US 10,502,671 B2 · Viscosity measuring method and viscosity measuring apparatus

A method of measuring an apparent viscosity of a sample of non-Newtonian fluid comprising:

(A) a step in which a plunger having an outer radius Ri is immersed into a sample contained in a cylindrical container having an inner radius R0, coaxially with the cylindrical container by an initial depth L0 and stopped thereat, the outer radius Ri of the plunger being smaller than the inner radius R0 of the cylindrical container;
(B) a step in which the plunger is further immersed into the sample coaxially with the cylindrical container at a first relative movement velocity vp1 by a first relative movement distance ΔL1, and during the further immersing operation and after the further immersing operation, a force applied to the plunger from the sample is measured with a passage of time;
(C) a step in which a first peak value FT1 and a first convergent value FTe1 of the force applied to the plunger from the sample are obtained, based on measured values of the force caused by the relative movement of the plunger at the first relative movement velocity vp1;
(D) a step in which the plunger is returned coaxially with the cylindrical container to the initial depth L0 and stopped thereat;
(E) a step in which the plunger is further immersed into the sample coaxially with the cylindrical container at a second relative movement velocity vp2 by a second relative movement distance ΔL2, and during the further immersing operation and after the further immersing operation, a force applied to the plunger from the sample is measured with a passage of time;
(F) a step in which a second peak value FT2 and a second convergent value FTe2 of the force applied to the plunger from the sample are obtained, based on measured values of the force caused by the relative movement of the plunger at the second relative movement velocity vp2;
(G) a step in which, based on a predetermined relationship established among:
the first relative movement distance ΔL1, the first peak value FT1 and the first convergent value FTe1, at the first relative movement velocity vp1;
the second relative movement distance ΔL2, the second peak value FT2 and the second convergent value FTe2, at the second relative movement velocity vp2;
a plunger ratio κ=Ri/R0;
and a flow behavior index n of the sample;
the flow behavior index n is obtained;
and
(H) a step in which, when the first relative movement velocity vp1 is represented as vp, the first relative movement distance ΔL1 is represented as ΔL, the first peak value FT1 is represented as FT, and the first convergent value FTe1 is represented as FTe, or when the second relative movement velocity vp2 is represented as vp, the second relative movement distance ΔL2 is represented as ΔL, the second peak value FT2 is represented as FT, and the second convergent value FTe2 is represented as FTe, an apparent viscosity μa of the sample is calculated based on the vp, the ΔL, the FT, the FTe, the plunger ratio κ, the flow behavior index n, a density ρ of the sample, a gravitational acceleration g, and the following Expression (1):
⁢
[
NO
⁢
⁢
1
]
⁢
μ
a
=
σ
w
dy
/
dt
=
σ
0
+
K
⁡
(
dy
dt
)
n
dy
/
dt
⁢
⁢
⁢
in
⁢
⁢
which
⁢
⁢
⁢
σ
w
=
T
w
⁢
PR
0
2
,
dy
dt
=
(
λ
2
κ
-
κ
-
T
0
)
s
⁢
(
PR
0
2
⁢
K
)
s
,
⁢
⁢
K
=
PR
0
2
⁢
(
Φ
⁢
⁢
R
0
v
p
⁢
κ
2
)
n
,
P
=
2
⁢
σ
y
T
0
⁢
R
0
,
T
w
=
λ
2
κ
-
κ
,
(
1
)
Φ
=
{
∫
κ
λ
-
⁢
(
λ
2
-
x
2
-
T
0
⁢
x
)
s
⁢
x
-
s
⁢
⁢
dx
-
∫
λ
+
1
⁢
(
x
2
-
λ
2
-
T
0
⁢
x
)
s
⁢
⁢
x
-
s
⁢
dx
}
⁢
κ
2
-
∫
κ
λ
-
⁢
(
λ
2
-
x
2
-
T
0
⁢
x
)
s
⁢
x
2
-
s
⁢
dx
+
⁢
∫
λ
+
1
⁢
(
x
2
-
λ
2
-
T
0
⁢
x
)
s
⁢
x
2
-
s
⁢
⁢
dx
(
2
)
0
=
∫
κ
λ
-
⁢
(
λ
2
-
x
2
-
T
0
⁢
x
)
s
⁢
x
-
s
⁢
⁢
dx
-
∫
λ
+
1
⁢
(
x
2
-
λ
2
-
T
0
⁢
x
)
s
⁢
x
-
s
⁢
⁢
dx
,
⁢
⁢
s
=
1
n
,
(
3
)
⁢
λ
-
=
1
2
⁡
[
(
T
0
2
+
4
⁢
λ
2
)
1
2
-
T
0
]
,
(
4
)
⁢
λ
+
=
1
2
⁡
[
(
T
0
2
+
4
⁢
λ
2
)
1
2
+
T
0
]
,
⁢
⁢
T
0
=
F
y
F
cb
,
σ
y
=
F
y
2
⁢
π
⁢
⁢
R
i
⁡
(
L
0
+
L
2
)
,
F
y
=
F
Te
-
F
b
,
⁢
⁢
F
cb
=
F
T
-
F
b
,
F
b
=
π
⁢
⁢
R
i
2
⁢
L
2
⁢
ρ
⁢
⁢
g
,
L
2
=
Δ
⁢
⁢
L
1
-
κ
2
.
(
5
)

447 more elements

A method of measuring an apparent viscosity of a sample of non-Newtonian fluid comprising:

