Shear-thinning drop formation

A volume-of-fluid numerical method is used to predict the dynamics of drop formation from a nozzle with a circular exit, directed vertically downwards in air, when the drop fluid is shear-thinning. The validity of the numerical calculation is first confirmed for a Newtonian fluid by comparison with experimental measurements. For the cases considered, predictions for a shear-thinning drop fluid result in more rapid pinch-off and a smaller final neck length consistent with a related study of liquid bridges

Stretching of polymers in a random three-dimensional flow

Behavior of a dilute polymer solution in a random three-dimensional flow with an average shear is studied experimentally. Polymer contribution to the shear stress is found to be more than two orders of magnitude higher than in a laminar shear flow. The results indicate that the polymer molecules get strongly stretched by the random motion of the fluid.Comment: 4 pages, 3 figure

Drop Formation and Breakup of Low Viscosity Elastic Fluids: Effects of Molecular Weight and Concentration

Submitted to Phys. FluidsThe dynamics of drop formation and pinch-off have been investigated for a series of low viscosity elastic fluids possessing similar shear viscosities, but differing substantially in elastic properties. On initial approach to the pinch region, the viscoelastic fluids all exhibit the same global necking behaviour that is observed for a Newtonian fluid of equivalent shear viscosity. For these low viscosity dilute polymer solutions, inertial and capillary forces form the dominant balance in this potential flow regime, with the viscous force being negligible. The approach to the pinch point, which corresponds to the point of rupture for a Newtonian fluid, is extremely rapid in such solutions, with the sudden increase in curvature producing very large extension rates at this location. In this region the polymer molecules are significantly extended, causing a localised increase in the elastic stresses, which grow to balance the capillary pressure. This prevents the necked fluid from breaking off, as would occur in the equivalent Newtonian fluid. Alternatively, a cylindrical filament forms in which elastic stresses and capillary pressure balance, and the radius decreases exponentially with time. A (0+1)-dimensional FENE dumbbell theory incorporating inertial, capillary and elastic stresses is able to capture the basic features of the experimental observations. Before the critical ‘pinch time’ tp , an inertial-capillary balance leads to the expected 2/3-power scaling of the minimum radius with time, Rmin ∼ (tp − t)^2/3. However, the diverging deformation rate results in large molecular deformations and rapid crossover to an elasto-capillary balance for times t > tp. In this region the filament radius decreases exponentially with time Rmin ~exp[(tp - t) / λ1], where λ1 is the characteristic time constant of the polymer molecules. Measurements of the relaxation times of PEO solutions of varying concentrations and molecular weights obtained from high speed imaging of the rate of change of filament radius are significantly higher than the relaxation times estimated from Rouse-Zimm theory, even though the solutions are within the dilute concentration region as determined using intrinsic viscosity measurements. The effective relaxation times exhibit the expected scaling with molecular weight but with an additional dependence on the concentration of the polymer in solution. This is consistent with the expectation that the polymer molecules are in fact highly extended during the approach to the pinch region (i.e. prior to the elasto-capillary filament thinning regime) and subsequently as the filament is formed they are further extended by filament stretching at a constant rate until full extension of the polymer coil is achieved. In this highly-extended state, inter-molecular interactions become significant producing relaxation times far above theoretical predictions for dilute polymer solutions under equilibrium conditions.Australian Research Counci

Formation of beads-on-a-string structures during break-up of viscoelastic filaments

Break-up of viscoelastic filaments is pervasive in both nature and technology. If a filament is formed by placing a drop of saliva between a thumb and forefinger and is stretched, the filament’s morphology close to break-up corresponds to beads of several sizes interconnected by slender threads. Although there is general agreement that formation of such beads-on-a-string (BOAS) structures occurs only for viscoelastic fluids, the underlying physics remains unclear and controversial. The physics leading to the formation of BOAS structures is probed by numerical simulation. Computations reveal that viscoelasticity alone does not give rise to a small, satellite bead between two much larger main beads but that inertia is required for its formation. Viscoelasticity, however, enhances the growth of the bead and delays pinch-off, which leads to a relatively long-lived beaded structure. We also show for the first time theoretically that yet smaller, sub-satellite beads can also form as seen in experiments.National Science Foundation (U.S.). ERC-SOPS (EEC-0540855)Nanoscale Interdisciplinary Research Thrust on 'Directed Self-assembly of Suspended Polymer Fibers' (NSF-DMS0506941

