Derivation of Two-Fluid Model Based on Onsager Principle.

Using the Onsager variational principle, we study the dynamic coupling between the stress and the composition in a polymer solution. In the original derivation of the two-fluid model of Doi and Onuki the polymer stress was introduced a priori; therefore, a constitutive equation is required to close the equations. Based on our previous study of viscoelastic fluids with homogeneous composition, we start with a dumbbell model for the polymer, and derive all dynamic equations using the Onsager variational principle.

Quantum critical behavior in heavy electron materials.

Quantum critical behavior in heavy electron materials is typically brought about by changes in pressure or magnetic field. In this paper, we develop a simple unified model for the combined influence of pressure and magnetic field on the effectiveness of the hybridization that plays a central role in the two-fluid description of heavy electron emergence. We show that it leads to quantum critical and delocalization lines that accord well with those measured for CeCoIn5, yields a quantitative explanation of the field and pressure-induced changes in antiferromagnetic ordering and quantum critical behavior measured for YbRh2Si2, and provides a valuable framework for describing the role of magnetic fields in bringing about quantum critical behavior in other heavy electron materials.

Emergence of superconductivity in heavy-electron materials.

Although the pairing glue for the attractive quasiparticle interaction responsible for unconventional superconductivity in heavy-electron materials has been identified as the spin fluctuations that arise from their proximity to a magnetic quantum critical point, there has been no model to describe their superconducting transition at temperature Tc that is comparable to that found by Bardeen, Cooper, and Schrieffer (BCS) for conventional superconductors, where phonons provide the pairing glue. Here we propose such a model: a phenomenological BCS-like expression for Tc in heavy-electron materials that is based on a simple model for the effective range and strength of the spin-fluctuation-induced quasiparticle interaction and reflects the unusual properties of the heavy-electron normal state from which superconductivity emerges. We show that it provides a quantitative understanding of the pressure-induced variation of Tc in the "hydrogen atoms" of unconventional superconductivity, CeCoIn5 and CeRhIn5, predicts scaling behavior and a dome-like structure for Tc in all heavy-electron quantum critical superconductors, provides unexpected connections between members of this family, and quantifies their variations in Tc with a single parameter.

An emerging global picture of heavy fermion physics.

Recent progresses using state-of-the-art experimental techniques have motivated a number of new insights on heavy fermion physics. This article gives a brief summary of the author's research along this direction. We discuss five major topics including: (1) development of phase coherence and two-stage hybridization; (2) two-fluid behavior and hidden universal scaling; (3) quantum phase transitions and fractionalized heavy fermion liquid; (4) quantum critical superconductivity; (5) material-specific properties. These cover the most essential parts of heavy fermion physics and lead to an emerging global picture beyond conventional theories based on mean-field or local approximations.

Systematic derivation of hydrodynamic equations for viscoelastic phase separation.

We present a detailed derivation of a simple hydrodynamic two-fluid model, which aims at the description of the phase separation of non-entangled polymer solutions, where viscoelastic effects play a role. It is directly based upon the coarse-graining of a well-defined molecular model, such that all degrees of freedom have a clear and unambiguous molecular interpretation. The considerations are based upon a free-energy functional, and the dynamics is split into a conservative and a dissipative part, where the latter satisfies the Onsager relations and the second law of thermodynamics. The model is therefore fully consistent with both equilibrium and non-equilibrium thermodynamics. The derivation proceeds in two steps: firstly, we derive an extended model comprising two scalar and four vector fields, such that inertial dynamics of the macromolecules and of the relative motion of the two fluids is taken into account. In the second step, we eliminate these inertial contributions and, as a replacement, introduce phenomenological dissipative terms, which can be modeled easily by taking into account the principles of non-equilibrium thermodynamics. The final simplified model comprises the momentum conservation equation, which includes both interfacial and elastic stresses, a convection-diffusion equation where interfacial and elastic contributions occur as well, and a suitably convected relaxation equation for the end-to-end vector field. In contrast to the traditional two-scale description that is used to derive rheological equations of motion, we here treat the hydrodynamic and the macromolecular degrees of freedom on the same basis. Nevertheless, the resulting model is fairly similar, though not fully identical, to models that have been discussed previously. Notably, we find a rheological constitutive equation that differs from the standard Oldroyd-B model. Within the framework of kinetic theory, this difference may be traced back to a different underlying statistical-mechanical ensemble that is used for averaging the stress. To what extent the model is able to reproduce the full phenomenology of viscoelastic phase separation is presently an open question, which shall be investigated in the future.

Microwave Measurements of Electromagnetic Properties of Materials.

