Towards the Development of a Strategy to Characterize and Model the Rheological Behavior of Filled, Uncured Rubber Compounds.

In this paper, an experimental strategy is presented to characterize the rheological behavior of filled, uncured rubber compounds. Oscillatory shear experiments on a regular plate-plate rheometer are combined with a phenomenological thixotropy model to obtain model parameters that can be used to describe the steady shear behavior. We compare rate- and stress-controlled kinetic equations for a structure parameter that determines the deformation history-dependent spectrum and, thus, the dynamic thixotropic behavior of the material. We keep the models as simple as possible and the characterization straightforward to maximize applicability. The model can be implemented in a finite element framework as a tool to simulate realistic rubber processing. This will be the topic of another work, currently under preparation. In shaping processes, such as rubber- and polymer extrusion, with realistic processing conditions, the range of shear rates is far outside the range obtained during rheological characterization. Based on some motivated choices, we will present an approach to extend this range.

Numerical design of a T-shaped microfluidic device for deformability-based separation of elastic capsules and soft beads.

We propose a square cross-section microfluidic channel with an orthogonal side branch (asymmetric T-shaped bifurcation) for the separation of elastic capsules and soft beads suspended in a Newtonian liquid on the basis of their mechanical properties. The design is performed through three-dimensional direct numerical simulations. When suspended objects start near the inflow channel centerline and the carrier fluid is equally partitioned between the two outflow branches, particle separation can be achieved based on their deformability, with the stiffer ones going "straight" and the softer ones being deviated to the "side" branch. The effects of the geometrical and physical parameters of the system on the phenomenon are investigated. Since cell deformability can be significantly modified by pathology, we give a proof of concept on the possibility of separating diseased cells from healthy ones, thus leading to illness diagnosis.

Dynamics of prolate spheroidal elastic particles in confined shear flow.

We investigate through numerical simulations the dynamics of a neo-Hookean elastic prolate spheroid suspended in a Newtonian fluid under shear flow. Both initial orientations of the particle within and outside the shear plane and both unbounded and confined flow geometries are considered. In unbounded flow, when the particle starts on the shear plane, two stable regimes of motion are found, i.e., trembling, where the particle shape periodically elongates and compresses in the shear plane and the angle between its major semiaxis and the flow direction oscillates around a positive mean value, and tumbling, where the particle shape periodically changes and its major axis performs complete revolutions around the vorticity axis. When the particle is initially oriented out of the shear plane, more complex dynamics arise. Geometric confinement of the particle between the moving walls also influences its deformation and regime of motion. In addition, when the particle is initially located in an asymmetric position with respect to the moving walls, particle lateral migration is detected. The effects on the particle dynamics of the geometric and physical parameters that rule the system are investigated.

Dynamics of magnetic particles near a surface: model and experiments on field-induced disaggregation.

Magnetic particles are widely used in biological research and bioanalytical applications. As the corresponding tools are progressively being miniaturized and integrated, the understanding of particle dynamics and the control of particles down to the level of single particles become important. Here, we describe a numerical model to simulate the dynamic behavior of ensembles of magnetic particles, taking account of magnetic interparticle interactions, interactions with the liquid medium and solid surfaces, as well as thermal diffusive motion of the particles. The model is verified using experimental data of magnetic field-induced disaggregation of magnetic particle clusters near a physical surface, wherein the magnetic field properties, particle size, cluster size, and cluster geometry were varied. Furthermore, the model clarifies how the cluster configuration, cluster alignment, magnitude of the field gradient, and the field repetition rate play a role in the particle disaggregation process. The simulation model will be very useful for further in silico studies on magnetic particle dynamics in biotechnological tools.

Bistability and metabistability scenario in the dynamics of an ellipsoidal particle in a sheared viscoelastic fluid.

The motion of an ellipsoidal particle in a viscoelastic liquid subjected to an unconfined shear flow is addressed by numerical simulations. A complex dynamics is found with different transients and long-time regimes depending on the Deborah number De (De is the product of the viscoelastic liquid intrinsic time times the applied shear rate). Spiraling orbits toward a log-rolling motion around the vorticity are observed for low Deborah numbers, whereas the particle aligns with its major axis near to the flow direction at high Deborah numbers. The transition from vorticity to flow alignment is characterized by a periodic regime with small amplitude oscillations around orientations progressively shifting from vorticity to flow direction by increasing De. A range of Deborah numbers is detected such that the periodic solution coexists with the flow alignment regime (bistability). A further range of De is found where flow alignment is attained differently for particles starting far from or next to the shear plane: in the latter case, very long transients are found; hence an effective bistability (metabistability) is predicted to occur in a large time lapse before reaching the fully aligned state. Finally, the computed Deborah number values for flow alignment favorably compare with available experimental data.

Numerical and experimental study of a rotating magnetic particle chain in a viscous fluid.

A simple and fast numerical method is developed capable of accurately determining the 3D rotational dynamics of a magnetic particle chain in an infinite fluid domain. The focus is to control the alternating breakup and reformation of the bead chain which we believe is essential to achieve effective fluid mixing at small scales. The numerical scheme makes use of magnetic dipole moments and extended forms of the Oseen-Burgers tensor to account for both the magnetic and hydrodynamic interactions between the particles. It is shown that the inclusion of hydrodynamic interaction between the particles is crucial to obtain a good description of the particle dynamics. Only a small error of deviation is observed when benchmarking the numerical scheme against a more computationally intensive method, the direct simulation method. The numerical results are compared with experiments and the simulated rotational dynamics correspond well with those obtained from video-microscopy experiments qualitatively and quantitatively. In addition, a dimensionless number (R(T)) is derived as the sole control parameter for the rotational bead chain dynamics. Numerically and experimentally, R(T)≈ 1 is the boundary between rigid "rod" and dynamic "breaking and reformation" behaviors.

Direct numerical simulation of a 2D-stented aortic heart valve at physiological flow rates.

We study the nonlinear interaction of an aortic heart valve, composed of hyperelastic corrugated leaflets of finite density attached to a stented vessel under physiological flow conditions. In our numerical simulations, we use a 2D idealised representation of this arrangement. Blood flow is caused by a time-varying pressure gradient that mimics that of the aortic valve and corresponds to a peak Reynolds number equal to 4050. Here, we fully account for the shear-thinning behaviour of the blood and large deformations and contact between the leaflets by solving the momentum and mass balances for blood and leaflets. The mixed finite element/Galerkin method along with linear discontinuous Lagrange multipliers for coupling the fluid and elastic domains is adopted. Moreover, a series of challenging numerical issues such as the finite length of the computational domain and the conditions that should be imposed on its inflow/outflow boundaries, the accurate time integration of the parabolic and hyperbolic momentum equations, the contact between the leaflets and the non-conforming mesh refinement in part of the domain are successfully resolved. Calculations for the velocity and the shear stress fields of the blood reveal that boundary layers appear on both sides of a leaflet. The one along the ventricular side transfers blood with high momentum from the core region of the vessel to the annulus or the sinusoidal expansion, causing the continuous development of flow instabilities. At peak systole, vortices are convected in the flow direction along the annulus of the vessel, whereas during the closure stage of the valve, an extremely large vortex develops in each half of the flow domain.