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A highly elastic constant-viscosity fluid
a7
Journal of Non-Newtonian Fluid Mechanics, 3 (1977/1978) 87-91 0 Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands
Short Communication A HIGHLY ELASTIC CONSTANT-VISCOSITY
FLUID
D.V. BOGER * Department (U.S.A.)
of Chemical Engineering,
University of Delaware, Newark, Delaware 19 711
(Received December 1, 1976)
Introduction A considerable gap exists between those who use constitutive equations for non-Newtoni~ fluids with the general flow equations in an attempt to solve realistic boundary value problems and those who are concerned with the experimental observation of the kinematics of these flows. One of the reasons for this gap is that when the constitutive equation is simple enough for solution of the boundary value problem, no material of ideal enough properties is available for experimental verification of the predicted kinematics. Another problem is that most of the experimental work done on the kinematics of non-viscometric flows has been carried out with shear thinning polymer solutions, where a high Reynolds number flow (Re > 1) usually must be used to generate significant elasticity in the flow field. In this class of experiment it has been difficult to differentiate between shear-thinning, elastic, and inertial effects. An ideal fluid from the viewpoint of the expe~men~ist is a constantviscosity fluid which is higly viscous and highly elastic at room temperature and at the same time is optically clear. With such a material the experimentalist could record the kinematics of important flows in the absence of inertia and shear thinning effects and clearly distinguish the influence of elasticity, while the theoretician could compare his solution to the experimental results and thereby check the validity of his constitutive assumptions. In this way a forward step could be made in the logical development of constitutive equations and in their use in the solution of realistic boundary value problems. * On leave from the Department of Chemical Engineering, Monash University, Clayton, Victoria, 3168, Australia.
88
The purpose of this paper is to present the fundamental flow properties of an optically clear, highly viscous and highly elastic fluid which exhibits a nearly constant viscosity and which can be processed at room temperature. Results and discussion Figure 1 shows the shear stress as a function of shear rate for a maltose syrup obtained from Fielders Starches, Melbourne, which is specified as a high maltose 43”Baume syrup. The syrup shown in Fig. 1 had a small amount of water added. Maltose syrups (or corn syrups) are slightly yellow in color, yet are optically clear and are obtainable in a wide range of viscosities. The results in the low shear rate range in Fig. 1 were obtained with an R16 Weissenberg rheogoniometer while those at the higher shear rates were obtained with a capillary rheometer with long (L/D = 374) and short (LID = 4,25, 100) capillary tubes. No end correction was necessary for L/l3 =
Fluid:
Maltose
Syrup
Temp: 209 C
IO2 IO'
IO' Shear
&
Weissenberg
l
Corrected Capillary for L#=4,25,100
Data
0
Capillary
LID-374
IU’
Rate
Data
Dato
for
IV
isec-‘1
Fig. 1. Shear stress versus shear rate for a maltose syrup as measured with a rheogoniometer and a capillary rheometer.
89
374 while the Bagley method [l J was used to correct for end effects in the shorter tubes. Measurements were made on a fresh sample and a previously sheared sample to demonstrate the absence of shear degradation. There is clear overlap and excellent agreement between the rheogon~ometer and tbe capillary data. The slope of the line through the data points is very close to one (n = 0.99). Therefore, the maltose syrup with some additional water is Ne~oni~ with a viscosity of 13,200 cp for a shear rate up to 4500 s-‘. Similarly, the maltose syrup without any water exhibited a viscosity of 22,000 cp. No normal stresses were observed for either fhaid with the rheogoniomet~r. The flow properties of the maltose syrup are drasticslffy changed by the addition of a very small amount af polya~~l~~de (Separan MG 500, Dow Chemical Company). The shear stress and the first normal stress difference measured with the rheogoniometer for a 0.08% Separan-maltose syrup SO~Ution are shown in Fig. 2. A very slight amount of shear thinning is introduced (n = 0.94). A viscosity variation of 12% from a mean value of 22,500 cp is observed for sheax rates less than 14 s-l.