(A) a step in which a plunger having an outer radius Ri is immersed into a sample contained in a cylindrical container having an inner radius R0, coaxially with the cylindrical container by an initial depth L0 and stopped thereat, the outer radius Ri of the plunger being smaller than the inner radius R0 of the cylindrical container;
(B) a step in which the plunger is further immersed into the sample coaxially with the cylindrical container at a first relative movement velocity vp1 by a relative movement distance ΔL, and during the further immersing operation and after the further immersing operation, a force applied to the plunger from the sample is measured with a passage of time;
(C) a step in which a first peak value FT1 and a first convergent value FTe1 of the force applied to the plunger from the sample are obtained, based on measured values of the force caused by the relative movement of the plunger at the first relative movement velocity vp1;
(D) a step in which the plunger is returned coaxially with the cylindrical container to the initial depth L0 and stopped thereat;
(E) a step in which the plunger is further immersed into the sample coaxially with the cylindrical container at a second relative movement velocity vp2 by the relative movement distance ΔL, and during the further immersing operation and after the further immersing operation, a force applied to the plunger from the sample is measured with a passage of time;
(F) a step in which a second peak value FT2 and a second convergent value FTe2 of the force applied to the plunger from the sample are obtained, based on measured values of the force caused by the relative movement of the plunger at the second relative movement velocity vp2;
(G) a step in which, based on a predetermined relationship established among:
the first peak value FT1 and the first convergent value FTe1 at the first relative movement velocity vp1;
the second peak value FT2 and the second convergent value FTe2 at the second relative movement velocity vp2;
the relative movement distance ΔL;
a plunger ratio κ=Ri/R0;
and a flow behavior index n of the sample;
the flow behavior index n is obtained;
(H) a step in which, when the first relative movement velocity vp1 is represented as vp, the first peak value FT1 is represented as FT, and the first convergent value FTe1 is represented as FTe, or when the second relative movement velocity vp2 is represented as vp, the second peak value FT2 is represented as FT, and the second convergent value FTe2 is represented as FTe, an apparent viscosity μa of the sample is calculated based on the vp, the FT, the FTe, the relative movement distance ΔL, the plunger ratio κ, the flow behavior index n, a density ρ of the sample, a gravitational acceleration g, and the following Expression (1):
⁢
[
NO
⁢
⁢
3
]
⁢
μ
a
=
σ
w
dy
/
dt
=
σ
0
+
K
⁡
(
dy
dt
)
n
dy
/
dt
⁢
⁢
⁢
in
⁢
⁢
which
⁢
⁢
⁢
σ
w
=
T
w
⁢
PR
0
2
,
dy
dt
=
(
λ
2
κ
-
κ
-
T
0
)
s
⁢
(
PR
0
2
⁢
K
)
s
,
⁢
⁢
K
=
PR
0
2
⁢
(
Φ
⁢
⁢
R
0
v
p
⁢
κ
2
)
n
,
P
=
2
⁢
σ
y
T
0
⁢
R
0
,
T
w
=
λ
2
κ
-
κ
,
(
1
)
Φ
=
{
∫
κ
λ
-
⁢
(
λ
2
-
x
2
-
T
0
⁢
x
)
s
⁢
x
-
s
⁢
⁢
dx
-
∫
λ
+
1
⁢
(
x
2
-
λ
2
-
T
0
⁢
x
)
s
⁢
⁢
x
-
s
⁢
dx
}
⁢
κ
2
-
∫
κ
λ
-
⁢
(
λ
2
-
x
2
-
T
0
⁢
x
)
s
⁢
x
2
-
s
⁢
dx
+
⁢
∫
λ
+
1
⁢
(
x
2
-
λ
2
-
T
0
⁢
x
)
s
⁢
x
2
-
s
⁢
⁢
dx
⁢
(
2
)
0
=
∫
κ
λ
-
⁢
(
λ
2
-
x
2
-
T
0
⁢
x
)
s
⁢
x
-
s
⁢
⁢
dx
-
∫
λ
+
1
⁢
(
x
2
-
λ
2
-
T
0
⁢
x
)
s
⁢
x
-
s
⁢
⁢
dx
,
⁢
⁢
s
=
1
n
,
(
3
)
⁢
λ
-
=
1
2
⁡
[
(
T
0
2
+
4
⁢
λ
2
)
1
2
-
T
0
]
,
(
4
)
⁢
λ
+
=
1
2
⁡
[
(
T
0
2
+
4
⁢
λ
2
)
1
2
+
T
0
]
,
⁢
⁢
T
0
=
F
y
F
cb
,
σ
y
=
F
y
2
⁢
π
⁢
⁢
R
i
⁡
(
L
0
+
L
2
)
,
F
y
=
F
Te
-
F
b
,
⁢
⁢
F
cb
=
F
T
-
F
b
,
F
b
=
π
⁢
⁢
R
i
2
⁢
L
2
⁢
ρ
⁢
⁢
g
,
L
2
=
Δ
⁢
⁢
L
1
-
κ
2
.
(
5
)

448 more elements

A method of measuring an apparent viscosity of a sample of non-Newtonian fluid comprising:

