Pier Luca Maffettone

Equation of change for ellipsoidal drops in viscous flow

Abstract A simple phenomenological model for the deformation of a droplet immersed in a fluid subjected to a flow field with a uniform, but otherwise arbitrary, velocity gradient is presented. The model is capable of describing the transient evolution of the drop. The steady state predictions for simple shear and elongational flows are analytical. The model degenerates into Taylor theory in the limit of slow flows as well as for high viscosity ratios. It also recovers the affine deformation under the appropriate limiting conditions. The predictions are compared with some representative experimental and numerical results available in the literature.

Quantifying dispersion of layered nanocomposites via melt rheology

Rheological measurements are used to compare clay nanocomposites prepared through melt mixing using two different polypropylene matrices. Steady state and transient nonlinear rheological experiments are employed to separate the contributions of flow induced orientation of the tactoids and particulate network build-up. The conditions under which the rheological properties are dominated by the aggregate network are subsequently identified. Under these conditions, the low frequency linear viscoelastic behavior is analyzed using scaling concepts for fractal networks to determine the degree of network formation by exfoliation. Moreover, the high frequency behavior of the moduli can be used to quickly assess the dispersion quality. The results from the analysis of the linear viscoelastic data are compared to structural features extracted from electron microscopy and small angle X-ray scattering data.

The rigid-rod model for nematic polymers: An analysis of the shear flow problem

The rigid-rod model is capable of predicting several rheological features of rodlike polymers in the nematic phase. The model is formulated in terms of a nonlinear partial differential equation that describes the evolution of an orientational distribution function. The morphological properties and the rheological response of the sample can be determined once the distribution function is known. In this article the rigid-rod model is thoroughly analyzed with tools typical of bifurcation analysis for the case of shear flows. New flow regimes, both stationary and periodic, are found and illustrated. The detailed description of the model bifurcation structure allows some considerations about up to date closure approximations.

Nematic phase of rodlike polymers. II. Polydomain predictions in the tumbling regime

The two‐dimensional model previously considered is here used to obtain predictions in the complex situation of the tumbling regime which prevails at low shear rates. Although each domain is permanently in a time‐dependent, periodic regime, the macroscopic response can be stationary in time because of the well‐known polydomain structure. First, the average steady rheological response for this situation is calculated by taking a polydomain structure which neglects interdomain interactions. Although the steady state predictions thus obtained favorably compare with the experimental results throughout the range of shear rates, the transient start‐up responses do not, because of the crucial role played by the interactions in such a case. These interactions, due to Frank elasticity, are then introduced in the model in the simplest possible way, i.e., by use of a mean field potential. Under this assumption, also the predictions of transient behavior in the tumbling regime show the correct qualitative features.

Ellipsoidal drop model for single drop dynamics with non-Newtonian fluids

A phenomenological model for the dynamics of a single drop immersed in an immiscible matrix is proposed with the two incompressible component liquids being in general viscoelastic. The model is formulated by assuming that the drop is always ellipsoidal, and the model parameters are determined once and for all in the small deformation limit. The model is thereafter applicable to whatever flow condition is imposed at infinity, and for whatever intensity of flow field. Predictions of steady state deformation, drop breakup, and drop relaxation display the effects of constitutive elasticity on the drop dynamics.

Rotation of a sphere in a viscoelastic liquid subjected to shear flow. Part I: Simulation results

In inertialess suspensions of rigid particles, the rotational motion of each particle is governed by the so-called freely rotating condition, whereby the total torque acting on the particle must be zero. In this work, we study the effect of viscoelasticity of the suspending liquid on the rotation period of a sphere by means of three-dimensional finite element simulations, for conditions corresponding to a macroscopic shear flow. The simulation results capture the slowing down of the rotation, relative to the Newtonian case, which was recently observed in experiments. It is shown that such a phenomenon depends on the specific constitutive equation adopted for the viscoelastic liquid. Analysis of transients shows a clear correlation between rotation rate and the development of first normal stress difference.

Drop shape dynamics under shear-flow reversal

The shape evolution of a liquid drop immersed in an immiscible liquid is studied under transient flow conditions. The drop is Newtonian and buoyancy free; the external liquid is Newtonian and subjected to shear flow reversal. Three model systems, polydimethylsiloxane/polyisobutylene, polybutene/silicone oil, and silicone oil/polybutene, all Newtonian under the experimental conditions investigated, have been selected to have a range of viscosity ratios. The three drop axes and the drop orientation within the shear plane are independently measured. The results are compared with the predictions of a phenomenological model. The agreement between experimental results and theory is good. Peculiar behavior of the orientation angle has been observed and correctly predicted. The results are also used to explain some rheological features typical of immiscible polymer blends.

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.

Microrheology with Optical Tweezers: Measuring the relative viscosity of solutions ‘ at a glance ’

We present a straightforward method for measuring the relative viscosity of fluids via a simple graphical analysis of the normalised position autocorrelation function of an optically trapped bead, without the need of embarking on laborious calculations. The advantages of the proposed microrheology method are evident when it is adopted for measurements of materials whose availability is limited, such as those involved in biological studies. The method has been validated by direct comparison with conventional bulk rheology methods, and has been applied both to characterise synthetic linear polyelectrolytes solutions and to study biomedical samples.

Rotation of a sphere in a viscoelastic liquid subjected to shear flow. Part II. Experimental results

The effect of the viscoelastic nature of the suspending medium on the rotation of spherical particles in a simple shear flow is studied experimentally using a counter-rotating device. To evaluate the effect of variations in rheological properties of the suspending media, fluids have been selected which highlight specific constitutive features. These include a reference Newtonian fluid, a constant viscosity, high elasticity Boger fluid, a single relaxation time wormlike micellar surfactant solution, and a broad spectrum shear-thinning elastic polymer solution. It is shown that particle rotation slows down, when compared to the Newtonian case, as elasticity increases, in qualitative agreement with computer simulation studies. Despite the variation in constitutive properties and the wide range of time scales of the fluids, it is found that the Weissenberg number suffices to scale the data: the dimensionless rotation speed of the spheres in the different fluids scales onto a single master curve as a function ...