Frank Snijkers

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.

Cone-partitioned-plate geometry for the ARES rheometer with temperature control

A cone-partitioned-plate fixture for the ARES rheometer (TA instruments, DE) has been designed, implemented, and validated. This geometry allows measuring the nonlinear shear flow properties of samples, which display edge fracture in regular cone-and-plate geometries, such as polymer melts and concentrated solutions. Reliable bulk shear flow data can be obtained with these systems at high rates and strains, using very small sample quantities. Measurements can be performed at temperatures ranging from at least − 50 °C up to over 200 °C in a controlled nitrogen environment. An extensive set of start-up shear measurements on moderately entangled linear monodisperse polyisoprene (60 kg/mol) and polystyrene (182 kg/mol) melts to validate the design are presented and discussed with focus on the Cox–Merz rule and the characteristics of the stress overshoot. With this new geometry, the range of artifact-free data is extended by a decade in Weissenberg number (WiD). It is shown that the obtained results compared w...

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 ...

Directed self-assembly of spheres into a two-dimensional colloidal crystal by viscoelastic stresses.

Ordering induced by shear flow can be used to direct the assembly of particles in suspensions. Flow-induced ordering is determined by the balance between a range of forces, such as direct interparticle, Brownian, and hydrodynamic forces. The latter are modified when dealing with viscoelastic rather than Newtonian matrices. In particular, 1D stringlike structures of spherical particles have been observed to form along the flow direction in shear thinning viscoelastic fluids, a phenomenon not observed in Newtonian fluids at similar particle volume fractions. Here we report on the formation of freestanding crystalline patches in planes parallel to the shearing surfaces. The novel microstructure is formed when particles are suspended in viscoelastic, wormlike micellar solutions and only when the applied shear rate exceeds a critical value. In spite of the very low volume fraction (less than 0.01), particles arrange themselves in 2D crystalline patches along the flow direction. This is a bulk phenomenon because 2D crystals form throughout the whole gap between plates, with the gap thickness being much larger than the particle size. Shear flow may hence be an easy method to drive particles into crystalline order in suspensions with viscoelastic properties. The crystalline structure reported here could be used to design new materials with special mechanical, optical, thermal, or electric properties.

Hydrodynamic Interactions between Two Equally Sized Spheres in Viscoelastic Fluids in Shear Flow

The effect of using a viscoelastic suspending medium on the in-plane hydrodynamic interaction between two equally sized spheres in shear flow is studied experimentally to understand flow-induced assembly behavior (i.e., string formation). A counterrotating device equipped with a Couette geometry is used together with quantitative videomicroscopy. To evaluate the effects of differences in rheological properties of the suspending media, fluids have been selected that highlight specific constitutive features. These include a reference Newtonian fluid (N), a constant-viscosity, high-elasticity Boger fluid (BF), a wormlike micellar surfactant solution with a single dominant relaxation time (WMS), and a broad spectrum shear-thinning elastic polymer solution (ST). As expected, the trajectories are symmetric in the Newtonian fluid. In the BF, the midpoints of the spheres are observed to remain in the same plane before and after the interaction, as in the Newtonian fluid, although the path lines are in this case no longer symmetric. Interactions in the ST and WMS are highly asymmetric. Two fundamentally different kinds of path lines are observed in the WMS and ST: reversing and open trajectories. The type of trajectory depends on the initial configuration of the spheres with respect to each other and on the shear rate. On the basis of the obtained results, shear-thinning of the viscosity seems to be the key rheological parameter that determines the overall nature of the interactions, rather than the relative magnitude of the normal stress differences.

Molecular rheology of branched polymers: decoding and exploring the role of architectural dispersity through a synergy of anionic synthesis, interaction chromatography, rheometry and modeling

An emerging challenge in polymer physics is the quantitative understanding of the influence of a macromolecular architecture (i.e., branching) on the rheological response of entangled complex polymers. Recent investigations of the rheology of well-defined architecturally complex polymers have determined the composition in the molecular structure and identified the role of side-products in the measured samples. The combination of different characterization techniques, experimental and/or theoretical, represents the current state-of-the-art. Here we review this interdisciplinary approach to molecular rheology of complex polymers, and show the importance of confronting these different tools for ensuring an accurate characterization of a given polymeric sample. We use statistical tools in order to relate the information available from the synthesis protocols of a sample and its experimental molar mass distribution (typically obtained from size exclusion chromatography), and hence obtain precise information about its structural composition, i.e. enhance the existing sensitivity limit. We critically discuss the use of linear rheology as a reliable quantitative characterization tool, along with the recently developed temperature gradient interaction chromatography. The latter, which has emerged as an indispensable characterization tool for branched architectures, offers unprecedented sensitivity in detecting the presence of different molecular structures in a sample. Combining these techniques is imperative in order to quantify the molecular composition of a polymer and its consequences on the macroscopic properties. We validate this approach by means of a new model asymmetric comb polymer which was synthesized anionically. It was thoroughly characterized and its rheology was carefully analyzed. The main result is that the rheological signal reveals fine molecular details, which must be taken into account to fully elucidate the viscoelastic response of entangled branched polymers. It is important to appreciate that, even optimal model systems, i.e., those synthesized with high-vacuum anionic methods, need thorough characterization via a combination of techniques. Besides helping to improve synthetic techniques, this methodology will be significant in fine-tuning mesoscopic tube-based models and addressing outstanding issues such as the quantitative description of the constraint release mechanism.