(A) a step in which a plunger having an outer radius Ri is immersed into a sample contained in a cylindrical container having an inner radius R0, coaxially with the cylindrical container by an initial depth L0 and stopped thereat, the outer radius Ri of the plunger being smaller than the inner radius R0 of the cylindrical container;
(B) a step in which the plunger is further immersed into the sample coaxially with the cylindrical container at a first relative movement velocity vp1 by a first relative movement distance ΔL1, and during the further immersing operation and after the further immersing operation, a force applied to the plunger from the sample is measured with a passage of time;
(C) a step in which a first peak value FT1 and a first convergent value FTe1 of the force applied to the plunger from the sample are obtained, based on measured values of the force caused by the relative movement of the plunger at the first relative movement velocity vp1;
(D) a step in which the plunger is returned coaxially with the cylindrical container to the initial depth L0 and stopped thereat;
(E) a step in which the plunger is further immersed into the sample coaxially with the cylindrical container at a second relative movement velocity vp2 by a second relative movement distance ΔL2, and during the further immersing operation and after the further immersing operation, a force applied to the plunger from the sample is measured with a passage of time;
(F) a step in which a second peak value FT2 and a second convergent value FTe2 of the force applied to the plunger from the sample are obtained, based on measured values of the force caused by the relative movement of the plunger at the second relative movement velocity vp2;
(G) a step in which, based on a predetermined relationship established among:
the first relative movement distance ΔL1, the first peak value FT1 and the first convergent value FTe1, at the first relative movement velocity vp1;
the second relative movement distance ΔL2, the second peak value FT2 and the second convergent value FTe2, at the second relative movement velocity vp2;
a plunger ratio κ=Ri/R0;
and a flow behavior index n of the sample;
the flow behavior index n is obtained;
(H) a step in which the plunger is returned coaxially with the cylindrical container to the initial depth L0 and stopped thereat;
(I) a step in which the plunger is further immersed into the sample coaxially with the cylindrical container at a third relative movement velocity vp3 by a third relative movement distance ΔL3, and during the further immersing operation and after the further immersing operation, a force applied to the plunger from the sample is measured with a passage of time;
(J) a step in which a third peak value FT3 and a third convergent value FTe3 of the force applied to the plunger from the sample are obtained, based on measured values of the force caused by the relative movement of the plunger at the third relative movement velocity vp3;
(K) a step in which, when the third relative movement velocity vp3 is represented as vp, the third relative movement distance ΔL3 is represented as ΔL, the third peak value FT3 is represented as FT and the third convergent value FTe3 is represented as FTe, an apparent viscosity μa of the sample is calculated based on the vp, the ΔL, the FT and the FTe, the plunger ratio κ, the flow behavior index n, a density ρ of the sample, a gravitational acceleration g, and the following Expression (1):
⁢
[
NO
⁢
⁢
4
]
⁢
μ
a
=
σ
w
dy
/
dt
=
σ
0
+
K
⁡
(
dy
dt
)
n
dy
/
dt
⁢
⁢
⁢
in
⁢
⁢
which
⁢
⁢
⁢
σ
w
=
T
w
⁢
PR
0
2
,
dy
dt
=
(
λ
2
κ
-
κ
-
T
0
)
s
⁢
(
PR
0
2
⁢
K
)
s
,
⁢
⁢
K
=
PR
0
2
⁢
(
Φ
⁢
⁢
R
0
v
p
⁢
κ
2
)
n
,
P
=
2
⁢
σ
y
T
0
⁢
R
0
,
T
w
=
λ
2
κ
-
κ
,
(
1
)
Φ
=
{
∫
κ
λ
-
⁢
(
λ
2
-
x
2
-
T
0
⁢
x
)
s
⁢
x
-
s
⁢
⁢
dx
-
∫
λ
+
1
⁢
(
x
2
-
λ
2
-
T
0
⁢
x
)
s
⁢
⁢
x
-
s
⁢
dx
}
⁢
κ
2
-
∫
κ
λ
-
⁢
(
λ
2
-
x
2
-
T
0
⁢
x
)
s
⁢
x
2
-
s
⁢
dx
+
⁢
∫
λ
+
1
⁢
(
x
2
-
λ
2
-
T
0
⁢
x
)
s
⁢
x
2
-
s
⁢
⁢
dx
⁢
(
2
)
0
=
∫
κ
λ
-
⁢
(
λ
2
-
x
2
-
T
0
⁢
x
)
s
⁢
x
-
s
⁢
⁢
dx
-
∫
λ
+
1
⁢
(
x
2
-
λ
2
-
T
0
⁢
x
)
s
⁢
x
-
s
⁢
⁢
dx
,
⁢
⁢
s
=
1
n
,
(
3
)
⁢
λ
-
=
1
2
⁡
[
(
T
0
2
+
4
⁢
λ
2
)
1
2
-
T
0
]
,
(
4
)
⁢
λ
+
=
1
2
⁡
[
(
T
0
2
+
4
⁢
λ
2
)
1
2
+
T
0
]
,
⁢
⁢
T
0
=
F
y
F
cb
,
σ
y
=
F
y
2
⁢
π
⁢
⁢
R
i
⁡
(
L
0
+
L
2
)
,
F
y
=
F
Te
-
F
b
,
⁢
⁢
F
cb
=
F
T
-
F
b
,
F
b
=
π
⁢
⁢
R
i
2
⁢
L
2
⁢
ρ
⁢
⁢
g
,
L
2
=
Δ
⁢
⁢
L
1
-
κ
2
.
(
5
)

450 more elements

A viscosity measuring apparatus comprising:

a cylindrical container having a predetermined inner radius R0, in which a sample is contained;
a plunger having an outer radius Ri that is smaller than the inner radius R0 of the cylindrical container, the plunger being arranged inside the cylindrical container coaxially therewith so as to be relatively movable;
a driving unit configured to relatively move the plunger coaxially with the cylindrical container;
a measuring unit disposed on the plunger and configured to measure a force applied to the plunger from the sample;
and
a control unit configured to control the driving unit;
wherein:
the control unit is configured to control the driving unit such that the plunger is immersed into the sample contained in the cylindrical container coaxially with the cylindrical container by a predetermined initial depth L0 and stopped thereat, and that the plunger is then further immersed into the sample coaxially with the cylindrical container at a first relative movement velocity vp1 by a first relative movement distance ΔL1;
the measuring unit is configured to measure a force applied to the plunger from the sample with a passage of time, during the further immersing operation of the plunger at the first relative movement velocity vp1 and after the further immersing operation thereof;
the control unit is configured to obtain a first peak value FT1 and a first convergent value FTe1 of the force applied to the plunger from the sample, based on measured values of the force caused by the relative movement of the plunger at the first relative movement velocity vp1;
the control unit is further configured to control the driving unit such that the plunger is returned coaxially with the cylindrical container to the initial depth L0 and stopped thereat, and that the plunger is then further immersed into the sample coaxially with the cylindrical container at a second relative movement velocity vp2 by a second relative movement distance ΔL2;
the measuring unit is configured to measure a force applied to the plunger from the sample with a passage of time, during the further immersing operation of the plunger at the second relative movement velocity vp2 and after the further immersing operation thereof;
the control unit is configured to obtain a second peak value FT2 and a second convergent value FTe2 of the force applied to the plunger from the sample, based on measured values of the force caused by the relative movement of the plunger at the second relative movement velocity vp2;
the control unit is further configured to obtain, based on a predetermined relationship established among:
the first relative movement distance ΔL1, the first peak value FT1 and the first convergent value FTe1, at the first relative movement velocity vp1;
the second relative movement distance ΔL2, the second peak value FT2 and the second convergent value FTe2, at the second relative movement velocity vp2;
a plunger ratio is κ=Ri/R0;
and a flow behavior index n of the sample;
the flow behavior index n;
and
the control unit is further configured to calculate, when the first relative movement velocity vp1 is represented as vp, the first relative movement distance ΔL1 is represented as ΔL, the first peak value FT1 is represented as FT, and the first convergent value FTe1 is represented as FTe, or when the second relative movement velocity vp2 is represented as vp, the second relative movement distance ΔL2 is represented as ΔL, the second peak value FT2 is represented as FT, and the second convergent value FTe2 is represented as FTe, an apparent viscosity μa of the sample based on the vp, the ΔL, the FT, the FTe, the plunger ratio κ, the flow behavior index n, a density ρ of the sample, a gravitational acceleration g, and the following Expression (1):
⁢
[
NO
⁢
⁢
5
]
⁢
μ
a
=
σ
w
dy
/
dt
=
σ
0
+
K
⁡
(
dy
dt
)
n
dy
/
dt
⁢
⁢
⁢
in
⁢
⁢
which
⁢
⁢
⁢
σ
w
=
T
w
⁢
PR
0
2
,
dy
dt
=
(
λ
2
κ
-
κ
-
T
0
)
s
⁢
(
PR
0
2
⁢
K
)
s
,
⁢
⁢
K
=
PR
0
2
⁢
(
Φ
⁢
⁢
R
0
v
p
⁢
κ
2
)
n
,
P
=
2
⁢
σ
y
T
0
⁢
R
0
,
T
w
=
λ
2
κ
-
κ
,
(
1
)
Φ
=
{
∫
κ
λ
-
⁢
(
λ
2
-
x
2
-
T
0
⁢
x
)
s
⁢
x
-
s
⁢
⁢
dx
-
∫
λ
+
1
⁢
(
x
2
-
λ
2
-
T
0
⁢
x
)
s
⁢
⁢
x
-
s
⁢
dx
}
⁢
κ
2
-
∫
κ
λ
-
⁢
(
λ
2
-
x
2
-
T
0
⁢
x
)
s
⁢
x
2
-
s
⁢
dx
+
⁢
∫
λ
+
1
⁢
(
x
2
-
λ
2
-
T
0
⁢
x
)
s
⁢
x
2
-
s
⁢
⁢
dx
⁢
(
2
)
0
=
∫
κ
λ
-
⁢
(
λ
2
-
x
2
-
T
0
⁢
x
)
s
⁢
x
-
s
⁢
⁢
dx
-
∫
λ
+
1
⁢
(
x
2
-
λ
2
-
T
0
⁢
x
)
s
⁢
x
-
s
⁢
⁢
dx
,
⁢
⁢
s
=
1
n
,
(
3
)
⁢
λ
-
=
1
2
⁡
[
(
T
0
2
+
4
⁢
λ
2
)
1
2
-
T
0
]
,
(
4
)
⁢
λ
+
=
1
2
⁡
[
(
T
0
2
+
4
⁢
λ
2
)
1
2
+
T
0
]
,
⁢
⁢
T
0
=
F
y
F
cb
,
σ
y
=
F
y
2
⁢
π
⁢
⁢
R
i
⁡
(
L
0
+
L
2
)
,
F
y
=
F
Te
-
F
b
,
⁢
⁢
F
cb
=
F
T
-
F
b
,
F
b
=
π
⁢
⁢
R
i
2
⁢
L
2
⁢
ρ
⁢
⁢
g
,
L
2
=
Δ
⁢
⁢
L
1
-
κ
2
.
(
5
)

