A numerical stabilization framework for viscoelastic fluid flow using the finite volume method on general unstructured meshes

A robust finite volume method for viscoelastic flow analysis on general unstructured meshes is developed. It is built upon a general-purpose stabilization framework for high Weissenberg number flows. The numerical framework provides full combinatorial flexibility between different kinds of rheological models on the one hand, and effective stabilization methods on the other hand. A special emphasis is put on the velocity-stress-coupling on co-located computational grids. Using special face interpolation techniques, a semi-implicit stress interpolation correction is proposed to correct the cell-face interpolation of the stress in the divergence operator of the momentum balance. Investigating the entry-flow problem of the 4:1 contraction benchmark, we demonstrate that the numerical methods are robust over a wide range of Weissenberg numbers and significantly alleviate the high Weissenberg number problem. The accuracy of the results is evaluated in a detailed mesh convergence study

Vector magnetometry using silicon vacancies in 4H-SiC at ambient conditions

Point defects in solids promise precise measurements of various quantities. Especially magnetic field sensing using the spin of point defects has been of great interest recently. When optical readout of spin states is used, point defects achieve optical magnetic imaging with high spatial resolution at ambient conditions. Here, we demonstrate that genuine optical vector magnetometry can be realized using the silicon vacancy in SiC, which has an uncommon S=3/2 spin. To this end, we develop and experimentally test sensing protocols based on a reference field approach combined with multi frequency spin excitation. Our works suggest that the silicon vacancy in an industry-friendly platform, SiC, has potential for various magnetometry applications at ambient conditions

Numerical simulation of non-isothermal viscoelastic flows at high Weissenberg numbers using a finite volume method on general unstructured meshes

In this numerical study, an original approach to simulate non-isothermal viscoelastic fluid flows at high Weissenberg numbers is presented. Stable computations over a wide range of Weissenberg numbers are assured by using the root conformation approach in a finite volume framework on general unstructured meshes. The numerical stabilization framework is extended to consider thermo-rheological properties in Oldroyd-B type viscoelastic fluids. The temperature dependence of the viscoelastic fluid is modeled with the time-temperature superposition principle. Both Arrhenius and WLF shift factors can be chosen, depending on the flow characteristics. The internal energy balance takes into account both energy and entropy elasticity. Partitioning is achieved by a constant split factor. An analytical solution of the balance equations in planar channel flow is derived to verify the results of the main field variables and to estimate the numerical error. The more complex entry flow of a polyisobutylene-based polymer solution in an axisymmetric 4:1 contraction is studied and compared to experimental data from the literature. We demonstrate the stability of the method in the experimentally relevant range of high Weissenberg numbers. The results at different imposed wall temperatures, as well as Weissenberg numbers, are found to be in good agreement with experimental data. Furthermore, the division between energy and entropy elasticity is investigated in detail with regard to the experimental setup.Comment: 25 pages, 13 figures, 2 table

An Extended Volume of Fluid Method and its Application to Single Bubbles Rising in a Viscoelastic Liquid

An extended volume of fluid method is developed for two-phase direct numerical simulations of systems with one viscoelastic and one Newtonian phase. A complete set of governing equations is derived by conditional volume-averaging of the local instantaneous bulk equations and interface jump conditions. The homogeneous mixture model is applied for the closure of the volume-averaged equations. An additional interfacial stress term arises in this volume-averaged formulation which requires special treatment in the finite-volume discretization on a general unstructured mesh. A novel numerical scheme is proposed for the second-order accurate finite-volume discretization of the interface stress term. We demonstrate that this scheme allows for a consistent treatment of the interface stress and the surface tension force in the pressure equation of the segregated solution approach. Because of the high Weissenberg number problem, an appropriate stabilization approach is applied to the constitutive equation of the viscoelastic phase to increase the robustness of the method at higher fluid elasticity. Direct numerical simulations of the transient motion of a bubble rising in a quiescent viscoelastic fluid are performed for the purpose of experimental code validation. The well-known jump discontinuity in the terminal bubble rise velocity when the bubble volume exceeds a critical value is captured by the method. The formulation of the interfacial stress together with the novel scheme for its discretization is found crucial for the quantitatively correct prediction of the jump discontinuity in the terminal bubble rise velocity

