Capillary break-up rheometry of low-viscosity elastic fluids

We investigate the dynamics of the capillary thinning and break-up process for low viscosity elastic fluids such as dilute polymer solutions. Standard measurements of the evolution of the midpoint diameter of the necking fluid filament are augmented by high speed digital video images of the break up dynamics. We show that the successful operation of a capillary thinning device is governed by three important time scales (which characterize the relative importance of inertial, viscous and elastic processes), and also by two important length scales (which specify the initial sample size and the total stretch imposed on the sample). By optimizing the ranges of these geometric parameters, we are able to measure characteristic time scales for tensile stress growth as small as 1 millisecond for a number of model dilute and semi-dilute solutions of polyethylene oxide (PEO) in water and glycerol. If the final aspect ratio of the sample is too small, or the total axial stretch is too great, measurements are limited, respectively, by inertial oscillations of the liquid bridge or by the development of the well-known beads-on-a-string morphology which disrupt the formation of a uniform necking filament. By considering the magnitudes of the natural time scales associated with viscous flow, elastic stress growth and inertial oscillations it is possible to construct an operability diagram characterizing successful operation of a capillary break-up extensional rheometer. For Newtonian fluids, viscosities greater than approximately 70 mPas are required; however for dilute solutions of high molecular weight polymer, the minimum Viscosity is substantially lower due to the additional elastic stresses arising from molecular extension. For PEO of molecular weight 2.10(6) g/mol, it is possible to measure relaxation times of order 1 ms in dilute polymer solutions with zero-shear-rate viscosities on the order of 2-10 mPas.

A quasi-chemical viscosity model for fully liquid slags in the Al2O3-CaO-'FeO'-SiO2 system

A structurally based viscosity model for fully liquid silicate slags has been proposed and applied to the Al2O3-CaO-'FeO'-SiO2 system at metallic iron saturation. The model links the slag viscosity to the internal structure of melts through the concentrations of various anion/cation structural units (SUs). The concentrations of structural units are equivalent to the second nearest neighbor bond concentrations calculated by the quasi-chemical thermodynamic model. This viscosity model describes experimental data over the entire temperature and composition range within the Al2O3-CaO-'FeO'-SiO2 system at metallic iron saturation and can be extended to other industrial slag systems.

A parametric study of droplet deformation through a microfluidic contraction: Low viscosity Newtonian droplets

Numerical simulations are conducted to investigate how a droplet of Newtonian liquid. entrained in a higher viscosity Newtonian liquid, behaves when passing through an axisymmetric microfluidic contraction. Simulations are performed using a transient Volume of Fluid finite volume algorithm, and cover ranges of Reynolds and Weber numbers relevant to microfluidic flows. Results are presented for a droplet to surrounding fluid viscosity ratio of 0.001. In contrast to behaviour at higher viscosity ratios obtained previously by the authors, shear and interfacial tension driven instabilities often develop along the droplet Surface. leading to complex shape development, and in some instances, droplet breakup. (c) 2006 Elsevier Ltd. All rights reserved.

Development of a quasi-chemical viscosity model for fully liquid slags in the Al2O3-CaO-'FeO'-MgO-SiO2 system. Part 1. Description of the model and its application to the MgO, MgO-SiO2, Al2O3-MgO and CaO-MgO sub-systems

A structurally-based quasi-chemical viscosity model for fully liquid slags in the Al2O3 CaO-'FeO'-MgO-SiO2 system has been developed. The model links the slag viscosities to the internal structures of the melts through the concentrations of various Si0.5O, Me2/nn+O and Me1/nn+Si0.25O viscous flow structural units. The concentrations of these structural units are derived from a quasi-chemical thermodynamic model of the system. The model described in this series of papers enables the viscosities of liquid slags to be predicted within experimental uncertainties over the whole range of temperatures and compositions in the Al2O3 CaOMgO-SiO2 system.

Development of a quasi-chemical viscosity model for fully liquid slags in the Al2O3-CaO-'FeO'-MgO-SiO2 system. Part 2. A review of the experimental data and the model predictions for the Al2O3-CaO-MgO, CaO-MgO-SiO2 and Al2O3-MgO-SiO2 systems

A structurally-based quasi-chemical viscosity model has been developed for the Al2O3 CaO-'FeO'-MgO-SiO2 system. The model links the slag viscosity to the internal structure of melts through the concentrations of various anion/cation Si0.5O, Me2/nn+O and Me1/nn+Si0.25O viscous flow structural units. The concentrations of structural units are derived from the quasi-chemical thermodynamic model. The focus of the work described in the present paper is the analysis of experimental data and the viscosity models for fully liquid slags in the Al2O3-CaO-MgO, Al2O3 MgO-SiO2 and CaO-MgO-SiO2 systems.

Development of a quasi-chemical viscosity model for fully liquid slags in the Al2O3-CaO-'FeO'-MgO-SiO2 system. Part 3. Summary of the model predictions for the Al2O3-CaO-MgO-SiO2 system and its sub-systems

A structurally-based quasi-chemical viscosity model for fully liquid slags in the Al2O3 CaO-'FeO'-MgOSiO2 system has been developed. The focus of the work described in the present paper is the analysis of the experimental data and viscosity models in the quaternary system Al2O3 CaO-MgO-SiO2 and its subsystems. A review of the experimental data, viscometry methods used and viscosity models available in the Al2O3 CaO-MgO-SiO2 and its sub-systems is reported. The quasi-chemical viscosity model is shown to provide good agreement between experimental data and predictions over the whole compositional range.

Drop formation and breakup of low viscosity elastic fluids: Effects of molecular weight and concentration

The 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 behavior 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 localized 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 finitely extensible nonlinear elastic dumbbell theory incorporating inertial, capillary, and elastic stresses is able to capture the basic features of the experimental observations. Before the critical "pinch time" t(p), an inertial-capillary balance leads to the expected 2/3-power scaling of the minimum radius with time: R-min similar to(t(p)-t)(2/3). However, the diverging deformation rate results in large molecular deformations and rapid crossover to an elastocapillary balance for times t>t(p). In this region, the filament radius decreases exponentially with time R-min similar to exp[(t(p)-t)/lambda(1)], where lambda(1) is the characteristic time constant of the polymer molecules. Measurements of the relaxation times of polyethylene oxide 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 elastocapillary 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, intermolecular interactions become significant, producing relaxation times far above theoretical predictions for dilute polymer solutions under equilibrium conditions. (C) 2006 American Institute of Physics