455 more elements

A viscosity measuring apparatus comprising:

a cylindrical container having a predetermined inner radius R0, in which a sample is contained;
a plunger having an outer radius Ri that is smaller than the inner radius R0 of the cylindrical container, the plunger being arranged inside the cylindrical container coaxially therewith so as to be relatively movable;
a driving unit configured to relatively move the plunger coaxially with the cylindrical container;
a measuring unit disposed on the plunger and configured to measure a force applied to the plunger from the sample;
and
a control unit configured to control the driving unit;
wherein:
the control unit is configured to control the driving unit such that the plunger is immersed into the sample contained in the cylindrical container coaxially with the cylindrical container by a predetermined initial depth L0 and stopped thereat, and that the plunger is then further immersed into the sample coaxially with the cylindrical container at a first relative movement velocity vp1 by a relative movement distance ΔL;
the measuring unit is configured to measure a force applied to the plunger from the sample with a passage of time, during the further immersing operation of the plunger at the first relative movement velocity vp1 and after the further immersing operation thereof;
the control unit is configured to obtain a first peak value FT1 and a first convergent value FTe1 of the force applied to the plunger from the sample, based on measured values of the force caused by the relative movement of the plunger at the first relative movement velocity vp1;
the control unit is further configured to control the driving unit such that the plunger is returned coaxially with the cylindrical container to the initial depth L0 and stopped thereat, and that the plunger is then further immersed into the sample coaxially with the cylindrical container at a second relative movement velocity vp2 by the relative movement distance ΔL;
the measuring unit is configured to measure a force applied to the plunger from the sample with a passage of time, during the further immersing operation of the plunger at the second relative movement velocity vp2 and after the further immersing operation thereof;
the control unit is configured to obtain a second peak value FT2 and a second convergent value FTe2 of the force applied to the plunger from the sample, based on measured values of the force caused by the relative movement of the plunger at the second relative movement velocity vp2;
the control unit is further configured to obtain, based on a predetermined relationship established among:
the first peak value FT1 and the first convergent value FTe1, at the first relative movement velocity vp1;
the second peak value FT2 and the second convergent value FTe2, at the second relative movement velocity vp2;
the relative movement distance ΔL;
a plunger ratio κ=Ri/R0;
and a flow behavior index n of the sample;
the flow behavior index n;
and
the control unit is further configured, when the first relative movement velocity vp1 is represented as vp, the first peak value FT1 is represented as FT, and the first convergent value FTe1 is represented as FTe, or when the second relative movement velocity vp2 is represented as vp, the second peak value FT2 is represented as FT, and the second convergent value FTe2 is represented as FTe, to calculate an apparent viscosity μa of the sample based on the vp, the FT, the FTe, the relative movement distance ΔL, the plunger ratio κ, the flow behavior index n, a density ρ of the sample, a gravitational acceleration g, and the following Expression (1):
⁢
[
NO
⁢
⁢
7
]
⁢
μ
a
=
σ
w
dy
/
dt
=
σ
0
+
K
⁡
(
dy
dt
)
n
dy
/
dt
⁢
⁢
⁢
in
⁢
⁢
which
⁢
⁢
⁢
σ
w
=
T
w
⁢
PR
0
2
,
dy
dt
=
(
λ
2
κ
-
κ
-
T
0
)
s
⁢
(
PR
0
2
⁢
K
)
s
,
⁢
⁢
K
=
PR
0
2
⁢
(
Φ
⁢
⁢
R
0
v
p
⁢
κ
2
)
n
,
P
=
2
⁢
σ
y
T
0
⁢
R
0
,
T
w
=
λ
2
κ
-
κ
,
(
1
)
Φ
=
{
∫
κ
λ
-
⁢
(
λ
2
-
x
2
-
T
0
⁢
x
)
s
⁢
x
-
s
⁢
⁢
dx
-
∫
λ
+
1
⁢
(
x
2
-
λ
2
-
T
0
⁢
x
)
s
⁢
⁢
x
-
s
⁢
dx
}
⁢
κ
2
-
∫
κ
λ
-
⁢
(
λ
2
-
x
2
-
T
0
⁢
x
)
s
⁢
x
2
-
s
⁢
dx
+
⁢
∫
λ
+
1
⁢
(
x
2
-
λ
2
-
T
0
⁢
x
)
s
⁢
x
2
-
s
⁢
⁢
dx
⁢
(
2
)
0
=
∫
κ
λ
-
⁢
(
λ
2
-
x
2
-
T
0
⁢
x
)
s
⁢
x
-
s
⁢
⁢
dx
-
∫
λ
+
1
⁢
(
x
2
-
λ
2
-
T
0
⁢
x
)
s
⁢
x
-
s
⁢
⁢
dx
,
⁢
⁢
s
=
1
n
,
(
3
)
⁢
λ
-
=
1
2
⁡
[
(
T
0
2
+
4
⁢
λ
2
)
1
2
-
T
0
]
,
(
4
)
⁢
λ
+
=
1
2
⁡
[
(
T
0
2
+
4
⁢
λ
2
)
1
2
+
T
0
]
,
⁢
⁢
T
0
=
F
y
F
cb
,
σ
y
=
F
y
2
⁢
π
⁢
⁢
R
i
⁡
(
L
0
+
L
2
)
,
F
y
=
F
Te
-
F
b
,
⁢
⁢
F
cb
=
F
T
-
F
b
,
F
b
=
π
⁢
⁢
R
i
2
⁢
L
2
⁢
ρ
⁢
⁢
g
,
L
2
=
Δ
⁢
⁢
L
1
-
κ
2
.
(
5
)

