Visco-Elasto-Capillary Thinning and Break-Up of Complex Fluids

Submitted to Annual Rheology Reviews, 2005.The progressive break-up of an initially stable fluid column or thread into a number of smaller droplets is an important dynamical process that impacts many commercial operations from spraying and atomization of fertilizers and pesticides, to paint application, roll-coating of adhesives and food processing operations such as container- and bottle-filling. The progressive thinning of a fluid filament is driven by capillarity and resisted by inertia, viscosity and additional stresses resulting from the extensional deformation of the fluid microstructure within the thread. In many processes of interest the fluid undergoing break-up is non-Newtonian and may contain dissolved polymer, suspended particles, surfactants or other microstructural constituents. In such cases the transient extensional viscosity of the fluid plays an important role in controlling the dynamics of break-up. The intimate connection between the degree of strain-hardening that develops during free extensional flow and the dynamical evolution in the profile of a thin fluid thread is also manifested in heuristic concepts such as âspinnability’, âtackiness’ and âstringiness’. In this review we survey recent experimental and theoretical developments in the field of capillarydriven thinning and break-up with a special focus on how quantitative measurements of the thinning and rupture processes can be used to quantify the material properties of the fluid. As a result of the absence of external forcing the dynamics of the necking process are often self-similar and observations of this âself-thinning’ can be used to extract qualitative, and even quantitative, measures of the transient extensional viscosity of a complex fluid.NASA, NSF, Schlumberger Foundatio

Analysis of the String Structure Near Break-up of A Slender Jet of An Upper Convected Maxwell Liquid

In this paper, we analytically study the string structure near the break-up of a slender jet of a viscoelastic liquid surrounded by air. The governing equations are derived from the conservation laws of mass and momentum, and the rheological equation of the jet. The rheological equation of the jet is assumed to satisfy an Upper Convected Maxwell (UCM) model. Introducing a stretch variable and then applying a transformation, we obtain a coupled system of nonlinear differential equations. Via these equations, we then show that the UCM jet does not break up in finite time, which physically means that it has sufficient time to exhibit the string structure before it breaks up due to the dominant surface force

Singularities in droplet pinching with vanishing viscosity

A slender-jet model for the pinching of a liquid column is considered in the limit of vanishing viscosity. We find the model to develop a singularity in the gradients of the local radius and the velocity at a finite thread radius, so it does not describe breakup. However, the observed steepening of the profile corresponds to experiments and simulations with fluids at low viscosity. The singularity has similarity form, which we compute analytically. The result agrees well with numerical simulations of the model equations.Comment: 18 pages including 4 eps figures, revte

Dynamics of bead formation, filament thinning and breakup in weakly viscoelastic jets

The spatiotemporal evolution of a viscoelastic jet depends on the relative magnitude of capillary, viscous, inertial and elastic stresses. The interplay of capillary and elastic stresses leads to the formation of very thin and stable filaments between drops, or to ‘beads-on-a-string’ structure. In this paper, we show that by understanding the physical processes that control different stages of the jet evolution it is possible to extract transient extensional viscosity information even for very low viscosity and weakly elastic liquids, which is a particular challenge in using traditional rheometers. The parameter space at which a forced jet can be used as an extensional rheometer is numerically investigated by using a one-dimensional nonlinear free-surface theory for Oldroyd-B and Giesekus fluids. The results show that even when the ratio of viscous to inertio-capillary time scales (or Ohnesorge number) is as low as Oh ~ 0.02, the temporal evolution of the jet can be used to obtain elongational properties of the liquid.Akzo Nobel (Firm

Iterated Stretching, Extensional Rheology and Formation of Beads-on-a-String Structures in Polymer Solutions

Accepted for publication in JNNFM, December 2005.The transient extensional rheology and the dynamics of elastocapillary thinning in aqueous solutions of polyethylene oxide (PEO) are studied with high-speed digital video microscopy. At long times, the evolution of the thread radius deviates from self-similar exponential decay and competition between elastic, capillary and inertial forces leads to the formation of a periodic array of beads connected by axially-uniform ligaments. This configuration is unstable and successive instabilities propagate from the necks connecting the beads and ligaments. This iterated process results in multiple generations of beads developing along the string in general agreement with predictions of Chang et al. [Phys Fluids, 11, 1717 (1999)] although the experiments yield a different recursion relation between the successive generations of beads. At long times, finite extensibility truncates the iterated instability, and slow axial translation of the bead arrays along the interconnecting threads leads to progressive coalescence before the ultimate rupture of the fluid column. Despite these dynamical complexities it is still possible to measure the steady growth in the transient extensional viscosity by monitoring the slow capillarydriven thinning in the cylindrical ligaments between beads.NASA and the Portuguese Science Foundatio

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