Shear-induced structure and dynamics of hydrophobically modified hydroxy ethyl cellulose (hmHEC) in the presence of SDS

The interaction between hydrophobically modified hydroxyethyl cellulose (hmHEC), containing approximately 1 wt% side-alkyl chains of C-16, and an anionic sodium dodecyl sulphate (SDS) surfactant was investigated. For a semi-dilute solution of 0.5 wt% hmHEC, the previously observed behaviour of a maximum in solution viscosity at intermediate SDS concentrations, followed by a drop at higher SDS concentrations, until above the cmc of surfactant when the solution resembles that of the unsubstituted polymer, was confirmed. Additionally, a two-phase region containing a hydrogel phase and a water-like supernatant was found at low SDS concentrations up to 0.2 wt%, a concentration which is akin to the critical association concentration, cac, of SDS in the presence of hmHEC. Above this concentration, SDS molecules bind strongly to form mixed micellar aggregates with the polymer alkyl side-chains, thus strengthening the network junctions, resulting in the observed increase in viscosity and elastic modulus of the solution. The shear behaviour of this polymer-surfactant complex during steady and step stress experiments was examined in great detail. Between SDS concentrations of 0.2 and 0.25 wt%, the shear viscosity of the hmHEC-polymer complex network undergoes shear-induced thickening, followed by a two-stage shear-induced fracture or break-up of the network. The thickening is thought to be due to structural rearrangement, causing the network of flexible polymers to expand, enabling some polymer hydrophobic groups to be converted from intra- to inter-chain associations. At higher applied stress, a partial local break-up of the network occurs, while at even higher stress, above the critical or network yield stress, a complete fracture of the network into small microgel-like units, is believed to occur. This second network rupture is progressive with time of shear and no steady state in viscosity was observed even after 300 s. The structure which was reformed after the cessation of shear is found to be significantly different from the original state

Drop formation dynamics of constant low-viscosity, elastic fluids

The dynamics of drop formation under gravity has been investigated as a function of elasticity using a set of low-viscosity, ideal elastic fluids and an equivalent Newtonian glycerol-water solution. All solutions had the same shear viscosity, equilibrium surface tension, and density, but differed greatly in elasticity. The minimum drop radius in the early stages of drop formation (necking) was found to scale as expected from potential flow theory, independent of the elasticity of the solutions. Thus, during this stage of drop formation when viscous force is still weak, the dynamics are controlled by a balance between inertial and capillary forces, and there is no contribution of elastic stresses of the polymer. However, upon formation of the pinch regions, there is a large variation in the drop development to break-off observed between the various solutions. The elastic solutions formed secondary fluid threads either side of a secondary drop from the necked region of fluid between the upper and lower pinches, which were sustained for increasing amounts of time. The break-off lengths and times increase with increasing elasticity of the solutions. Evolution of the filament, length is, however, identical in shape and form for all of the polymer solutions tested, regardless of differing elasticity. This de-coupling between filament growth rate and break-up time (or equivalently, final filament length at break-up) is rationalised. A modified force balance to that of Jones and Rees [48] is capable of correctly predicting the filament growth of these low-viscosity, elastic fluids in the absence of any elastic contributions due to polymer extension within the elongating filament. The elongation of the necked region of fluid (which becomes the filament) is dominated by the inertia of the drop, and is independent of the elasticity of the solution. However, elasticity does strongly influence the resistance of the pinch regions to break-off, with rapid necking resulting in extremely high rates of surface contraction on approach to the pinch point, initiating extension of the polymer chains within the pinch regions. This de-coupling phenomenon is peculiar to low-viscosity, elastic fluids as extension does not occur prior to the formation of the pinch points (i.e. just prior to break-up), as opposed to the high viscosity counterparts in which extension of polymers in solution may occur even during necking. Once steady-state extension of the polymers is achieved within the pinch at high extension rates, the thread undergoes elasto-capillary break-up as the capillarity again overcomes the viscoelastic forces. The final length at detachment and time-to-break-off (relative to the equivalent Newtonian fluid) is shown to be linearly proportional to the longest relaxation time of the fluid. (C) 2002 Elsevier Science B.V. All rights reserved