Measuring and testing – Liquid analysis or analysis of the suspension of solids in a... – Viscosity
Reexamination Certificate
1999-10-19
2002-05-14
Williams, Hezron (Department: 2856)
Measuring and testing
Liquid analysis or analysis of the suspension of solids in a...
Viscosity
C073S054060, C073S054110
Reexamination Certificate
active
06386016
ABSTRACT:
This application claims Paris Convention priority of DE 198 48 687.1 filed Oct. 22, 1998 the complete disclosure of which is hereby incorporated by reference.
BACKGROUND OF THE INVENTION
Conventional continuous or discontinuous measuring capillary viscometers or rheometers determine the pressure difference between the input and the output of a measuring capillary having constant cross section through which a measuring liquid flows. The volume flow and the pressure differences can be used in conjunction with the dimensions of the capillary to determine a characteristic flow quantity (the “viscosity”) for the liquid. The constant cross section of the capillary leads to pure shear flow and this “viscosity” is the shear viscosity &eegr;,
&eegr;=&tgr;/{dot over (&ggr;)} (1)
where &tgr; is the shear stress and {dot over (&ggr;)} the shear velocity. For Newtonian liquids whose shear viscosity is independent of the shear velocity, &eegr; can be directly calculated from these measurements using conventional equations (Hagen-Poiseuille law).
A plurality of technical liquids (materials which occur in the liquid state during manufacturing processes) are non-Newtonian liquids whose viscosity depends on the shear velocity (for a given capillary dimension of volume flow). Principal examples therefor are primarily polymer melts and polymer solutions. In order to describe their flow behavior, viscosity functions or other flow functions, e.g. the shear-stress function, are required. The shear-stress function describes the shear stress in dependence on the shear velocity &tgr;=f(&ggr;). In a capillary rheometer of constant capillary cross section, only “apparent” viscosity values can be determined for these liquids, at constant volume flow, i.e. the Newtonian flow equation is utilized for the calculation.
In order to determined a flow function or parts of a flow function for process monitoring purposes, capillary rheometers have been used in recent times having wedge shaped or conical capillaries (see for example laid open publication DE-A-42 36 407, U.S. Pat. No. 4624 132 and A. Papendinskas, W. R. Cluett, S. T. Balke in Polymer Engineering and Science Mid-March 1991, Vol. 31. No. 5, pages 365-375). Capillary rheometers of this kind are equipped with pressure measuring probes to measure the pressure drop across parts of the capillary. Using e.g. a wedge-shaped capillary equipped with at least three pressure measuring locations, the actual non-Newtonian viscosity, for the shear velocity within the capillary, can be determined for constant operating conditions (e.g. {dot over (V)}=a constant or &Dgr;p=a constant). If, within the range of shear velocities occurring between the input and output of such a capillary, the flow function can be described using a simple flow law such as that given by Ostwald and de Waele (also referred to as the potential law) in accordance with equation (2) or (3) below, then the flow law is also known for these capillaries.
&tgr;({dot over (&ggr;)})=K{dot over (&ggr;)}
n
(2)
&eegr;({dot over (&ggr;)})=K{dot over (&ggr;)}
n−1
=K{dot over (&ggr;)}
m
(3)
Such rheometers are utilized for on-line processing and quality control and, when operated at constant pressure differentials, can even directly provide quantitative information concerning the average molecular weight and the molecular weight distribution (DE-A-42 36 407).
Capillary rheometers having such narrowing or widening capillaries do not however produce pure shear flow so that the result does not lead to a pure shear viscosity in all cases. In such capillaries, the shear flow is overlapped with an additional extensional flow (extension of an extrusion liquid in consequence of the cross section narrowing) and the overall flow resistance is a combination of shear and extensional components. Analogous to the shear resistance which results from the shear viscosity &eegr; and the shear velocity {dot over (&ggr;)}, the extensional resistance is caused by the extensional viscosity &eegr;
E
and the extensional velocity {overscore (&egr;)}. The extensional resistance results from the tensile stress &sgr; produced in the flow. The extensional viscosity
&eegr;E=&sgr;/{dot over (&egr;)} (4)
is also designated Trouton-viscosity &eegr;T and, for Newtonian liquids, is three times larger than the shear viscosity.
&eegr;T=3&eegr; (5)
In non-Newtonian liquids, in particular in plastic melts, this simple relationship as formulated in equation (5) is not satisfied. On the contrary, the ratio between &eegr;
E
and &eegr; is often substantially more than three. In some fluids, &eegr;
E
is even an order of magnitude larger than &eegr;. The extent to which &eegr;
E
exceeds &eegr; depends on the molecular properties and/or the molecular weight distribution of the plastic melt. In general, &eegr;
E
does not depend on &eegr; and is only coupled to &eegr; via molecular or structural properties. The extensional viscosity of high molecular liquids is particular sensitive to very small fractions of large molecules and on the degree of branching of the macro-molecules (K. K. Chao et al. AIChE J. 30 (1984), page 111 ff; J. Ferguson, M.K.H El-Tawashi Proc. VIII Int. Congr. on Rheol. Vol. II, page 235 ff). However, the degree of branching changes the viscosity function only to a limited extent and can therefore not be determined using the shear viscosity. If shear viscosity or shear viscosity functions can be measured in a particular process, information is thereby available concerning the average value and width of the molecular weight distribution of the liquid. If, in addition and independently thereof, the extensional viscosity can be determined, changes in the range of very large molecules and changes in the degree of branching can be detected with high sensitivity. An independent material quantity is therefore available which is definitive for specific liquid and product properties to better describe the quality of a product in a comprehensive and directed fashion.
It is the underlying purpose of the invention to create a method and a device with which the shear viscosity (e.g. in the range of 10 mPas≦&eegr;≦10
5
Pas) and the extensional viscosity (e.g. in the range 30 mPas≦&eegr;
E
≦10
8
Pas) can be simultaneously determined on the same sample.
A method and apparatus with which the problem in accordance with the invention is solved is characterized in the patent claims.
SUMMARY OF THE INVENTION
Using a capillary having changing cross section and with a plurality of pressure measuring locations, the viscosity function of a liquid can be determined within a well defined shear velocity range under constant operating conditions (constant volume flow or pressure drop) (Papendinskas et al., DE-A-42 36 407). Although such capillaries do not have pure shear flow, the capillaries can be configured in such a fashion, e.g. having large length, that the influence of the extensional properties on the pressure drop is smaller than that of the shear properties by many orders of magnitude so that it can, in practice, be neglected. For a capillary of this type, the flow function is defined for the shear velocity range occurring between the input and the output.
The average extensional velocity {overscore ({dot over (&egr;)})} can be extracted from the difference between the average input and output velocities {overscore (V)}
A
−{overscore (V)}
E
, divided by the capillary length &Dgr;L (Equation (6)):
ϵ
.
_
=
v
_
A
-
v
_
E
Δ
L
=
V
.
/
F
A
-
V
.
/
F
E
Δ
L
(
6
)
The shear velocity {dot over (&ggr;)}
E
and {dot over (&ggr;)}
A
at the input and output are directly proportional to their average velocities {overscore (V)}
E
and {overscore (V)}
A
at the locations E and A, for constant cross section. A simple shortening of a wedge-shaped or conical capillary with otherwise constant input (F
E
) and output (F
A
) cross sections results, in accordance w
Thermo Haake GmbH
Vincent Paul
Wiggins David J.
Williams Hezron
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