Han E. H. Meijer

Viscoelastic flow past a confined cylinder of a low-density polyethylene melt

The capabilities of the exponential version of the Phan-Thien-Tanner (PTT) model and the Giesekus model to predict stress fields for the viscoelastic flow of a low density polyethylene melt around a confined cylinder are investigated. Computations are based on a newly developed version of the discontinuous Galerkin method. This method gives convergent results up to a Deborah number of 2.5 for the falling sphere in a tube benchmark problem. Moreover, the specific implicit-explicit implementation allows the efficient resolution of problems with multiple relaxation times which are mandatory for polymer melts. Experimentally, stress fields are related to birefringence distributions by means of the stress optical rule. Three different fits, of equal quality, to available viscometric shear data are used: two for the PTT model and one for the Giesekus model. Comparison of computed and measured fringes reveals that neither of the models is capable of describing the full birefringence pattern sufficiently well. In particular it appears difficult to predict both the birefringent tail at the wake of the cylinder that is dominated by elongational effects and the fringe pattern between cylinder and the walls where a combined shear-elongational flow is present.

On the performance of enhanced constitutive models for polymer melts in a cross-slot flow

Abstract A new class of viscoelastic constitutive equations is proposed that provides enhanced control of shear and elongational properties. Together with the widely used Giesekus and Phan-Thien Tanner model, these enhanced models are evaluated for a polymer melt (LDPE) in a cross-slot flow. This stagnation flow has a strong planar elongational deformation component. The material is characterized, in both viscometric simple shear flow and in uniaxial elongation. Velocities are measured with particle tracking velocimetry while field-wise flow-induced birefringence is used for correlation with stresses. The experimental results are compared with 2D viscoelastic simulations. With equal quality of describing viscometric data, the enhanced models can predict the flow properties of the cross-slot flow significantly better than the well known PTT and Giesekus model.

Nonsingular boundary integral method for deformable drops in viscous flows

A three-dimensional boundary integral method for deformable drops in viscous flows at low Reynolds numbers is presented. The method is based on a new nonsingular contour-integral representation of the single and double layers of the free-space Greens function. The contour integration overcomes the main difficulty with boundary-integral calculations: the singularities of the kernels. It also improves the accuracy of the calculations as well as the numerical stability. A new element of the presented method is also a higher-order interface approximation, which improves the accuracy of the interface-to-interface distance calculations and in this way makes simulations of polydispersed foam dynamics possible. Moreover, a multiple time-step integration scheme, which improves the numerical stability and thus the performance of the method, is introduced. To demonstrate the advantages of the method presented here, a number of challenging flow problems is considered: drop deformation and breakup at high viscosity ratios for zero and finite surface tension; drop-to-drop interaction in close approach, including film formation and its drainage; and formation of a foam drop and its deformation in simple shear flow, including all structural and dynamic elements of polydispersed foams.

Viscoelastic flow past a confined cylinder of a polyisobutylene solution

Viscoelastic constitutive equations are evaluated using the benchmark problem of the planar flow past a confined cylinder for a well‐characterized solution of 5%(w/w) polyisobutylene in tetradecane. The ratio of channel height to cylinder diameter is equal to two. We compare finite element simulations with point‐wise measured velocities and stresses obtained by means of laser Doppler anemometry and a flow‐induced birefringence technique, respectively. The Deborah number (De) ranges from 0.25 to 2.32. In the case of the geometry with a symmetrically confined cylinder, computations were made with a generalized Newtonian model and with both a single‐ and a four‐mode Phan‐Thien and Tanner (PTT) model. All model parameters were determined in simple shear flow. A similar analysis is presented in case of an asymmetrically confined cylinder (with De=1.87). Impressively good agreement was found between the predictions of the four‐mode PTT model and the measured velocities and stresses. The agreement was even excel...

An experimental and numerical investigation of a viscoelastic flow around a cylinder

In this paper the plane flow of a shear thinning solution of 5 wt% polyisobutylene (PIB) in tetradecane (C14) (PIB/C14) around a cylinder placed between parallel plates is investigated numerically and experimentally. Both Laser Doppler Anemometry and Flow Induced Birefringence measurements are performed and compared with numerical results, using a Discontinuous Galerkin method and a one‐mode Phan‐Thien Tanner model. Previous work has shown a good agreement between measured and computed stress fields for the flow through a planar four‐to‐one contraction with this fluid. The flow around a cylinder, however, leads to some surprising differences.

