Instabilities in stagnation point flows of polymer solutions

Abstract

A recently-developed microfluidic device, the optimized shape cross-slot extensional rheometer, or OSCER [S.J. Haward, M.S.N. Oliveira, M.A. Alves and G.H. McKinley, Phys. Rev. Lett. 109, 128301 (2012)], is used to investigate the stability of viscoelastic polymer solutions in an idealized planar stagnation point flow. Aqueous polymer solutions, consisting of poly(ethylene oxide) and of hyaluronic acid with various molecular weights and concentrations, are formulated in order to provide fluids with a wide range of rheological properties. Semi-dilute solutions of high molecular weight polymers provide highly viscoelastic fluids with long relaxation times, which achieve a high Weissenberg number (Wi) at flow rates for which the Reynolds number (Re) remains low; hence the elasticity number El = Wi/Re is high. Lower concentration solutions of moderate molecular weight polymers provide only weakly viscoelastic fluids in which inertia remains important and El is relatively low. Flow birefringence observations are used to visualize the nature of flow instabilities in the fluids as the volume flow rate through the OSCER device is steadily incremented. At low Wi and Re, all of the fluids display a steady, symmetric and uniform 'birefringent strand' of highly oriented polymer molecules aligned along the outflowing symmetry axis of the test geometry, indicating the stability of the flow field under such conditions. In fluids of El > 1, we observe steady elastic flow asymmetries beyond a critical Weissenberg number, Wi crit , that are similar in character to those already reported in standard cross-slot geometries [e.g. P.E. Arratia, C.C. Thomas, J. Diorio and J.P. Gollub, Phys. Rev. Lett. 96, 144502 (2006)]. However, in fluids with El < 1 we observe a sequence of timedependent inertio-elastic instabilities beyond a critical Reynolds number, Re crit , characterized by high frequency spatiotemporal oscillations of the birefringent strand. By plotting the critical limits of stability for the various fluids in the Wi-Re operating space, we are able to construct a stability diagram delineating the distinct steady symmetric, steady asymmetric and inertio-elastic flow regimes in this idealized planar elongational flow device.

Pore‐Scale Flow Characterization of Polymer Solutions in Microfluidic Porous Media

“…Flow birefringence and single‐molecule imaging confirm this expectation. In particular, they demonstrate that flow fluctuations are indeed linked to the continual elongation of polymer chains, which arises for sufficiently large Wi . This picture is further supported by the finding that polymers with more backbone rigidity have suppressed fluctuations, demonstrating that polymer chain stretching is indeed required for this instability …”

Relaxation time of dilute polymer solutions: A microfluidic approach

“…The measurement of k ext is not carried out due to the low birefringence of the HA solutions at these small concentrations. Moreover, we have found that with low viscosity solvents, measurements in the OSCER device can be complicated by the onset of inertial instabilities at the high strain rates required to achieve orientation in polymer samples with such short relaxation times [20,68]. By focusing on the data of k shear for HA in water with PBS (open blue diamonds), the relaxation time increases with increasing HA concentrations in the range of 0.04 < c=c à < 1, thus suggesting the existence of intermolecular interactions, as for a-PS in both near-theta and good solvents.…”

Equilibrium circulation and stress distribution in viscoelastic creeping flow

“…However it is precisely at these points in the flow that interesting dynamics arise. Instabilities have been found in experiments at internal stagnation points [1,2,3,4,5], and related numerical instabilities are found in similar geometries [6,7,8,9,10,11]. It is unclear what is driving these instabilities, but it is reasonable to conjecture that they are related to the large polymer stresses and stress gradients which accumulate along the incoming and outgoing streamlines of these internal stagnation points.…”

“…is independent of the Weissenberg number, as it must be from equation (4). The stress induced velocity field is…”

“…The inner region corresponds to the layer where the stress divergence, Q 1 , is concentrated. 4. At this point, having prescribed the total velocity (at least locally near the stress island), the conformation tensor and the velocity field induced by the conformation tensor are computed.…”