59th Annual Report on Research 2014

The goal of this project is to explore high Deborah (De) number elastic instabilities that occur upstream of a confined cylinder and their effect on porous flow. In particular, the phase space, pressure drop/mobility, and effect on oil displacement are being evaluated. A description of current efforts is given.

1) Description of Instabilities

The instabilities occur at extremely high De which are difficult to achieve in macroscale systems; microfluidics, which provide extremely high De due to confinement, have been used study this phenomenon. The instability is first noted as a temporal and spatial varying flow behind a cylinder a moderate De. As De increases, upstream stream lines diverge taking a “wine glass” shape.  This is followed by the upstream stagnation point detaching from cylinder, creating an upstream vortex that is both spatially and temporally varying.

2) Role of Geometry and Fluid Properties on Instability Phase Space

In previously published work,¹ a Reynold number (Re)-De phase space for the observed instabilities was evaluated for a single geometry and small range of fluids. In current work, a much broader examination of the instability has been undertaken in order to better understand the phase space of onset for the instabilities. Over 300 experiments incorporating 4 additional fluids and 9 separate geometry combinations were examined, varying both the blockage ratio and channel aspect ratio. Furthermore, the phase space and onset of the instability were reconsidered in a viscoelastic Mach number (Ma)- Elasticity number (El) regime, which has been found in the past to be a useful way to conceive of inertio-elastic instabilities.¹ The viscoelastic Ma is the ratio speed of the visoelastic shear wave to local velocity.  When its value exceeds 1 the solution to the vorticity equation of motion undergoes a “change of type” from symmetric to elliptical; at the same time, fluid flow is seen to show new behaviors. We observe that using the proposed Ma-El phase space to condense the large number of tests onto a single plot; the downstream instabilities begins to occur at Ma_crit ~ 1 and transition to the upstream instabilities at a Ma_crit  ~ 10.  Since all data collapses, it appears that geometry and fluid properties have no effect on the instabilities beyond their effect on Ma and El.

3) Role of instability on Excess Pressure drop around a Single Cylinder

Having assessed the phase space for the observed instabilities as a function of the both geometry of a single cylinder and fluid properties, we are now examining their role on pressure drop. To do this we have incorporated pressure sensors to allow measurement of pressure drop within the microfluidic channels. We have examined those fluids which provide instabilities over the largest range of tested flowrates. We have measured the pressure drop of our solutions and comparable Newtonian fluids in both straight channels and those with cylinders. Initial results show that pressure increases with increasing El at comparable flow rates. When dimensional pressure drop is plotted against Ma, we observe that fluids tested all demonstrate similar behavior.  First we see a marked increase in pressure drop at Ma~1 corresponding to the downstream instability.  Then we see a dramatic rise in pressure for Ma>10 which corresponds to the upstream instability.  These results are consistent with our phase space diagrams.  We see that when plotted vs. Ma that the lower El fluid has higher pressure drops than the larger El; similar results have been observed for planar contraction flows.

4) Future work

Based on our current results, we will examine how the formation of the instability and pressure drop is affected by multiple cylinders in a single channel. We will then extrapolate these results to porous flows by extracting mobilities and friction factors from pressure measurements.³ Finally, we will begin to examine the role of these instabilities on oil displacement.

5) Impact Of Research on the PI and Graduate Student

Currently this work has led the PI in the direction of porous flow phenomenon and elastic instabilities, which he had not previously examined. The current results on phase space and pressure drop are being prepared for both publication and presentation (at the 2014 annual meeting of the Society of Rheology). The Graduate student working on this project has developed new expertise polymer solution rheology, elastic instabilities, and porous flow.

1.            Kenney, S., K. Poper, G. Chapagain, and G. Christopher, Large Deborah number flows around confined microfluidic cylinders. Rheologica Acta, 2013. 52(5): p. 485-497.

2.            Rodd, L.E., J.J. Cooper-White, D.V. Boger, and G.H. McKinley, Role of the elasticity number in the entry flow of dilute polymer solutions in micro-fabricated contraction geometries. Journal of Non-Newtonian Fluid Mechanics, 2007. 143(2–3): p. 170-191.

3.            Galindo-Rosales, F.J., L. Campo-Deano, F.T. Pinho, E. van Bokhorst, P.J. Hamersma, M.S.N. Oliveira, and M.A. Alves, Microfluidic systems for the analysis of viscoelastic fluid flow phenomena in porous media. Microfluidics and Nanofluidics, 2012. 12(1-4): p. 485-498.