A review of measurement methods of the basic electromagnetic parameters of materials at microwave frequencies is presented. Materials under study include dielectrics, semiconductors, conductors, superconductors, and ferrites. Measurement methods of the complex permittivity, the complex permeability tensor, and the complex conductivity and related parameters, such as resistivity, the sheet resistance, and the ferromagnetic linewidth are considered. For dielectrics and ferrites, the knowledge of their complex permittivity and the complex permeability at microwave frequencies is of practical interest. Microwave measurements allow contactless measurements of their resistivity, conductivity, and sheet resistance. These days contactless conductivity measurements have become more and more important, due to the progress in materials technology and the development of new materials intended for the electronic industry such as graphene, GaN, and SiC. Some of these materials, such as GaN and SiC are not measurable with the four-point probe technique, even if they are conducting. Measurement fixtures that are described in this paper include sections of transmission lines, resonance cavities, and dielectric resonators.

Feeding spent coffee grounds into reactors: TFM simulation of a non-mechanical spouted bed type feeder.

Due to the increasing coffee production, Spent Coffee Grounds' (SCGs) generation has grown dramatically, hence appropriate management of this solid biomass waste is imperative. SCGs can be used as feedstocks for renewable energy and fuel generation provided that a stable feeding of powders to reactors is maintained. Recently, a non-mechanical spouted bed feeder proved itself an excellent alternative in feeding SCGs to a pilot-scale circulating fluidized bed reactor. Nonetheless, further studies are necessary for the feeder's implementation in commercial applications. Here the feeding of SCGs with the spouted bed feeder is addressed by using Computational Fluid Dynamics. Firstly, a Two-Fluid Model (TFM) is validated against experimental data, and then the effects of five operating and design parameters were analyzed aiming at improving the handling of SCGs. The solids flowrate (WS) in the reactor could be stably controlled from 4 to 30 g/s depending on the settings. The feeder performance is enhanced by operating it under high gas flowrate (Q), high entrainment length (z), and high mass of solids in the feeder (HS). Using feeders with low cone angle (γ) or reactors with large diameter (DR) increases WS, which is appealing for the operation of medium-to large-scale units. The proposed TFM is a cost-effective tool for implementing spouted bed feeders in commercial applications. With the feeder coupled to the process, SCGs are treated continuously in the reactor for energy generation, thus reducing the disposal problems associated with this waste and improving the management of SCGs globally.

Shear Banding in 4:1 Planar Contraction.

We study shear banding in a planar 4:1 contraction flow using our recently developed two-fluid model for semidilute entangled polymer solutions derived from the generalized bracket approach of nonequilibrium thermodynamics. In our model, the differential velocity between the constituents of the solution allows for coupling between the viscoelastic stress and the polymer concentration. Stress-induced migration is assumed to be the triggering mechanism of shear banding. To solve the benchmark problem, we used the OpenFOAM software package with the viscoelastic solver RheoTool v.2.0. The convection terms are discretized using the high-resolution scheme CUBISTA, and the governing equations are solved using the SIMPLEC algorithm. To enter into the shear banding regime, the uniform velocity at the inlet was gradually increased. The velocity increases after the contraction due to the mass conservation; therefore, shear banding is first observed at the downstream. While the velocity profile in the upstream channel is still parabolic, the corresponding profile changes to plug-like after the contraction. In agreement with experimental data, we found that shear banding competes with flow recirculation. Finally, the profile of the polymer concentration shows a peak in the shear banding regime, which is closer to the center of the channel for larger inlet velocities. Nevertheless, the increase in the polymer concentration in the region of flow recirculation was significantly larger for the inlet velocities studied in this work. With our two-fluid finite-volume solver, localized shear bands in industrial applications can be simulated.

Effect of Varying Viscosity on Two-Fluid Model of Blood Flow through Constricted Blood Vessels: A Comparative Study.