456 more elements

A viscosity measuring apparatus comprising:

a cylindrical container having a predetermined inner radius R0, in which a sample is contained;
a plunger having an outer radius Ri that is smaller than the inner radius R0 of the cylindrical container, the plunger being arranged inside the cylindrical container coaxially therewith so as to be relatively movable;
a driving unit configured to relatively move the plunger coaxially with the cylindrical container;
a measuring unit disposed on the plunger and configured to measure a force applied to the plunger from the sample;
and
a control unit configured to control the driving unit;
wherein:
the control unit is configured to control the driving unit such that the plunger is immersed into the sample contained in the cylindrical container coaxially with the cylindrical container by a predetermined initial depth L0 and stopped thereat, and that the plunger is then further immersed into the sample coaxially with the cylindrical container at a first relative movement velocity vp1 by a first relative movement distance ΔL1;
the measuring unit is configured to measure a force applied to the plunger from the sample with a passage of time, during the further immersing operation of the plunger at the first relative movement velocity vp1 and after the further immersing operation thereof;
the control unit is configured to obtain a first peak value FT1 and a first convergent value FTe1 of the force applied to the plunger from the sample, based on measured values of the force caused by the relative movement of the plunger at the first relative movement velocity vp1;
the control unit is further configured to control the driving unit such that the plunger is returned coaxially with the cylindrical container to the initial depth L0 and stopped thereat, and that the plunger is then further immersed into the sample coaxially with the cylindrical container at a second relative movement velocity vp2 by a second relative movement distance ΔL2;
the measuring unit is configured to measure a force applied to the plunger from the sample with a passage of time, during the further immersing operation of the plunger at the second relative movement velocity vp2 and after the further immersing operation thereof;
the control unit is configured to obtain a second peak value FT2 and a second convergent value FTe2 of the force applied to the plunger from the sample, based on measured values of the force caused by the relative movement of the plunger at the second relative movement velocity vp2;
the control unit is further configured to obtain, based on a predetermined relationship established among:
the first relative movement distance ΔL1, the first peak value FT1 and the first convergent value FTe1, at the first relative movement velocity vp1;
the second relative movement distance ΔL2, the second peak value FT2 and the second convergent value FTe2, at the second relative movement velocity vp2;
a plunger ratio κ=Ri/R0;
and a flow behavior index n of the sample;
the flow behavior index n;
the control unit is further configured to control the driving unit such that the plunger is returned coaxially with the cylindrical container to the initial depth L0 and stopped thereat, and that the plunger is then further immersed into the sample coaxially with the cylindrical container at a third relative movement velocity vp3 by a third relative movement distance ΔL3;
the measuring unit is configured to measure a force applied to the plunger from the sample with a passage of time, during the further immersing operation of the plunger at the third relative movement velocity vp3 and after the further immersing operation thereof;
the control unit is configured to obtain a third peak value FT3 and a third convergent value FTe3 of the force applied to the plunger from the sample, based on measured values of the force caused by the relative movement of the plunger at the third relative movement velocity vp3;
and
the control unit is further configured to calculate, when the third relative movement velocity vp3 is represented as vp, the third relative movement distance ΔL3 is represented as ΔL, the third peak value FT3 is represented as FT and the third convergent value FTe3 is represented as FTe, an apparent viscosity μa of the sample based on the vp, the ΔL, the FT and the FTe, the plunger ratio κ, the flow behavior index n, a density ρ of the sample, a gravitational acceleration g, and the following Expression (1):
⁢
[
NO
⁢
⁢
8
]
⁢
μ
a
=
σ
w
dy
/
dt
=
σ
0
+
K
⁡
(
dy
dt
)
n
dy
/
dt
⁢
⁢
⁢
in
⁢
⁢
which
⁢
⁢
⁢
σ
w
=
T
w
⁢
PR
0
2
,
dy
dt
=
(
λ
2
κ
-
κ
-
T
0
)
s
⁢
(
PR
0
2
⁢
K
)
s
,
⁢
⁢
K
=
PR
0
2
⁢
(
Φ
⁢
⁢
R
0
v
p
⁢
κ
2
)
n
,
P
=
2
⁢
σ
y
T
0
⁢
R
0
,
T
w
=
λ
2
κ
-
κ
,
(
1
)
Φ
=
{
∫
κ
λ
-
⁢
(
λ
2
-
x
2
-
T
0
⁢
x
)
s
⁢
x
-
s
⁢
⁢
dx
-
∫
λ
+
1
⁢
(
x
2
-
λ
2
-
T
0
⁢
x
)
s
⁢
⁢
x
-
s
⁢
dx
}
⁢
κ
2
-
∫
κ
λ
-
⁢
(
λ
2
-
x
2
-
T
0
⁢
x
)
s
⁢
x
2
-
s
⁢
dx
+
⁢
∫
λ
+
1
⁢
(
x
2
-
λ
2
-
T
0
⁢
x
)
s
⁢
x
2
-
s
⁢
⁢
dx
⁢
(
2
)
0
=
∫
κ
λ
-
⁢
(
λ
2
-
x
2
-
T
0
⁢
x
)
s
⁢
x
-
s
⁢
⁢
dx
-
∫
λ
+
1
⁢
(
x
2
-
λ
2
-
T
0
⁢
x
)
s
⁢
x
-
s
⁢
⁢
dx
,
⁢
⁢
s
=
1
n
,
(
3
)
⁢
λ
-
=
1
2
⁡
[
(
T
0
2
+
4
⁢
λ
2
)
1
2
-
T
0
]
,
(
4
)
⁢
λ
+
=
1
2
⁡
[
(
T
0
2
+
4
⁢
λ
2
)
1
2
+
T
0
]
,
⁢
⁢
T
0
=
F
y
F
cb
,
σ
y
=
F
y
2
⁢
π
⁢
⁢
R
i
⁡
(
L
0
+
L
2
)
,
F
y
=
F
Te
-
F
b
,
⁢
⁢
F
cb
=
F
T
-
F
b
,
F
b
=
π
⁢
⁢
R
i
2
⁢
L
2
⁢
ρ
⁢
⁢
g
,
L
2
=
Δ
⁢
⁢
L
1
-
κ
2
.
(
5
)

