In this work, we optimise microfluidic converging/diverging geometries in order to produce constant strain-rates along the centreline of the flow, for performing studies under homogeneous extension. The design is examined for both two-dimensional and three-dimensional flows where the effects of aspect ratio and dimensionless contraction length are investigated. Initially, pressure driven flows of Newtonian fluids under creeping flow conditions are considered, which is a reasonable approximation in microfluidics, and the limits of the applicability of the design in terms of Reynolds numbers are investigated. The optimised geometry is then used for studying the flow of viscoelastic fluids and the practical limitations in terms of Weissenberg number are reported. Furthermore, the optimisation strategy is also applied for electro-osmotic driven flows, where the development of a plug-like velocity profile allows for a wider region of homogeneous extensional deformation in the flow field.

A number of important industrial applications exploit the ability of small quantities of high molecular weight polymer to suppress instabilities that arise in the equivalent flow of Newtonian fluids, a particular example being turbulent drag reduction. However, it can be extremely difficult to probe exactly how the polymer acts to, e.g., modify the streamwise near-wall eddies in a fully turbulent flow. Using a novel crossslot flow configuration, we exploit a flow instability in order to create and study a single steady-state streamwise vortex. By quantitative experiment, we show how the addition of small quantities (parts per million) of a flexible polymer to a Newtonian solvent dramatically affects both the onset conditions for this instability and the subsequent growth of the axial vorticity. Complementary numerical simulations with a finitely extensible nonlinear elastic dumbbell model show that these modifications are due to the growth of polymeric stress within specific regions of the flow domain. Our data fill a significant gap in the literature between the previously reported purely inertial and purely elastic flow regimes and provide a link between the two by showing how the instability mode is transformed as the fluid elasticity is varied. Our results and novel methods are relevant to understanding the mechanisms underlying industrial uses of weakly elastic fluids and also to understanding inertioelastic instabilities in more confined flows through channels with intersections and stagnation points.

For many commonly used viscoelastic constitutive equations, it is well known that the limiting behavior is that of the Oldroyd-B model. Here, we compare the response of the simplified linear form of the Phan-Thien–Tanner model (“sPTT”) [Phan-Thien and Tanner, “A new constitutive equation derived from network theory,” J. Non-Newtonian Fluid Mech. 2, 353–365 (1977)] and the finitely extensible nonlinear elastic (“FENE”) dumbbell model that follows the Peterlin approximation (“FENE-P”) [Bird et al., “Polymer solution rheology based on a finitely extensible bead—Spring chain model,” J. Non-Newtonian Fluid Mech. 7, 213–235 (1980)]. We show that for steady homogeneous flows such as steady simple shear flow or pure extension, the response of both models is identical under precise conditions ([Formula: see text]). The similarity of the “spring” functions between the two models is shown to help understand this equivalence despite a different molecular origin of the two models. We then use a numerical approach to investigate the response of the two models when the flow is “complex” in a number of different definitions: first, when the applied deformation field is homogeneous in space but transient in time (so-called “start-up” shear and planar extensional flow), then, as an intermediate step, the start-up of the planar channel flow; and finally, “complex” flows (through a range of geometries), which, although being Eulerian steady, are unsteady in a Lagrangian sense. Although there can be significant differences in transient conditions, especially if the extensibility parameter is small [Formula: see text], under the limit that the flows remain Eulerian steady, we once again observe very close agreement between the FENE-P dumbbell and sPTT models in complex geometries.

The transport of bio-particles in viscous flows exhibits a rich variety of dynamical behaviour, such as morphological transitions, complex orientation dynamics or deformations. Characterising such complex behaviour under well controlled...

Microfluidic contraction devices have been proposed for extensional rheometry measurements, in particular as a useful method for determining the extensional viscosity of low elasticity solutions. The first commercially available "Extensional Viscometer-Rheometer-On-a-Chip" (e-VROC TM), developed by Rheosense, is a hyperbolically-shaped contraction/expansion geometry which incorporates pressure-drop measurement capabilities. To better understand the underlying flow kinematics within this geometry we have conducted a numerical study performing three-dimensional numerical simulations for both Newtonian and viscoelastic fluids. For the viscoelastic fluids the simplified Phan-Thien and Tanner (sPTT) and the Finitely Extensible Nonlinear Elastic models (FENE-P) are employed, in order to investigate the efficiency of this configuration in terms of increasing Weissenberg numbers and to understand the effects of various model parameters on the flow field. Our Newtonian fluid results suggest that the e-VROC TM geometry produces only a small region of extensional flow and is mainly shear-dominated, potentially suggesting any pressure-drop measurements from this device may be related to viscoelastic first normal-stress differences developed via a combination of shear and extension, rather than solely pure extension. By a careful selection of the sPTT and FENE-P model parameters, such that steady-state viscometric properties in homogeneous flows are matched, we are able to show that a small enhanced pressure-drop is seen for both models, which is larger for the FENE-P model.