The Incidence and Clinical Relevance of Graft Hypertrophy After Matrix-Based Autologous Chondrocyte Implantation

Background: Graft hypertrophy is the most common complication of periosteal autologous chondrocyte implantation (p-ACI). Purpose: The aim of this prospective study was to analyze the development, the incidence rate, and the persistence of graft hypertrophy after matrix-based autologous chondrocyte implantation (mb-ACI) in the knee joint within a 2-year postoperative course. Study Design: Case series; Level of evidence, 4. Methods: Between 2004 and 2007, a total of 41 patients with 44 isolated cartilage defects of the knee were treated with the mb-ACI technique. The mean age of the patients was 35.8 years (standard deviation [SD], 11.3 years), and the mean body mass index was 25.9 (SD, 4.2; range, 19-35.3). The cartilage defects were arthroscopically classified as Outerbridge grades III and IV. The mean area of the cartilage defect measured 6.14 cm2 (SD, 2.3 cm2). Postoperative clinical and magnetic resonance imaging (MRI) examinations were conducted at 3, 6, 12, and 24 months to analyze the incidence and course of the graft. Results: Graft hypertrophy developed in 25% of the patients treated with mb-ACI within a postoperative course of 1 year; 16% of the patients developed hypertrophy grade 2, and 9% developed hypertrophy grade 1. Graft hypertrophy occurred primarily in the first 12 months and regressed in most cases within 2 years. The International Knee Documentation Committee (IKDC) and visual analog scale (VAS) scores improved during the postoperative follow-up time of 2 years. There was no difference between the clinical results regarding the IKDC and VAS pain scores and the presence of graft hypertrophy. Conclusion: The mb-ACI technique does not lead to graft hypertrophy requiring treatment as opposed to classic p-ACI. The frequency of occurrence of graft hypertrophy after p-ACI and mb-ACI is comparable. Graft hypertrophy can be considered as a temporary excessive growth of regenerative cartilage tissue rather than a true graft hypertrophy. It is therefore usually not a persistent or systematic complication in the treatment of circumscribed cartilage defects with mb-ACI

Coherent electrical readout of defect spins in 4H-SiC by photo-ionization at ambient conditions

Quantum technology relies on proper hardware, enabling coherent quantum state control as well as efficient quantum state readout. In this regard, wide-bandgap semiconductors are an emerging material platform with scalable wafer fabrication methods, hosting several promising spin-active point defects. Conventional readout protocols for such defect spins rely on fluorescence detection and are limited by a low photon collection efficiency. Here, we demonstrate a photo-electrical detection technique for electron spins of silicon vacancy ensembles in the 4H polytype of silicon carbide (SiC). Further, we show coherent spin state control, proving that this electrical readout technique enables detection of coherent spin motion. Our readout works at ambient conditions, while other electrical readout approaches are often limited to low temperatures or high magnetic fields. Considering the excellent maturity of SiC electronics with the outstanding coherence properties of SiC defects the approach presented here holds promises for scalability of future SiC quantum devices

Quantum properties of dichroic silicon vacancies in silicon carbide

The controlled generation and manipulation of atom-like defects in solids has a wide range of applications in quantum technology. Although various defect centres have displayed promise as either quantum sensors, single photon emitters or light-matter interfaces, the search for an ideal defect with multi-functional ability remains open. In this spirit, we investigate here the optical and spin properties of the V1 defect centre, one of the silicon vacancy defects in the 4H polytype of silicon carbide (SiC). The V1 centre in 4H-SiC features two well-distinguishable sharp optical transitions and a unique S=3/2 electronic spin, which holds promise to implement a robust spin-photon interface. Here, we investigate the V1 defect at low temperatures using optical excitation and magnetic resonance techniques. The measurements, which are performed on ensemble, as well as on single centres, prove that this centre combines coherent optical emission, with up to 40% of the radiation emitted into the zero-phonon line (ZPL), a strong optical spin signal and long spin coherence time. These results single out the V1 defect in SiC as a promising system for spin-based quantum technologies