458 more elements

A control apparatus for controlling a viscosity measuring apparatus including:

a cylindrical container having a predetermined inner radius R0, in which a sample is contained;
a plunger having an outer radius Ri that is smaller than the inner radius R0 of the cylindrical container, the plunger being arranged inside the cylindrical container coaxially therewith so as to be relatively movable;
a driving unit configured to relatively move the plunger coaxially with the cylindrical container;
and
a measuring unit disposed on the plunger and configured to measure a force applied to the plunger from the sample;
wherein:
the control apparatus is configured to control the driving unit such that the plunger is immersed into the sample contained in the cylindrical container coaxially with the cylindrical container by a predetermined initial depth L0 and stopped thereat, and that the plunger is then further immersed into the sample coaxially with the cylindrical container at a first relative movement velocity vp1 by a first relative movement distance ΔL1;
the measuring unit is configured to measure a force applied to the plunger from the sample with a passage of time, during the further immersing operation of the plunger at the first relative movement velocity vp1 and after the further immersing operation thereof;
the control apparatus is configured to obtain a first peak value FT1 and a first convergent value FTe1 of the force applied to the plunger from the sample, based on measured values of the force caused by the relative movement of the plunger at the first relative movement velocity vp1;
the control apparatus is further configured to control the driving unit such that the plunger is returned coaxially with the cylindrical container to the initial depth L0 and stopped thereat, and that the plunger is then further immersed into the sample coaxially with the cylindrical container at a second relative movement velocity vp2 by a second relative movement distance ΔL2;
the measuring unit is configured to measure a force applied to the plunger from the sample with a passage of time, during the further immersing operation of the plunger at the second relative movement velocity vp2 and after the further immersing operation thereof;
the control apparatus is configured to obtain a second peak value FT2 and a second convergent value FTe2 of the force applied to the plunger from the sample, based on measured values of the force caused by the relative movement of the plunger at the second relative movement velocity vp2;
the control apparatus is further configured to obtain, based on a predetermined relationship established among:
the first relative movement distance ΔL1, the first peak value FT1 and the first convergent value FTe1, at the first relative movement velocity vp1;
the second relative movement distance ΔL2, the second peak value FT2 and the second convergent value FTe2, at the second relative movement velocity vp2;
a plunger ratio κ=Ri/R0;
and a flow behavior index n of the sample;
the flow behavior index n;
the control apparatus is further configured to calculate, when the first relative movement velocity vp1 is represented as vp, the first relative movement distance ΔL1 is represented as ΔL, the first peak value FT1 is represented as FT, and the first convergent value FTe1 is represented as FTe, or when the second relative movement velocity vp2 is represented as vp, the second relative movement distance ΔL2 is represented as ΔL, the second peak value FT2 is represented as FT, and the second convergent value FTe2 is represented as FTe, an apparent viscosity μa of the sample based on the vp, the ΔL, the FT, the FTe, the plunger ratio κ, the flow behavior index n, a density ρ of the sample, a gravitational acceleration g, and the following Expression (1):
⁢
[
NO
⁢
⁢
9
]
⁢
μ
a
=
σ
w
dy
/
dt
=
σ
0
+
K
⁡
(
dy
dt
)
n
dy
/
dt
⁢
⁢
⁢
in
⁢
⁢
which
⁢
⁢
⁢
σ
w
=
T
w
⁢
PR
0
2
,
dy
dt
=
(
λ
2
κ
-
κ
-
T
0
)
s
⁢
(
PR
0
2
⁢
K
)
s
,
⁢
⁢
K
=
PR
0
2
⁢
(
Φ
⁢
⁢
R
0
v
p
⁢
κ
2
)
n
,
P
=
2
⁢
σ
y
T
0
⁢
R
0
,
T
w
=
λ
2
κ
-
κ
,
(
1
)
Φ
=
{
∫
κ
λ
-
⁢
(
λ
2
-
x
2
-
T
0
⁢
x
)
s
⁢
x
-
s
⁢
⁢
dx
-
∫
λ
+
1
⁢
(
x
2
-
λ
2
-
T
0
⁢
x
)
s
⁢
⁢
x
-
s
⁢
dx
}
⁢
κ
2
-
∫
κ
λ
-
⁢
(
λ
2
-
x
2
-
T
0
⁢
x
)
s
⁢
x
2
-
s
⁢
dx
+
⁢
∫
λ
+
1
⁢
(
x
2
-
λ
2
-
T
0
⁢
x
)
s
⁢
x
2
-
s
⁢
⁢
dx
⁢
(
2
)
0
=
∫
κ
λ
-
⁢
(
λ
2
-
x
2
-
T
0
⁢
x
)
s
⁢
x
-
s
⁢
⁢
dx
-
∫
λ
+
1
⁢
(
x
2
-
λ
2
-
T
0
⁢
x
)
s
⁢
x
-
s
⁢
⁢
dx
,
⁢
⁢
s
=
1
n
,
(
3
)
⁢
λ
-
=
1
2
⁡
[
(
T
0
2
+
4
⁢
λ
2
)
1
2
-
T
0
]
,
(
4
)
⁢
λ
+
=
1
2
⁡
[
(
T
0
2
+
4
⁢
λ
2
)
1
2
+
T
0
]
,
⁢
⁢
T
0
=
F
y
F
cb
,
σ
y
=
F
y
2
⁢
π
⁢
⁢
R
i
⁡
(
L
0
+
L
2
)
,
F
y
=
F
Te
-
F
b
,
⁢
⁢
F
cb
=
F
T
-
F
b
,
F
b
=
π
⁢
⁢
R
i
2
⁢
L
2
⁢
ρ
⁢
⁢
g
,
L
2
=
Δ
⁢
⁢
L
1
-
κ
2
.
(
5
)

