Mario Minale

Rheology and rheological morphology determination in immiscible two-phase polymer model blends

Abstract The Maffettone–Minale analysis describes the shape of ellipsoidal droplets in immiscible two-phase polymer model blends during flow. It is used here to calculate the elastic interfacial contribution to the shear stress (σ12,int), and first normal stress difference (N1,int). The ratio N1,int/σ12,int can be linked to the orientation angle of the inclusions. Under steady state flow the Maffettone–Minale model gives an analytical expression between the orientation angle and the capillary number. In this manner the capillary number can be deduced from the orientation angle. From this the droplet size is calculated. Good agreement is found between the results and droplet sizes determined independently from dynamic measurements using the Palierne model. The stresses calculated from the model, with given values for the droplet size, compare quite well with the stresses measured on a model system for relatively small capillary numbers.

Drop shape dynamics of a Newtonian drop in a non-Newtonian matrix during transient and steady shear flow

Transient and steady deformation of a single Newtonian drop immersed in a non-Newtonian matrix subjected to a homogeneous shear flow is investigated microscopically. Two model Boger fluids have been used as non-Newtonian matrices. The three-dimensional drop shape is completely determined as observations from both the velocity-vorticity and velocity-velocity gradient plane are available. Start-up and relaxation are investigated varying both the capillary number and the elasticity of the matrix fluid, while the viscosity ratio is kept constant. The extensive data set demonstrates that matrix elasticity reduces the steady drop deformation and promotes droplet orientation, can induce a drop deformation overshoot in the start-up experiments and slows down the relaxation phenomena. The experimental results have been compared with predictions of a phenomenological model [M. Minale, J. Non-Newtonian Fluid Mech. 123, 151–160 (2004)], that is slightly modified in the present work. It shows good agreement with the experimental data up to moderate capillary numbers (Ca≈0.2). For higher Ca, the observed trends are still correctly predicted, although quantitative agreement is less satisfying. A systematic deviation is observed at the end of the relaxation process. This result, together with a systematic, quantitative discrepancy in the experimental data between the two Boger fluids, suggests that the underlying rheological model is probably too simplistic to allow a quantitative prediction of all effects caused by matrix elasticity.Transient and steady deformation of a single Newtonian drop immersed in a non-Newtonian matrix subjected to a homogeneous shear flow is investigated microscopically. Two model Boger fluids have been used as non-Newtonian matrices. The three-dimensional drop shape is completely determined as observations from both the velocity-vorticity and velocity-velocity gradient plane are available. Start-up and relaxation are investigated varying both the capillary number and the elasticity of the matrix fluid, while the viscosity ratio is kept constant. The extensive data set demonstrates that matrix elasticity reduces the steady drop deformation and promotes droplet orientation, can induce a drop deformation overshoot in the start-up experiments and slows down the relaxation phenomena. The experimental results have been compared with predictions of a phenomenological model [M. Minale, J. Non-Newtonian Fluid Mech. 123, 151–160 (2004)], that is slightly modified in the present work. It shows good agreement with the e...

Rheology of semi-dilute emulsions: viscoelastic effects caused by the interfacial tension

Abstract The steady state rheological properties of viscous emulsions are discussed in the dilute and semi-dilute concentration regions. In these systems the first normal stress differences can be measured as well. Such data have been collected over a wide range of ratios of droplet over matrix viscosity. In this manner data became available to evaluate the Choi-Schowalter model. Application of the latter to the normal stresses requires that the droplet diameter be known. At high shear rates the droplet diameter changes nearly inversely proportional to the shear rate. This results in a first normal stress difference proportional to shear rate and hence a ‘normal viscosity’ can be defined. This is used to compare the data with the available theoretical predictions. At low shear rates deviations from a constant normal viscosity can be observed. They are associated with a hysteresis region, where no single steady state droplet size can be defined anymore. Slightly viscoelastic components have been used as well to investigate whether this would result in deviations from the behaviour observed for mixtures of Newtonian fluids.

