The extensional rheological properties of dilute polymer solutions play a dominant role in many commercial processes such as air-assisted atomization. This is a high deformation rate process important in application of diverse materials such as paints, fertilizer sprays and delivery of airborne drugs. Dilute polymeric solutions which have identical values of high shear-rate viscosity (HSV) often exhibit different values of Sauter Mean Diameter (SMD) in their spray size distributions as a result of differing extensional rheological properties. We explore the atomization of a series of model Poly(ethylene oxide) (PEO) solutions dissolved in water/glycerol mixtures. Each solution is sprayed with an air-assisted spray gun under similar conditions and imaged with a commercial spray measurement system. The values of HSV for PEO solutions are close to the solvent viscosity and matched to those of typical ink or paint samples. The surface tensions of the fluids are also tuned to be very similar, however both the SMD and the droplet size distribution change considerably. For the highest molecular weight PEO systems, interconnected beads-on-string structures are observed at different positions of the spray fan. Capillary Break-up Extensional Rheometry (CaBER) can be used to measure the extensional properties of the more viscous solutions, but the well-known limitations of this approach include inertially-induced asymmetries, gravitational sagging and the very short filament lifetimes of low viscosity samples all of which constrain the range of relaxation times that can be probed. Consequently we also explore the use of Rayleigh Ohnesorge Jet Elongational Rheometry (ROJER) to probe the extensional response of these viscoelastic solutions at realistic timescales and deformation rates. A cylindrical liquid jet is excited by a piezo-actuator at a known frequency as it exits a micromachined nozzle, and stroboscopic imaging provides high temporal and spatial resolution in the break-up process. Analyzing the evolution in the jet diameter before break-up enables meaningful measurement of relaxation times down to values as small as 60 μs, and these values can be directly correlated with the differences in the final spray size distributions and the mean diameters. We outline a simple model for the fluid dynamics of the thinning filaments close to breakup that accurately describes the variation of the average droplet diameter as a function of the elongational relaxation time measured for each fluid.

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Studying the effects of elongational properties on atomization of weakly viscoelastic solutions using Rayleigh Ohnesorge Jetting Extensional Rheometry (ROJER)

Wormlike micellar surfactant solutions are encountered in a wide variety of important applications, including enhanced oil recovery and ink-jet printing, in which the fluids are subjected to high extensional strain rates. In this contribution we present an experimental investigation of the flow of a model wormlike micellar solution (cetyl pyridinium chloride and sodium salicylate in deionised water) in a well-defined stagnation point extensional flow field generated within a microfluidic cross-slot device. We use micro-particle image velocimetry (μ-PIV) and full-field birefringence microscopy coupled with macroscopic measurements of the bulk pressure drop to make a quantitative characterization of the fluid's rheological response over a wide range of deformation rates. The flow field in the micromachined cross-slot is first characterized for viscous flow of a Newtonian fluid, and μ-PIV measurements show the flow field remains symmetric and stable up to moderately high Reynolds number, Re ≈ 20, and nominal strain rate, nom ≈ 635 s−1. By contrast, in the viscoelastic micellar solution the flow field remains symmetric only for low values of the strain rate such that nom ≤ λM−1, where λM = 2.5 s is the Maxwell relaxation time of the fluid. In this stable flow regime the fluid displays a localized and elongated birefringent strand extending along the outflow streamline from the stagnation point, and estimates of the apparent extensional viscosity can be obtained using the stress-optical rule and from the total pressure drop measured across the cross-slot channel. For moderate deformation rates (nom ≥ λM−1) the flow remains steady, but becomes increasingly asymmetric with increasing flow rate, eventually achieving a steady state of complete anti-symmetry characterized by a dividing streamline and birefringent strand connecting diagonally opposite corners of the cross-slot. Eventually, as the nominal imposed deformation rate is increased further, the asymmetric divided flow becomes time dependent. These purely elastic instabilities are reminiscent of those observed in cross-slot flows of polymer solutions, but seem to be strongly influenced by the effects of shear localization of the micellar fluid within the microchannels and around the re-entrant corners of the cross-slot.

