Vortex generation in a finitely extensible nonlinear polymeric Peterlin fluid

What is it about?

It is well known that the mixing of two or more species in flows at low Reynoldsnumbers cannot be easily achieved since inertial effects are essentially absentand molecular diffusion is slow. To achieve mixing in Newtonian fluids underthese circumstances requires innovative new ideas such as the use of externalbody forces (eg, electromagnetic mixers) or the stretching and folding of fluidelements (eg, chaotic advection). For non-Newtonian fluids with elasticity, mix-ing can be achieved by enabling the emergence of elastic instabilities that resultsinchaoticflowsinwhichmixingissignificantlyenhanced.Inthiswork,ourgoalis to demonstrate that clearly identifiable vortical structures (eg, vortex rings)can be generated in a viscoelastic fluid initially at rest by the release of elasticstresses.Inturn,thesevortexmotionspromotebulkmixingbytransportingfluidelements from one location to another more efficiently than diffusion alone.We demonstrate this first theoretically by using the finitely extensible nonlinearelastic Peterlin (FENE-P) model to show that elastic forces can generate torque.Using this model, we derive an expression for the time rate of change of vortic-ity in an elastic fluid initially at rest caused by a sudden release of stored elasticstress. This process can be thought of as the release of elastic energy from astretched rubber band that is suddenly cut at its center. We confirm this ansatzby performing a series of direct numerical simulations based on an in-housepseudo-spectral code that couples the FENE-P model to the equations of motionfor an incompressible fluid.

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Why is it important?

The simulations reveal that a pair of vortex ringstraveling in opposite directions, with Reynolds numbers on the order of one, isgenerated from the sudden release of elastic stresses. Secondary vortical struc-tures are also generated. In the concluding section of this work, we address thepotential for vortex motions generated by elastic stresses to promote mixing inmicroflows, and we describe a possible experiment that may demonstrate thiseffect.