Chaotic fluid mixing in non-quasi-static time-periodic cavity flows

Abstract Fluid mixing in a two-dimensional square cavity with a time-periodic pulsating lid velocity is studied. A spectral element technique for spatial discretization is combined with a continuous projection scheme for temporal discretization to obtain a numerical representation of the non-quasi-static velocity field in the cavity. It is well known that mixing in a cavity with a steady lid velocity results in linear mixing of fluid inside the cavity. Here, it is shown that superposition of a pulsating component on the steady lid velocity can lead to chaotic mixing in the core of the cavity. An extra steady motion of the opposite cavity wall, resulting in a small perturbation to the original flow, causes the chaotically mixed region to be spread over almost the whole cavity. Poincare and periodic point analysis reveal the main characteristics for these transient time-periodic flows, and elucidate the details and properties of the chaotic mixing in these flows.

A recoverable strain-based model for flow-induced crystallization

A model for the combined processes of quiescent and flow-induced crystallization of polymers is presented. This modeling should provide the necessary input data, in terms of the structure distribution in a product, for the prediction of mechanical properties and shape- and dimensional-stability. The model is partly based on the work of Schneider et al. [1] and Eder et al. [2] where the shear rate was taken as the relevant parameter for flow-induced crystallization. Rather then the shear rate as the driving force, a viscoelastic approach is proposed here, where the resulting recoverable strain (expressed by the elastic Finger tensor) with the highest relaxation time is the driving force for flow-induced crystallization. Thus we focus on the polymer that experiences the flow, rather then on the flow itself. For a fully characterized isotactic Polypropylene (iPP), i.e. a polymer for which all data needed as input for the computational model are available, comparison with experimental results from literature shows good agreement. For results from extensional flow, part of this data set is missing and therefore comparison is only qualitative.

Droplet behavior in the presence of insoluble surfactants

The time-dependent behavior of droplets in the presence of insoluble surfactants, i.e., droplet elongation in supercritical flow (capillary number Ca=0.1) and droplet breakup in a quiescent matrix, is studied using a finite element method. The interfacial tension coefficient σ as a function of the surfactant concentration Γ is described using the Langmuir equation of state, σ=σ0+RTΓ∞ ln(1−Γ/Γ∞). For droplets in an equal viscosity system, the influence of parameters Γ, Γ∞, and the Peclet number (ratio between surfactant convection and diffusion rate) on the elongation behavior has been investigated, whereas droplet breakup is considered for various values of the Peclet number for trace concentrations Γ≪Γ∞ of an insoluble surfactant. Depending on the surfactant used, a surfactant covered droplet in supercritical flow may deform more than or less than a clean droplet, as is the case in subcritical flow. Two processes compete: surfactant accumulation near the tips due to convection and overall surfactant dilu...

A mapping approach for three-dimensional distributive mixing analysis

Abstract A mapping approach is proposed for the numerical simulation of distributive mixing in three-dimensional laminar flows. The method is based on a spatial discretization of the locally averaged concentration of fluid components in the mixture (the so-called “coarse grain density”). A distribution matrix, that describes the changes in component concentration, is composed. The proposed method makes it possible to rapidly predict the (short- and long-term) mixing performances, and to compare a large number of different mixing protocols in an efficient way. The consistency and accuracy of this algorithm is validated by comparing the results obtained on grids with different spatial resolution, and by comparison with front tracking results. The technique is evaluated in a prototype mixing flow in a cubic cavity, generated by sliding opposite walls. Different mixing protocols are compared quantitatively, and result in optimal mixing protocol parameters.

Near-surface mechanical properties of amorphous polymers

Abstract Polymeric material near a free surface can have properties which deviate considerably from the bulk properties. Many researchers have reported a reduced glass transition temperature in thin polymeric films and attributed this effect to an enhanced segmental mobility near a free surface. It was also reported that sufficiently thin polymeric structures show a higher ductility than the bulk material. In this paper, we therefore investigate the hypothesis that the near-surface mechanical properties of amorphous polymers differ from the bulk properties owing to the presence of an absolute length scale. Microindentations and nanoindentations are performed on polystyrene, using a range of indenter sizes and indentation loads. In addition, numerical simulations are carried out with an advanced material model for polystyrene. A comparison between the experimental and numerical results indeed indicates that a length-scale effect is present near the surface. Simulations performed at an elevated temperature indicate that our results are consistent with the observations of a reduced T g.