PURPOSE: Most of the previously studied non-Newtonian blood flow models considered blood viscosity to be constant but for correct measurement of flow rate and flow resistance, the hematocrit dependent viscosity will be better as various literature suggested the variable nature of blood viscosity. Present work concerns the steady and pulsatile nature of blood flow through constricted blood vessels. Two-fluid model for blood is considered with the suspension of all the RBCs (erythrocytes) in the core region as a non-Newtonian (Herschel-Bulkley) fluid and the plasma in the cell free region near wall as a Newtonian fluid. No slip condition on the wall and radially varying viscosity has been taken. METHODS: For steady flow the analytical approach has been taken to obtain the exact solution. Regular perturbation expansion method has been used to solve the governing equations for pulsatile flow up to first order of approximation by assuming the pulsatile Reynolds number to be very small (much less than unity). RESULTS: Flow rate, wall shear stress and velocity profile have been graphically analyzed and compared with constant viscosity model. A noteworthy observation of the present study is that rise in viscosity index leads to decay in velocity, velocity of plug flow region, flow rate while flow resistance increases with rising viscosity index (m). The results for Power-law fluid (PL), Bingham-plastic fluid (BP), Newtonian fluid (NF) are found as special cases from this model. Like the constant viscosity model, it has been also observed that the velocity, flow rate and plug core velocity of two-fluid model are higher than the single-fluid model for variable viscosity. CONCLUSIONS: The two-phase fluid model is more significant than the single-fluid model. Effect of viscosity parameter on various hemodynamical quantities has been obtained. It is also concluded that a rising viscosity parameter (varying nature of viscosity) significantly distinguishes the single and two-fluid models in terms of changes in blood flow resistance. The outcome of present study may leave a significant impact on analyzing blood flow through small blood vessels with constriction, where correct measurement of flow rate and flow resistance for medical treatment is very important.

Sensitivity Analysis and Accuracy of a CFD-TFM Approach to Bubbling Bed Using Pressure Drop Fluctuations.

Based upon the two fluid model (TFM) theory, a CFD model was implemented to investigate a cold multiphase-fluidized bubbling bed reactor. The key variable used to characterize the fluid dynamic of the experimental system, and compare it to model predictions, was the time-pressure drop induced by the bubble motion across the bed. This time signal was then processed to obtain the power spectral density (PSD) distribution of pressure fluctuations. As an important aspect of this work, the effect of the sampling time scale on the empirical power spectral density (PSD) was investigated. A time scale of 40 s was found to be a good compromise ensuring both simulation performance and numerical validation consistency. The CFD model was first numerically verified by mesh refinement process, after what it was used to investigate the sensitivity with regards to minimum fluidization velocity (as a calibration point for drag law), restitution coefficient, and solid pressure term while assessing his accuracy in matching the empirical PSD. The 2D model provided a fair match with the empirical time-averaged pressure drop, the relating fluctuations amplitude, and the signal's energy computed as integral of the PSD. A 3D version of the TFM was also used and it improved the match with the empirical PSD in the very first part of the frequency spectrum.

Study on the distribution characteristics of aerosol produced by powder dumping in glove box / 中国辐射卫生

Objective To investigate the effects of particle size, wind speed and dumping velocity on aerosol concentration distribution during powder dumping in a reprocessing plant. Methods CeO2 powder was selected as the substitute material of PuO2. FLUENT software was used to calculate the pouring process of CeO2 powder under different operation conditions. Then the aerosol concentration distribution under different dumping speeds was measured by particle size spectrometer to verify the accuracy of simulation results. Results The particles with small particle size are more likely to be separated from the mainstream area by the drag force of the surrounding gas, and the radius of the diffusion range also increases with the decrease of the particle size. 2) When the ventilation speed is less than 1 m/s, the dust lifting can be reduced and the concentration of dust particles in the chamber can be reduced to a certain extent. 3) In the process of powder dumping, the spoon is rotated anticlockwise at a speed of 100° in 2～3 s, and less dust aerosol is produced on the right side of the tray. Conclusion When operating the powder particles with smaller particle size, more attention should be paid to the monitoring of aerosol at different positions; the change of air inlet velocity makes the flow field in glove box more complex, and the volume fraction of dust particles is related to the size and location of vortex formed by airflow. The greater the wind speed, the greater the impact on the powder dumping process. The experimental results are basically consistent with the simulation results, and the results show that the lower the dumping speed, the smaller the aerosol concentration near the tray.

An Immersed Boundary Method for Two-fluid Mixtures.

We present an Immersed Boundary method for interactions between elastic boundaries and mixtures of two fluids. Each fluid has its own velocity field and volume-fraction. A penalty method is used to enforce the condition that both fluids' velocities agree with that of the elastic boundaries. The method is applied to several problems: Taylor's swimming sheet problem for a mixture of two viscous fluids, peristaltic pumping of a mixture of two viscous fluids, with and without immersed particles, and peristaltic pumping of a mixture of a viscous fluid and a viscoelastic fluid. The swimming sheet and peristalsis problems have received much attention recently in the context of a single viscoelastic fluid. Numerical results demonstrate that the method converges and show its capability to handle a number of flow problems of substantial current interest. They illustrate that for each of these problems, the relative motion between the two fluids changes the observed behaviors profoundly compared to the single fluid case.