Viscoelastic instabilities in micro-scale flows

Abstract

Many artificial and natural fluids contain macromolecules, particles or droplets that impart complex flow behaviour to the fluid. This complex behaviour results in a non-linear relationship between stress and deformation standing in between Newton's law of viscosity for an ideal viscous liquid and Hooke's law for an ideal elastic material. Such non-linear viscoelastic behaviour breaks down flow reversibility under creeping flow conditions, as encountered at the micro-scale, and can lead to flow instabilities. These instabilities offer an alternative to the development of systems requiring unstable flows under conditions where chaotic advection is unfeasible. Flows of viscoelastic fluids are characterized by the Weissenberg (W i) and Reynolds (Re) numbers, and at the micro-scale flow instabilities occur in regions in the W i-Re space typically unreachable at the macro-scale, namely high W i and low Re. In this paper, we review recent experimental work by the authors on the topic of elastic instabilities in flows having a strong extensional component, includ- * Corresponding author. Tel:+ 35 22 508 15 97 : flow through a hyperbolic contraction followed by a sudden expansion; flow in a microfluidic diode and in a flow focusing device; flow around a confined cylinder; flow through porous media and simplified porous media analogues. These flows exhibit different types of flow transitions depending on geometry, W i and Re, including: transition from a steady symmetric to a steady asymmetric flow, often followed by a second transition to unsteady flow at high W i; direct transition between steady symmetric and unsteady flows.

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

“…Similarly, in the inertia‐free case of polymer solutions at Re ≪ 1, a flow instability analogous to turbulence arises because nonlinearities in the constitutive relation between stress and deformation (Section ) destabilize the steady‐state laminar solution. Such instabilities were theorized as early as the 1970s and have been catalogued in diverse geometries, including concentric cylinders, rotating disks, and curved channels since the late 1980s . In all cases, an instability is observed for strong enough flow in geometries with a large amount of streamline curvature.…”

Assessing the Dynamic Performance of Microbots in Complex Fluid Flows

“…As it was mentioned previously, at the micro-scales (typical scales from the human circulatory system), the elastic effects are enhanced even at low Reynolds numbers [7,54,55]. The complex rheological behaviour of whole blood has been studied and continues to be investigated using new technological advances [56,57].…”

“…In the shear-layer transition regime, the increase of the wake angle and pressure rise coefficient reduced the drag coefficient and narrowed the near wake. At the micro scale, the relevance of fluid elasticity is enhanced and elastic instabilities can be observed easily even at low or negligible Re [7,67]. Campo-Deaño et al [54] showed that, for a viscoelastic fluid (Boger fluid), symmetric vortices started to form upstream of a hyperbolic contraction at a critical Re of 0.82; meanwhile, for the same micro channel and flow conditions, for a Newtonian fluid, the critical Re at which symmetric vortices start to form downstream of the hyperbolic contraction is higher (Re = 49.3) due to inertial effects ( Figure 2).…”

“…The most common dimensionless numbers that characterize these kinds of viscoelastic fluid flows are the Reynolds number (Re), defined as the ratio between inertial and viscous forces, Re= ρVL/η, and the Weissenberg number (Wi), which is the ratio between elastic and viscous forces, Wi= λV/L [7]. V represents the average velocity, L the characteristic length-scale and ρ, λ and η are the density, relaxation time and viscosity of the fluid, respectively.…”

Enhanced viscoelastic focusing of particle in microchannel

“…Additionally, in the channel with periodical cross sections, such as the channel with side wells or with expansion/contraction cavity arrays, the hoop stress or the secondary flow force was induced for the particle focusing in different media . Significant secondary flow was generated in these microchannels because of suddenly changed cross section and viscoelastic instabilities in micro‐scale flow , which would induce high pressure drop and disturb focused particle stream . Although numerous studies have been done on the viscoelastic particle focusing, the length of existing microchannels is typically long because of the weak elastic effect at low flow rates (most were longer than 4 cm), making it unsuitable to be integrated in small chip area.…”