453 more elements

A control apparatus for controlling a viscosity measuring apparatus including:

a cylindrical container having a predetermined inner radius R0, in which a sample is contained;
a plunger having an outer radius Ri that is smaller than the inner radius R0 of the cylindrical container, the plunger being arranged inside the cylindrical container coaxially therewith so as to be relatively movable;
a driving unit configured to relatively move the plunger coaxially with the cylindrical container;
and
a measuring unit disposed on the plunger and configured to measure a force applied to the plunger from the sample;
wherein:
the control apparatus is configured to control the driving unit such that the plunger is immersed into the sample contained in the cylindrical container coaxially with the cylindrical container by a predetermined initial depth L0 and stopped thereat, and that the plunger is then further immersed into the sample coaxially with the cylindrical container at a first relative movement velocity vp1 by a relative movement distance ΔL;
the measuring unit is configured to measure a force applied to the plunger from the sample with a passage of time, during the further immersing operation of the plunger at the first relative movement velocity vp1 and after the further immersing operation thereof;
the control apparatus is configured to obtain a first peak value FT1 and a first convergent value FTe1 of the force applied to the plunger from the sample, based on measured values of the force caused by the relative movement of the plunger at the first relative movement velocity vp1;
the control apparatus is further configured to control the driving unit such that the plunger is returned coaxially with the cylindrical container to the initial depth L0 and stopped thereat, and that the plunger is then further immersed into the sample coaxially with the cylindrical container at a second relative movement velocity vp2 by the relative movement distance ΔL;
the measuring unit is configured to measure a force applied to the plunger from the sample with a passage of time, during the further immersing operation of the plunger at the second relative movement velocity vp2 and after the further immersing operation thereof;
the control apparatus is configured to obtain a second peak value FT2 and a second convergent value FTe2 of the force applied to the plunger from the sample, based on measured values of the force caused by the relative movement of the plunger at the second relative movement velocity vp2;
the control apparatus is further configured to obtain, based on a predetermined relationship established among:
the first peak value FT1 and the first convergent value FTe1, at the first relative movement velocity vp1;
the second peak value FT2 and the second convergent value FTe2, at the second relative movement velocity vp2;
the relative movement distance ΔL;
a plunger ratio κ=Ri/R0;
and a flow behavior index n of the sample;
the flow behavior index n;
and
the control apparatus is further configured to calculate, when the first relative movement velocity vp1 is represented as vp, the first peak value FT1 is represented as FT, and the first convergent value FTe1 is represented as FTe, or when the second relative movement velocity vp2 is represented as vp, the second peak value FT2 is represented as FT, and the second convergent value FTe2 is represented as FTe, an apparent viscosity μa of the sample based on the vp, the FT, the FTe, the relative movement distance ΔL, the plunger ratio κ, the flow behavior index n, a density ρ of the sample, a gravitational acceleration g, and the following Expression (1):
⁢
[
NO
⁢
⁢
11
]
⁢
μ
a
=
σ
w
dy
/
dt
=
σ
0
+
K
⁡
(
dy
dt
)
n
dy
/
dt
⁢
⁢
⁢
in
⁢
⁢
which
⁢
⁢
⁢
σ
w
=
T
w
⁢
PR
0
2
,
dy
dt
=
(
λ
2
κ
-
κ
-
T
0
)
s
⁢
(
PR
0
2
⁢
K
)
s
,
⁢
⁢
K
=
PR
0
2
⁢
(
Φ
⁢
⁢
R
0
v
p
⁢
κ
2
)
n
,
P
=
2
⁢
σ
y
T
0
⁢
R
0
,
T
w
=
λ
2
κ
-
κ
,
(
1
)
Φ
=
{
∫
κ
λ
-
⁢
(
λ
2
-
x
2
-
T
0
⁢
x
)
s
⁢
x
-
s
⁢
⁢
dx
-
∫
λ
+
1
⁢
(
x
2
-
λ
2
-
T
0
⁢
x
)
s
⁢
⁢
x
-
s
⁢
dx
}
⁢
κ
2
-
∫
κ
λ
-
⁢
(
λ
2
-
x
2
-
T
0
⁢
x
)
s
⁢
x
2
-
s
⁢
dx
+
⁢
∫
λ
+
1
⁢
(
x
2
-
λ
2
-
T
0
⁢
x
)
s
⁢
x
2
-
s
⁢
⁢
dx
⁢
(
2
)
0
=
∫
κ
λ
-
⁢
(
λ
2
-
x
2
-
T
0
⁢
x
)
s
⁢
x
-
s
⁢
⁢
dx
-
∫
λ
+
1
⁢
(
x
2
-
λ
2
-
T
0
⁢
x
)
s
⁢
x
-
s
⁢
⁢
dx
,
⁢
⁢
s
=
1
n
,
(
3
)
⁢
λ
-
=
1
2
⁡
[
(
T
0
2
+
4
⁢
λ
2
)
1
2
-
T
0
]
,
(
4
)
⁢
λ
+
=
1
2
⁡
[
(
T
0
2
+
4
⁢
λ
2
)
1
2
+
T
0
]
,
⁢
⁢
T
0
=
F
y
F
cb
,
σ
y
=
F
y
2
⁢
π
⁢
⁢
R
i
⁡
(
L
0
+
L
2
)
,
F
y
=
F
Te
-
F
b
,
⁢
⁢
F
cb
=
F
T
-
F
b
,
F
b
=
π
⁢
⁢
R
i
2
⁢
L
2
⁢
ρ
⁢
⁢
g
,
L
2
=
Δ
⁢
⁢
L
1
-
κ
2
.
(
5
)