Start-up and relaxation of well-characterized comb polymers in simple shear

We report on the shear flow start-up and the relaxation upon flow cessation of anionically synthesized comb polymers of different chemistries. The experimental data, obtained with a cone partitioned-plate geometry in order to avoid artifacts, showed that the start-up shear flow of combs exhibits systematic dependencies on the branching structure. They were interpreted by invoking dynamic dilution and hierarchical relaxation, which are known to control the linear viscoelastic response. For all combs studied here, the backbones remained entangled after dynamic dilution due to branch relaxation. We combined the important molecular parameters (i.e., the number and molar mass of the branches) into a single parameter, the number of entanglements of the dynamically diluted backbone, ZBBDIL., which we found to be the main scaling parameter for the observed nonlinear flow behavior. The steady viscosities as function of Weissenberg number were less shear-thinning compared to linear analogues, and the higher the amo...

Migration of a sphere suspended in viscoelastic liquids in Couette flow: experiments and simulations

The intrinsically coupled effects of the curvature of the flow-field and of the viscoelastic nature of suspending medium on the cross-stream lateral migration of a single non-Brownian sphere in wide-gap Couette flow are studied. Quantitative videomicroscopy experiments using a counterrotating device are compared to the results of 3D finite element simulations. To evaluate the effects of differences in rheological properties of the suspending media, fluids have been selected which highlight specific constitutive features, including a reference Newtonian fluid, a single relaxation time wormlike micellar surfactant solution, a broad spectrum shear-thinning elastic polymer solution and a constant viscosity, highly elastic Boger fluid. As expected for conditions corresponding to Stokes flow, migration is absent in the Newtonian fluid. In the wormlike micellar solution and the shear-thinning polymer solution, spheres are observed to migrate in the direction of decreasing shear rate gradient, i.e. the outer cylinder, except when the sphere is initially released close to the inner cylinder, in which case the migration is towards it. The migration is enhanced by faster relative angular velocities of the cylinders. Shear-thinning reduces the migration velocity, showing an opposite behavior as compared to previous results in planar shear flow. In the Boger fluid, within experimental error no migration could be observed, likely due to the large solvent contribution to the overall viscosity. For small Deborah numbers the migration results are well described by an heuristic argument based on a local stress balance.

Viscoelasticity and nonlinear simple shear flow behavior of an entangled asymmetric exact comb polymer solution

We report upon the characterization of the steady-state shear stresses and first normal stress differences as a function of shear rate using mechanical rheometry (both with a standard cone and plate and with a cone partitioned plate) and optical rheometry (with a flow-birefringence setup) of an entangled solution of asymmetric exact combs. The combs are polybutadienes (1,4-addition) consisting of an H-skeleton with an additional off-center branch on the backbone. We chose to investigate a solution in order to obtain reliable nonlinear shear data in overlapping dynamic regions with the two different techniques. The transient measurements obtained by cone partitioned plate indicated the appearance of overshoots in both the shear stress and the first normal stress difference during start-up shear flow. Interestingly, the overshoots in the start-up normal stress difference started to occur only at rates above the inverse stretch time of the backbone, when the stretch time of the backbone was estimated in analogy with linear chains including the effects of dynamic dilution of the branches but neglecting the effects of branch point friction, in excellent agreement with the situation for linear polymers. Flow-birefringence measurements were performed in a Couette geometry, and the extracted steady-state shear and first normal stress differences were found to agree well with the mechanical data, but were limited to relatively low rates below the inverse stretch time of the backbone. Finally, the steady-state properties were found to be in good agreement with model predictions based on a nonlinear multimode tube model developed for linear polymers when the branches are treated as solvent.

Rotation of a sphere in a viscoelastic fluid under flow

The rotation speed of spherical particles in a shear flow is studied experimentally in rheologically different fluids. The fluids, selected to highlight specific constitutive features, include a Newtonian fiuid, a Boger fluid, a wormhke micellar surfactant solution, and a shear thinning elastic polymer solution. It is shown experimentally that particle rotation slows down, when compared to the Newtonian case, as elasticity increases. This is in qualitative agreement with TFEM simulation studies. Furthermore, the dimensionless rotation speed of the spheres in the different fluids as function of the elasticity of the medium scales onto a single curve. This scaling with the Weissenberg number was somewhat unexpected given simulation results for different rheological models, where significant differences are observed for selected single relaxation time differential models.