Viscoelastic liquid curtains: experimental results on the flow of a falling sheet of polymer solution

Abstract

We experimentally investigate the extensional flow of a sheet – or curtain – of viscoelastic liquid falling freely from a slot at constant flow rate under gravity. Extruded liquids are aqueous solutions of flexible polyethylene oxide (PEO) and of semi-rigid partially hydrolysed polyacrylamide (HPAM) with low shear viscosities. Velocimetry measurements reveal that the mean velocity field $U(z)$ (where $z$ is the distance from the slot exit) does not reduce to a free fall. More precisely, we show that the liquid falls initially with sub-gravitational accelerations up to a distance from the slot which scales as $g\unicode[STIX]{x1D70F}_{fil}^{2}$ (where $g$ is gravity and $\unicode[STIX]{x1D70F}_{fil}$ is the extensional relaxation time of the liquid) due to the stretching of polymer molecules. Beyond this elastic length, inertia dominates and the local acceleration reaches the asymptotic free-fall value $g$ . The length of the sub-gravitational part of the curtain is shown to be much larger than the equivalent viscous length $((4\unicode[STIX]{x1D702}/\unicode[STIX]{x1D70C})^{2}/g)^{1/3}$ for Newtonian liquids of density $\unicode[STIX]{x1D70C}$ and dynamic viscosity $\unicode[STIX]{x1D702}$ which is usually small compared to the curtain length. By analogy with Newtonian curtains, we show that the velocity field $U(z)$ rescales on a master curve. Besides, the flow is shown to be only weakly affected by the history of polymer deformations in the die upstream of the curtain. Furthermore, investigations on the curtain stability reveal that polymer addition reduces the minimum flow rate required to maintain a continuous sheet of liquid.

Drop dynamics of viscoelastic filaments

“…To the best of the authors knowledge, there is no theoretical model available to compare this simple scaling law. It is also interesting to note that the number of drops for PEG+PEO solutions are higher than agreement with previous studies [10,42]. Note that at pinching, η E tends to a constant, which seems to depend on the polymer concentration.…”

“…In contrast to Newtonian fluids, which have their extensional viscosity directly proportional to the shear viscosity, the extensional viscosity of viscoelastic fluids is more complex. Macromolecular solutions exhibit large extensional viscosity [1][2][3][4][5][6][7][8][9][10] because extensional flows are irrotational and presumably more efficient at disentangling or orienting flexible polymer molecules.…”

Fingering instability in Marangoni spreading on a deep layer of polymer solution

“…12). Shear thinning has been shown to play an important role in amplification of velocity perturbation 38,44 . Here we propose a mechanism that shear thinning may have in the amplification of the leading edge perturbation.…”

Liquid Transfer for Viscoelastic Solutions

“…Aqueous solutions of poly-ethylene oxide (PEO), which is a high molecular weight polymer, and poly-ethylene glycol (PEG), which is a relatively low molecular weight, are used, either separately or in combination. PEO solutions are commonly used to investigate viscoelastic behavior of liquid jets, 28,29 beads-ona-string, 10,14,30,31 coatings [32][33][34] and liquid transfer. 25,27 Broadly, our strategy is to control the shear viscosity with PEG and the extensional viscosity with the mass fraction of PEO.…”