Fluid:
Shear
Rute
0.08%
(se63
Separon
MG500
Maltose
Syrup
in
90
The results in Fig. 2 clearly show that this very viscous solutions has a nearly constant viscosity and at the same time it is highly elastic. For instance, at shear rates of 1 and 10 s-’ the stress ratio P,, - P22/r12 is 8.5 and 25.5, respectively, while at 1 s-i the Maxwell relaxation time P, t - Pz2/ 2~~~7 is 4.25 s. The syrup solution has rheological properties approaching those of a polymer melt, but marked shear thinning is absent and the material can be processed at room temperature. Notice also that the first normal stress difference becomes quadratic at the lower shear rates. In order to examine the extent of the shear rate range in which the viscosity remains essentially constant, additional data, shown in Fig. 3, were obtained with the capillary rheometer. Again no significant shear degradation was observed when a fresh and a previously sheared sample was used. It was not possible to overlap the shear rate range of the rheogoniometer and the capillary rheometer, but the two sets of data shown in Fig. 3 are colinear. Therefore, the solution has a nearly constant viscosity for shear rates up to 1050 s-‘.
Fluid:
0.08%
Temp:
20°
A
Weissenberg
a
Corrected
IORate
MG500
Maltose
Syrup
in
C Data
Capillary Doto for
Sheor
Separon
LID = 4,25,50.75.
IOI
(see-‘1
3. Shear stress versus shear rate for a solution of 0.08% poIyaerylamide in maftose syrup as measured with a capillary rheometer. Fig.
91
Clearly the maltose syrup-Separan solution is an optically clear, highly viscous and highly elastic fluid which exhibits a nearly constant viscosity and which can be processed at room temperature. Acknowledgment Our experimental work on the flow of non-Newtonian fluids is supported by the Australian Research Grants Commission. References 1 E.B. Bagley, J. Appl. Phys., 28 (1957)
624.
Journal of Non-Newtonian Fluid Mechanics, 3 (1977/1978) 87-91 0 Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands
Short Communication A HIGHLY ELASTIC CONSTANT-VISCOSITY
FLUID
D.V. BOGER * Department (U.S.A.)
of Chemical Engineering,
University of Delaware, Newark, Delaware 19 711
(Received December 1, 1976)
Introduction A considerable gap exists between those who use constitutive equations for non-Newtoni~ fluids with the general flow equations in an attempt to solve realistic boundary value problems and those who are concerned with the experimental observation of the kinematics of these flows. One of the reasons for this gap is that when the constitutive equation is simple enough for solution of the boundary value problem, no material of ideal enough properties is available for experimental verification of the predicted kinematics. Another problem is that most of the experimental work done on the kinematics of non-viscometric flows has been carried out with shear thinning polymer solutions, where a high Reynolds number flow (Re > 1) usually must be used to generate significant elasticity in the flow field. In this class of experiment it has been difficult to differentiate between shear-thinning, elastic, and inertial effects. An ideal fluid from the viewpoint of the expe~men~ist is a constantviscosity fluid which is higly viscous and highly elastic at room temperature and at the same time is optically clear. With such a material the experimentalist could record the kinematics of important flows in the absence of inertia and shear thinning effects and clearly distinguish the influence of elasticity, while the theoretician could compare his solution to the experimental results and thereby check the validity of his constitutive assumptions. In this way a forward step could be made in the logical development of constitutive equations and in their use in the solution of realistic boundary value problems. * On leave from the Department of Chemical Engineering, Monash University, Clayton, Victoria, 3168, Australia.
