the entire length of said belt in a direction transverse to said process direction.
2. The system of claim 1, wherein said structure engaging said belt comprises a low friction compressible material.
3. The system of claim 1, wherein said structure engaging said belt is located at a generally opposite side of said housing from said pressure roll.
4. The system of claim 1, wherein said structure engaging said belt comprises at least one tension pad supported on said housing.
5. The system of claim 4, wherein said structure engaging said belt comprises first and second tension pads located in engagement with outer portions of said belt.
6. The system of claim 1, wherein the height of the crown of said pressure roll is approximately 0.3 mm to 0.9 mm.
7. The system of claim 6, wherein said pressure roll comprises a steel shaft covered with an outer layer of elastomeric material having a hardness of approximately 65 Asker C to 85 Asker C.
8. The system of claim 1, wherein said belt comprises a polyimide inner member having a release coating on an outer surface thereof.
9. The system of claim 8, wherein said polyimide inner member has a thickness of approximately 90 microns.
10. The system of claim 1, wherein said housing structure further comprises a rotatable support roll positioned upstream of said pressure roll to support said belt at a location adjacent and spaced from said hot roll.
11. A system for fusing an unfixed toner image to a substrate passing through said system in a process direction, said system comprising:
a rotatable hot fusing roll;
a backup belt assembly comprising a backup belt and a housing structure including a nip forming pressure roll, said backup belt being wrapped about said housing structure including said nip forming pressure roll, said pressure roll comprising a crown shape having a larger diameter at a central portion of said pressure roll than at the ends of said pressure roll; and
a belt tensioning structure located on said housing structure and engaging said belt adjacent at least outer portions of said belt.
12. The system of claim 11, wherein said belt tensioning structure comprises first and second tensioning pads located at opposite sides of said belt.
13. The system of claim 12, wherein said first and second tensioning pads comprise a low friction compressible material.
14. The system of claim 12, wherein said first and second tensioning pads are located at a generally opposite side of said housing from said pressure roll.
15. The system of claim 12, wherein said first and second tensioning pads have a thickness of approximately 3 mm to 5 mm.
16. The system of claim 15, wherein the height of the crown of said pressure roll is approximately 0.3 mm to 0.9 mm.
17. The system of claim 16, wherein said pressure roll comprises a steel shaft covered with an outer layer of elastomeric material having a hardness of approximately 65 Asker C to 85 Asker C.
18. The system of claim 11, wherein said belt comprises a polyimide inner member having a release coating on an outer surface thereof.
19. The system of claim 18, wherein said polyimide inner member has a thickness of approximately 90 microns.
20. The system of claim 11, wherein said housing structure further comprises a rotatable support roll positioned upstream of said pressure roll to support said belt at a location adjacent and spaced from said hot roll.