Onset of Thermal Instabilities in the Plane Poiseuille Flow of Weakly Elastic Fluids: Viscous Dissipation Effects

The onset of thermal instabilities in the plane Poiseuille flow of weakly elastic fluids is examined through a linear stability analysis by taking into account the effects of viscous dissipation. The destabilizing thermal gradients may come from the different temperatures imposed on the external boundaries and/or from the volumetric heating induced by viscous dissipation. The rheological properties of the viscoelastic fluid are modeled using the Oldroyd-B constitutive equation. As in the Newtonian fluid case, the most unstable structures are found to be stationary longitudinal rolls (modes with axes aligned along the streamwise direction). For such structures, it is shown that the viscoelastic contribution to viscous dissipation may be reduced to one unique parameter: γ=λ1(1−Γ), where λ1 and Γ represent the relaxation time and the viscosity ratio of the viscoelastic fluid, respectively. It is found that the influence of the elasticity parameter γ on the linear stability characteristics is non-monotonic. The fluid elasticity stabilizes (destabilizes) the basic Poiseuille flow if γ<γ* (γ>γ*) where γ* is a particular value of γ that we have determined. It is also shown that when the temperature gradient imposed on the external boundaries is zero, the critical Reynolds number for the onset of such viscous dissipation/viscoelastic-induced instability may be well below the one needed to trigger the pure hydrodynamic instability in weakly elastic solutions.

Stabilizing effect of elasticity on the motion of viscoelastic/elastic fluids

<p style='text-indent:20px;'>It is well-known that viscoelasticity is a material property that exhibits both viscous and elastic characteristics with deformation. In particular, an elastic fluid strains when it is stretched and quickly returns to its original state once the stress is removed. In this review, we first introduce some mathematical results, which exhibit the stabilizing effect of elasticity on the motion of viscoelastic fluids. Then we further briefly introduce similar stabilizing effect in the elastic fluids.</p>

Delayed Leidenfrost phenomenon during impact of elastic fluid droplets

This article highlights the role of non-Newtonian (elastic) effects on the droplet impact phenomenon at temperatures considerably higher than the boiling point, especially at or above the Leidenfrost regime. The Leidenfrost point (LFP) was found to decrease with an increase in the impact Weber number (based on the velocity just before the impact) for fixed polymer (polyacrylamide) concentrations. Water droplets fragmented at very low Weber numbers (approx. 22), whereas the polymer droplets resisted fragmentation at much higher Weber numbers (approx. 155). We also varied the polymer concentration and observed that, up to 1000 ppm, the LFP was higher than that for water. This signifies that the effect can be delayed by the use of elastic fluids. We have shown the possible role of elastic effects (manifested by the formation of long lasting filaments) during retraction in the increase of the LFP. However, for 1500 ppm, the LFP was lower than that for water, but had a similar residence time during the initial impact. In addition, we studied the role of the Weber number and viscoelastic effects on the rebound behaviour at 405°C. We observed that the critical Weber number up to the point at which the droplet resisted fragmentation at 405°C increased with the polymer concentration. In addition, for a fixed Weber number, the droplet rebound height and the hovering time period increased up to 500 ppm, and then decreased. Similarly, for fixed polymer concentrations like 1000 and 1500 ppm, the rebound height showed an increasing trend up to certain a certain Weber number and then decreased. This non-monotonic behaviour of rebound heights was attributed to the observed diversion of the rebound kinetic energy to rotational energy during the hovering phase. Finally, a relationship between the non-dimensional Leidenfrost temperature and the associated Weber and Weissenberg numbers is developed, and a scaling relation is proposed.

Three-dimensional viscoelastic instabilities in microchannels

Whereas the flow of simple single-phase Newtonian fluids tends to become more complex as the characteristic length scale in the problem (and hence the Reynolds number) increases, for complex elastic fluids such as dilute polymer solutions the opposite holds true. Thus small-scale, so-called ‘microfluidic’ flows of complex fluids can exhibit rich dynamics in situations where the ‘equivalent’ flow of Newtonian fluids remains linear and predictable. In the recent study of Qin et al. (J. Fluid Mech., vol. 864, 2019, R2) of the flow of a dilute polymeric fluid past a $50~\unicode[STIX]{x03BC}\text{m}$ cylinder (in a $100\times 60~\unicode[STIX]{x03BC}\text{m}$ channel), a novel 3-D holographic particle velocimetry technique reveals the underlying complexity of the flow, including inherent three-dimensionality and symmetry breaking as well as strong upstream propagation effects via elastic waves.