88
The purpose of this paper is to present the fundamental flow properties of an optically clear, highly viscous and highly elastic fluid which exhibits a nearly constant viscosity and which can be processed at room temperature. Results and discussion Figure 1 shows the shear stress as a function of shear rate for a maltose syrup obtained from Fielders Starches, Melbourne, which is specified as a high maltose 43”Baume syrup. The syrup shown in Fig. 1 had a small amount of water added. Maltose syrups (or corn syrups) are slightly yellow in color, yet are optically clear and are obtainable in a wide range of viscosities. The results in the low shear rate range in Fig. 1 were obtained with an R16 Weissenberg rheogoniometer while those at the higher shear rates were obtained with a capillary rheometer with long (L/D = 374) and short (LID = 4,25, 100) capillary tubes. No end correction was necessary for L/l3 =
Fluid:
Maltose
Syrup
Temp: 209 C
IO2 IO'
IO' Shear
&
Weissenberg
l
Corrected Capillary for L#=4,25,100
Data
0
Capillary
LID-374
IU’
Rate
Data
Dato
for
IV
isec-‘1
Fig. 1. Shear stress versus shear rate for a maltose syrup as measured with a rheogoniometer and a capillary rheometer.
89
374 while the Bagley method [l J was used to correct for end effects in the shorter tubes. Measurements were made on a fresh sample and a previously sheared sample to demonstrate the absence of shear degradation. There is clear overlap and excellent agreement between the rheogon~ometer and tbe capillary data. The slope of the line through the data points is very close to one (n = 0.99). Therefore, the maltose syrup with some additional water is Ne~oni~ with a viscosity of 13,200 cp for a shear rate up to 4500 s-‘. Similarly, the maltose syrup without any water exhibited a viscosity of 22,000 cp. No normal stresses were observed for either fhaid with the rheogoniomet~r. The flow properties of the maltose syrup are drasticslffy changed by the addition of a very small amount af polya~~l~~de (Separan MG 500, Dow Chemical Company). The shear stress and the first normal stress difference measured with the rheogoniometer for a 0.08% Separan-maltose syrup SO~Ution are shown in Fig. 2. A very slight amount of shear thinning is introduced (n = 0.94). A viscosity variation of 12% from a mean value of 22,500 cp is observed for sheax rates less than 14 s-l.
Fluid:
Shear
Rute
0.08%
(se63
Separon
MG500
Maltose
Syrup
in
90
The results in Fig. 2 clearly show that this very viscous solutions has a nearly constant viscosity and at the same time it is highly elastic. For instance, at shear rates of 1 and 10 s-’ the stress ratio P,, - P22/r12 is 8.5 and 25.5, respectively, while at 1 s-i the Maxwell relaxation time P, t - Pz2/ 2~~~7 is 4.25 s. The syrup solution has rheological properties approaching those of a polymer melt, but marked shear thinning is absent and the material can be processed at room temperature. Notice also that the first normal stress difference becomes quadratic at the lower shear rates. In order to examine the extent of the shear rate range in which the viscosity remains essentially constant, additional data, shown in Fig. 3, were obtained with the capillary rheometer. Again no significant shear degradation was observed when a fresh and a previously sheared sample was used. It was not possible to overlap the shear rate range of the rheogoniometer and the capillary rheometer, but the two sets of data shown in Fig. 3 are colinear. Therefore, the solution has a nearly constant viscosity for shear rates up to 1050 s-‘.
Fluid:
0.08%
Temp:
20°
A
Weissenberg
a
Corrected
IORate
MG500
Maltose
Syrup
in
C Data
Capillary Doto for
Sheor
Separon
LID = 4,25,50.75.
IOI
(see-‘1
3. Shear stress versus shear rate for a solution of 0.08% poIyaerylamide in maftose syrup as measured with a capillary rheometer. Fig.
91
Clearly the maltose syrup-Separan solution is an optically clear, highly viscous and highly elastic fluid which exhibits a nearly constant viscosity and which can be processed at room temperature. Acknowledgment Our experimental work on the flow of non-Newtonian fluids is supported by the Australian Research Grants Commission. References 1 E.B. Bagley, J. Appl. Phys., 28 (1957)
624.