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Orifice Flowmeter for Measuring Extensional Rheological Properties

Profile image of Edmundo Brito-de la FuenteEdmundo Brito-de la Fuente

2008, Canadian Journal of Chemical Engineering

https://doi.org/10.1002/CJCE.5450800621
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Abstract

Extensional rheological properties play an important role in processes in which the fluid is subjected to highly decelerated or accelerated flows. This paper describes an orifice flowmeter used to measure extensional properties of rheologically complex fluids at high strain rates. The operating principle of the flowmeter is based on the pressure drop due to the flow through a small size orifice. The flowmeter was first calibrated, by plotting the pressure drop-flow rate curve of the orifice, in terms of a dimensionless Euler number versus Reynolds number. Newtonian fluids consisting of aqueous solutions of corn syrup were used as calibration fluids. The calibration curve was then used to determine the apparent extensional viscosity of three different paper coating colors. The apparent extensional viscosity is compared to the shear viscosity in terms of the Trouton ratio. The Trouton ratio for one coating color is shown to exceed considerably the theoretical value of 3 expected for Newtonian fluids.Les propriétés rhéologiques élongationnelles jouent un rôle important dans les processus dans lesquels le fluide est soumis à des décélérations ou accélérations rapides. Cet article décrit un rhéomètre à orifice utilisé pour mesurer les propriétés élongationnelles de fluides rhéologiquement complexes à des vitesses de déformation élevées. Le principe de fonctionnement du rhéomètre est basé sur la chute de pression du fluide qui passe au travers d'un petit orifice. Le rhéomètre a été initialement étalonné en traçant la courbe du nombre d'Euler en fonction du nombre de Reynolds pour des fluides newtoniens (solutions aqueuses du sirop de maïs). La courbe d'étalonnage a été alors employée pour déterminer la viscosité élongationnelle de trois différentes sauces de couchage de papier. La viscosité élongationnelle est comparée à la viscosité de cisaillement en terme du rapport de Trouton. Le rapport de Trouton pour une sauce de couchage excède considérablement la valeur théorique de 3 qui devrait être obtenue pour des fluides newtoniens.

Figures (10)
Figure 1. Orifice plate.
Figure 1. Orifice plate.
Figure 2. Experimental setup: a) hydraulic system; b) general configuration of the orifice flowmeter.
Figure 2. Experimental setup: a) hydraulic system; b) general configuration of the orifice flowmeter.
Figure 3. Flow through a conical die. where E is the dissipated energy, AP, is the pressure drop due to shear flow, AP, is the pressure drop due to extensional flow and Q is the volumetric flow rate. The following assumptions were made. 1) The shear viscosity obeys the power law model:
Figure 3. Flow through a conical die. where E is the dissipated energy, AP, is the pressure drop due to shear flow, AP, is the pressure drop due to extensional flow and Q is the volumetric flow rate. The following assumptions were made. 1) The shear viscosity obeys the power law model:
where AP, is the pressure drop due to kinetic energy variation. AP, is given by Equation (5) and AP, is determined by:
where AP, is the pressure drop due to kinetic energy variation. AP, is given by Equation (5) and AP, is determined by:
Table 1. Coating color composition.
Table 1. Coating color composition.
Figure 4. Euler number versus Reynolds number for Newtonian fluids.
Figure 4. Euler number versus Reynolds number for Newtonian fluids.
Figure 5. Shear viscosity as a function of shear rate for the coating colors.
Figure 5. Shear viscosity as a function of shear rate for the coating colors.
Table 2. Power-law parameters and infinite shear viscosity for the coating colors. Figure 6. Extensional viscosity as a function of the effective strain rate for the coating colors.
Table 2. Power-law parameters and infinite shear viscosity for the coating colors. Figure 6. Extensional viscosity as a function of the effective strain rate for the coating colors.
Figure 7. Euler number versus Reynolds number for coating colors. The straight line is the theoretical result (Equation 23).
Figure 7. Euler number versus Reynolds number for coating colors. The straight line is the theoretical result (Equation 23).
Figure 8. Trouton ratio as a function of the effective strain rate for the coating colors (open symbols correspond to n,/n and closed symbols to Equation 29).
Figure 8. Trouton ratio as a function of the effective strain rate for the coating colors (open symbols correspond to n,/n and closed symbols to Equation 29).

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