455 more elements

A control apparatus for controlling a viscosity measuring apparatus including:

a cylindrical container having a predetermined inner radius R0, in which a sample is contained;
a plunger having an outer radius Ri that is smaller than the inner radius R0 of the cylindrical container, the plunger being arranged inside the cylindrical container coaxially therewith so as to be relatively movable;
a driving unit configured to relatively move the plunger coaxially with the cylindrical container;
and
a measuring unit disposed on the plunger and configured to measure a force applied to the plunger from the sample;
wherein:
the control apparatus is configured to control the driving unit such that the plunger is immersed into the sample contained in the cylindrical container coaxially with the cylindrical container by a predetermined initial depth L0 and stopped thereat, and that the plunger is then further immersed into the sample coaxially with the cylindrical container at a first relative movement velocity vp1 by a first relative movement distance ΔL1;
the measuring unit is configured to measure a force applied to the plunger from the sample with a passage of time, during the further immersing operation of the plunger at the first relative movement velocity vp1 and after the further immersing operation thereof;
the control apparatus is configured to obtain a first peak value FT1 and a first convergent value FTe1 of the force applied to the plunger from the sample, based on measured values of the force caused by the relative movement of the plunger at the first relative movement velocity vp1;
the control apparatus is further configured to control the driving unit such that the plunger is returned coaxially with the cylindrical container to the initial depth L0 and stopped thereat, and that the plunger is then further immersed into the sample coaxially with the cylindrical container at a second relative movement velocity vp2 by a second relative movement distance ΔL2;
the measuring unit is configured to measure a force applied to the plunger from the sample with a passage of time, during the further immersing operation of the plunger at the second relative movement velocity vp2 and after the further immersing operation thereof;
the control apparatus is configured to obtain a second peak value FT2 and a second convergent value FTe2 of the force applied to the plunger from the sample, based on measured values of the force caused by the relative movement of the plunger at the second relative movement velocity vp2;
the control apparatus is further configured to obtain, based on a predetermined relationship established among:
the first relative movement distance ΔL1, the first peak value FT1 and the first convergent value FTe1, at the first relative movement velocity vp1;
the second relative movement distance ΔL2, the second peak value FT2 and the second convergent value FTe2, at the second relative movement velocity vp2;
a plunger ratio κ=Ri/R0;
and a flow behavior index n of the sample;
the flow behavior index n;
the control apparatus is further configured to control the driving unit such that the plunger is returned coaxially with the cylindrical container to the initial depth L0 and stopped thereat, and that the plunger is then further immersed into the sample coaxially with the cylindrical container at a third relative movement velocity vp3 by a third relative movement distance ΔL3;
the measuring unit is configured to measure a force applied to the plunger from the sample with a passage of time, during the further immersing operation of the plunger at the third relative movement velocity vp3 and after the further immersing operation thereof;
the control apparatus is configured to obtain a third peak value FT3 and a third convergent value FTe3 of the force applied to the plunger from the sample, based on measured values of the force caused by the relative movement of the plunger at the third relative movement velocity vp3;
and
the control apparatus is further configured to calculate, when the third relative movement velocity vp3 is represented as vp, the third relative movement distance ΔL3 is represented as ΔL, the third peak value FT3 is represented as FT and the third convergent value FTe3 is represented as FTe, an apparent viscosity μa of the sample based on the vp, the ΔL, the FT and the FTe, the plunger ratio κ, the flow behavior index n, a density ρ of the sample, a gravitational acceleration g, and the following Expression (1):
⁢
[
NO
⁢
⁢
12
]
⁢
μ
a
=
σ
w
dy
/
dt
=
σ
0
+
K
⁡
(
dy
dt
)
n
dy
/
dt
⁢
⁢
⁢
in
⁢
⁢
which
⁢
⁢
⁢
σ
w
=
T
w
⁢
PR
0
2
,
dy
dt
=
(
λ
2
κ
-
κ
-
T
0
)
s
⁢
(
PR
0
2
⁢
K
)
s
,
⁢
⁢
K
=
PR
0
2
⁢
(
Φ
⁢
⁢
R
0
v
p
⁢
κ
2
)
n
,
P
=
2
⁢
σ
y
T
0
⁢
R
0
,
T
w
=
λ
2
κ
-
κ
,
(
1
)
Φ
=
{
∫
κ
λ
-
⁢
(
λ
2
-
x
2
-
T
0
⁢
x
)
s
⁢
x
-
s
⁢
⁢
dx
-
∫
λ
+
1
⁢
(
x
2
-
λ
2
-
T
0
⁢
x
)
s
⁢
⁢
x
-
s
⁢
dx
}
⁢
κ
2
-
∫
κ
λ
-
⁢
(
λ
2
-
x
2
-
T
0
⁢
x
)
s
⁢
x
2
-
s
⁢
dx
+
⁢
∫
λ
+
1
⁢
(
x
2
-
λ
2
-
T
0
⁢
x
)
s
⁢
x
2
-
s
⁢
⁢
dx
⁢
(
2
)
0
=
∫
κ
λ
-
⁢
(
λ
2
-
x
2
-
T
0
⁢
x
)
s
⁢
x
-
s
⁢
⁢
dx
-
∫
λ
+
1
⁢
(
x
2
-
λ
2
-
T
0
⁢
x
)
s
⁢
x
-
s
⁢
⁢
dx
,
⁢
⁢
s
=
1
n
,
(
3
)
⁢
λ
-
=
1
2
⁡
[
(
T
0
2
+
4
⁢
λ
2
)
1
2
-
T
0
]
,
(
4
)
⁢
λ
+
=
1
2
⁡
[
(
T
0
2
+
4
⁢
λ
2
)
1
2
+
T
0
]
,
⁢
⁢
T
0
=
F
y
F
cb
,
σ
y
=
F
y
2
⁢
π
⁢
⁢
R
i
⁡
(
L
0
+
L
2
)
,
F
y
=
F
Te
-
F
b
,
⁢
⁢
F
cb
=
F
T
-
F
b
,
F
b
=
π
⁢
⁢
R
i
2
⁢
L
2
⁢
ρ
⁢
⁢
g
,
L
2
=
Δ
⁢
⁢
L
1
-
κ
2
.
(
5
)

457 more elements

Viscosity measuring method and viscosity measuring apparatus

Life of this patent

Viscosity measuring method and viscosity measuring apparatus

Life of this patent

Abstract

Claims21