/pdf/extensional-rheology-and-elastic-instabilities-of-a-wormlike-57jhh9n8qz.pdf

Extensional rheology and elastic instabilities of a wormlike micellar solution in a microfluidic cross-slot device

Delayed capillary break-up of viscoelastic filaments presents scientific and technical challenges relevant for drop formation, dispensing, and adhesion in industrial and biological applications. The flow kinematics are primarily dictated by the viscoelastic stresses contributed by the polymers that are stretched and oriented in a strong extensional flow field resulting from the streamwise gradients created by the capillarity-driven squeeze flow. After an initial inertiocapillary (IC) or viscocapillary (VC) regime, where elastic effects seem to play no role, the interplay of capillarity and viscoelasticity can lead to an elastocapillary (EC) response characterized by exponentially-slow thinning of neck radius (extensional relaxation time is determined from the delay constant). Less frequently, a terminal visco-elastocapillary (TVEC) response with linear decay in radius can be observed and used for measuring terminal, steady extensional viscosity. However, both IC/VC-EC and EC-TVEC transitions are inaccessible in devices that create stretched necks by applying a step strain to a liquid bridge (e.g., capillary breakup extensional rheometer). In this study, we use dripping-onto-substrate rheometry to obtain radius evolution data for unentangled polymer solutions. We deduce that the plots of transient extensional viscosity vs. Hencky strain (scaled by the respective values at the EC-TVEC transition) emulate the functional form of the birefringence-macromolecular strain relationship based on Peterlin's theory. We quantify the duration and strain between the IC/VC-EC and the EC-TVEC transitions using measures we term elastocapillary span and elastocapillary strain increment and find both measures show values directly correlated with the corresponding variation in extensional relaxation time.

https://www.pnas.org/content/pnas/116/18/8766.full.pdf

Macromolecular relaxation, strain, and extensibility determine elastocapillary thinning and extensional viscosity of polymer solutions.

An experimental investigation is conducted to determine the effect of rheological properties (viscoelasticity) on the air-blast atomization of coal water slurry. In air-blast atomization, aerodynamic force causes the liquid to deform and breakup. To observe breakup morphology of coal water slurry atomization, a high speed digital camera is used at various operating conditions. In this test, primary atomization is the condition that a cylindrical liquid jet surrounded by a coaxial annular airflow, and secondary atomization is the process that a liquid drop encounters a continuous air jet. The results show that the viscoelasticity of coal water slurry has great influence on the breakup morphology, breakup length, frequency characteristics. The corresponding correlations for these characteristics also are developed.

Influence of rheological properties on air-blast atomization of coal water slurry

Spray characteristics of gelled propellants in swirl injectors

This article reports experimental observations of the flow kinematics and stability of thin fluid sheets produced by a series of commercially available flat-fan and hollow-cone spray nozzles for a series of viscoelastic wormlike micelle solutions. As the flow rate through the nozzle is increased, the sheets of viscoelastic fluid grow larger and eventually becoming unstable and atomizing into drops. For the sheets of water produced by the flat-fan nozzles, the fluid rims of the sheets were found to destabilize first. The addition of viscoelasticity was found to stabilize the rim while simultaneously destabilizing the internal fluid sheet. What results is a series of novel flow structures comprised of highly interconnected filaments created by the growth of multiple internal holes that develop within the fluid sheet. Increasing viscoelasticity of the test fluid was found to stabilize the thin films produced by both the flat-fan and hollow-cone spray nozzles, thereby shifting the break-up of the sheets to larger flow rates. However, beyond the critical flow rate for sheet rupture, increases to the fluid elasticity were found to alter the dynamics of the atomization of the viscoelastic fluid sheets by increasing the number and growth rate of holes in the sheet while simultaneously reducing the initiation time for sheet rupture.

/pdf/the-atomization-of-viscoelastic-fluids-in-flat-fan-and-f3an2mh58i.pdf

Jeffery C. Thompson

Papers

The atomization of viscoelastic fluids in flat-fan and hollow-cone spray nozzles