Transient flow experiments in a model immiscible polymer blend

The rheological and morphological changes that are induced in emulsions or simple polymer blends by simple flow histories are relatively well understood. Here these results are extended to more complex flow histories, which not only approach more closely real processing conditions but also provide more critical tests in model assessment. For this purpose, a semiconcentrated, incompatible, model blend is subjected to a stepwise increase in shear rate followed by a flow reversal. The blend morphology consists of droplets immersed in a matrix. Two different types of behavior are identified, depending on the instant at which the flow is reversed. When this occurs after the droplets are broken up, the stress transients resemble those of the corresponding step-up experiment. When flow is reversed prior to the droplet break-up, the stress transients are much longer than those in simple step-up experiments, the normal stress curves also become more complex. A model is presented for flow reversal prior to droplet ...

Two-fluid demixing theory predictions of stress-induced turbidity of polystyrene solutions in dioctyl phthalate

Stress induced demixing of a polymer solution is predicted by a two fluid theory reformulated to be able to impose all the interface boundary conditions required. The theory has now been applied to the data on solutions of polystyrene in dioctylphthalate of Rangel-Nafaile et al. [Macromolecules 17, 1187–1195 (1984)] at one molecular weight at various temperatures, to additional unpublished data at various molecular weights, and to various published experiments in which there was evidence for phase separation. The dependence of elastic compliance on concentration was approximated by an equation which permitted the analytic differentiations and integrations required for the equations of the theory. The prediction of visual cloud point stresses at various temperatures were excellent within the concentration range over which the compliances had been fitted. The calculated demixing stresses were somewhat higher than those measured by extrapolation of photometric data to onset of turbidity, possibly because the...

Numerical predictions of the viscosity of non-Brownian suspensions in the semidilute regime

The viscosity of a non-Brownian suspension in simple shear cannot be theoretically predicted in the limit of the semidilute approximation, since it depends on the initial configuration. Batchelor and Green [J. Fluid Mech. 56, 401–427 (1972)] proved that the suspension viscosity can be expressed in power series of the solid volume fraction and the second order coefficient, b, resulted undetermined. On the contrary, experimentally Pasquino et al. [J. Rheol. 52, 1369–1384 (2008)] obtained a single steady state and estimated the value of b. We here numerically show that laminar mixing is able to induce a unique steady state also in the semidilute regime, since it is effective to break the closed orbits that may occur in these suspensions. To this end, we investigated the effect of the initial conditions on the steady state starting from seven different configurations ranging from the fully uniform and ordered one to the agglomerated one, passing through different random distributions. We, finally, numerically...

ICE STREAMS IN ANTARCTICA: TRANSVERSE INSTABILITY OF GRAVITY DRIVEN FLOW

Abstract We analyse the gravity driven flow of ice down the slopes of Antarctica. Ice streams are almost invariably observed, and these could be explained by a transverse instability of the gravity driven flow of ice. In Newtonian fluids, the longitudinal instability is guaranteed to be the predominant one, and hence any transverse instability, if possible, must be due to the non-Newtonian character of ice. We show that the second-order Coleman-Noll fluid, and the lower-convected Maxwell fluid, could indeed show a predominant instability in the transverse direction, and we advance two speculations: first, that the predominant instability is either the longitudinal or the transverse one, and second, that the latter may be the case only for fluids which exhibit a non-zero second normal stress difference in shear flow. We also show that, for the specific problem at hand, the second-order constitutive equation is plausible.

On mass diffusion effects in a Stefan-like problem arising in the melting of antarctic ice shelves

Abstract In this paper we analyse the effect of mass diffusion in a Stefan-like problem, referring to the interaction between ice shelves and seawater in Antarctica. This interaction is particularly important, being responsible for the vast majority of ice loss from Antarctica. We conclude that, in our specific case, the results obtained with the model which takes into account mass diffusion are almost indistinguishable from those obtained from the mass diffusion free model, and that therefore possible inversion layers are to be attributed to effects other than mass transfer of salt.