Perspectives on viscoelastic flow instabilities and elastic turbulence

Abstract

Viscoelastic fluids are a common subclass of rheologically complex materials that are encountered in diverse fields from biology to polymer processing. Often the flows of viscoelastic fluids are unstable in situations where ordinary Newtonian fluids are stable, owing to the nonlinear coupling of the elastic and viscous stresses. Perhaps more surprisingly, the instabilities produce flows with the hallmarks of turbulence-even though the effective Reynolds numbers may be O(1) or smaller. We provide perspectives on viscoelastic flow instabilities by integrating the input from speakers at a recent international workshop: historical remarks, characterization of fluids and flows, discussion of experimental and simulation tools, and modern questions and puzzles that motivate further studies of this fascinating subject. The materials here will be useful for researchers and educators alike, especially as the subject continues to evolve in both fundamental understanding and applications in engineering and the sciences.I.

Pressure-driven flow of the viscoelastic Oldroyd-B fluid in narrow non-uniform geometries: analytical results and comparison with simulations

“…While throughout this work we consider steady and stable flows, it should be noted that the flow of viscoelastic fluids within non-uniform geometries may become unstable above a certain flow rate even at low Reynolds numbers due to the fluid's complex rheology (Larson 1992;Shaqfeh 1996;Datta et al 2021;Steinberg 2021). We consider low-Reynolds-number flows, so that the fluid inertia is negligible relative to viscous stresses.…”

Understanding viscoelastic flow instabilities: Oldroyd-B and beyond

“…4 below) on how the use of genuinely nonlinear constitutive equations that account for shear-thinning effects plays an important role in more accurate predictions of experimental observations. Another recent multi-author review article [40], based on the virtual workshop on viscoelastic flow instabilities and elastic turbulence organized by the Princeton Center for Theoretical Sciences, also provides a state-of-the-art summary of the various challenges in this broad area. It is worth recalling that Oldroyd, in his seminal 1950 paper [35], proposed a constitutive model for viscoelastic flows purely from a continuum viewpoint, by requiring the model to satisfy the principle of material frame indifference.…”

Splitting of localized disturbances in viscoelastic channel flow

“…The elastic stress field is coupled to the fluid's motion due to polymer stretching by the velocity gradients (Larson 1999;Liu & Steinberg 1999;Smith, Babcock & Chu 1999), which is characterized by the Weissenberg number Wi ≡ (U/L)λ (where U, L and λ are the characteristic velocity, length scale and longest polymer relaxation time, respectively). As a result, flow instabilities and elastic turbulence might occur in viscoelastic fluid flows at Wi 1, even at vanishingly small Reynolds numbers, Re 1 (Re ≡ UL/ν, where ν is the fluid's kinematic viscosity) (Larson 1992;Pakdel & McKinley 1996;Shaqfeh 1996;Datta et al 2021;Steinberg 2021). Despite several decades of research and the prevalence of viscoelastic fluids in industrial and biological processes, the understanding of instability mechanisms in the high-elasticity regime (Re 1 and Wi 1) is still lacking in several fundamental cases, such as in channel flow, also known as plane Poiseuille flow (Morozov & van Saarloos 2007;Steinberg 2021), which is discussed here.…”