Extensional Flow Oscillatory Rheometry of Polymer Solutions Background
Extensional flows involving polymer solutions occur and are utilised in a wide variety of important
industrial and commercial processes including enhanced oil recovery (EOR), turbulent drag reduction,
food, cosmetic and paint formulation, and ink-jet printing technology. Many of these applications
utilise a non-Newtonian increase in the apparent viscosity of polymer solutions, which occurs due
to increased polymer-solvent interactions as the polymer molecules uncoil and extend in the flow.
We are using an extensional flow oscillatory rheometer (EFOR), originally developed by Odell and
Carrington (2006), to study the behaviour of aqueous poly(ethylene oxide) (PEO) solutions in both
stagnation point and contraction extensional flows. The solutions we are studying have particular
relevance in the area of ink formulation for ink-jet printing, where polymer additives are found to
facilitate control of droplet size and droplet break-up at the point of ejection from the print head.
Methods The EFOR device, see figure 1, consists of a central X-slot flow cell with a piezo-electric micro pump on each limb of the 'X'. One pair of opposing pumps are driven in phase with each other and 180° out of phase with the other pair, generating an oscillating extensional flow field centred on the stagnation point in the centre of the cross.
Figure 1(a). Schematic of the EFOR device to generate an oscillating extensional flow field. |
Figure 1(b). Schematic of control electronics, optical probe and pressure measurement. |
The stagnation point is important because the fluid velocity there is zero, but the velocity gradient
is finite. This means a fluid element in this vicinity is subjected to the extensional flow for an
infinite time, allowing a polymer molecule within the fluid element to accumulate a high strain,
provided that is, the velocity gradient is high enough to overcome the entropic elasticity of the
molecule. This condition is achieved when the Deborah number, De of the flow exceeds unity, where
De = extension rate x molecular relaxation time.
In our experiment we also have control over the accumulation of fluid strain at the stagnation
point since we control the length of time over which a given strain rate is applied by
controlling the frequency of the pump oscillation.
The X-slot itself is fabricated from stainless steel and the slot is machined using electrical
discharge wire erosion. We have slots covering a range of widths from 200 μm down to 60 μm.
Each limb of the X-slot also incorporates an 8:1 contraction at the entrance, allowing the study of
contraction flow without changing the experimental set-up.
We use an optical probe, essentially consisting of a laser directed orthogonally through the
stagnation point/contraction region and through polarizers crossed on either side of the X-slot,
to observe and measure birefringent signals due to the extended and optically anisotropic polymer
molecules, see figure 2. These measurements can be used to assess the polymer molecular strain.
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Figure 2. Birefringence in a 0.02% aqueous solution of MW = 5x106 PEO in a 200 μm wide X-slot. In the left image the flow enters through the channels top right and bottom left and exits through the channels top left and bottom right. In right image the flow is reversed. The stagnation point is located at the centre of the image.
Whilst looking for birefringence we simultaneously measure the pressure difference across an inlet and an outlet of the X-slot, which allows us to determine the fluid viscosity. By disconnecting two of the micro pumps and flowing liquid around just one corner of the X, we can remove the stagnation point from the flow and perform measurements of shear viscosity. This can be subtracted from the viscosity found in full stagnation point flow to reveal the extensional viscosity of the polymer solution, see figure 3.
 Figure 3. Extensional viscosity as a function of strain rate for a 0.1% aqueous solution of MW = 1.25x106 PEO in a 200 μm wide X-slot for fixed values of fluid strain. The increase in extensional viscosity at strain rate = 2000/s indicates the onset of polymer stretching. |
Additionally we have re-designed the EFOR to integrate with a micro particle image
velocimeter, with our collaborators in Xue-Feng Yuan's group at the University of
Manchester Interdisciplinary Biocentre. This will allow us to measure the flow-field
in the X-slot and observe flow modification effects due to the viscous regions of solution
containing highly stretched polymer molecules.
We are also interested in applying our methods to suitable biological systems as well as
to more model synthetic polymer systems, particularly polystyrene in dioctylphthalate.
Related publications
[1] J.A. Odell and S.J. Haward, Viscosity enhancement in the flow of hydrolysed poly(acrylamide) saline solutions around spheres: implications for enhanced oil recovery, Rheologica Acta, 47, 129-137 (2008).
[2] J.A. Odell and S.P. Carrington, Extensional Flow Oscillatory Rheometry, J. Non-Newtonian Fluid Mechanics, 137, 110-120 (2006).
[3] J.A. Odell and S.J. Haward, Viscosity enhancement in non-Newtonian flow of dilute aqueous polymer solutions through crystallographic and random porous media, Rheologica Acta, 45, 853-863 (2006).
[4] S.J. Haward and J.A. Odell, Molecular orientation in non-Newtonian flow of dilute polymer solutions around spheres, Rheologica Acta, 43, 350-363 (2004).
[5] S.J. Haward and J.A. Odell, Viscosity enhancement In non-Newtonian flow of dilute polymer solutions through crystallographic porous media, Rheologica Acta, 42, 516-526 (2003).