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Register a new userA Mathematical Model for Flash Sintering
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A mathematical model is presented for the Joule heating that occurs in a ceramic powder compact during the process of flash sintering. The ceramic is assumed to have an electrical conductivity that increases with temperature, and this leads to the possibility of runaway heating that could facilitate and explain the rapid sintering seen in experiments. We consider reduced models that are sufficiently simple to enable concrete conclusions to be drawn about the mathematical nature of their solutions. In particular we discuss how different local and non-local reaction terms, which arise from specified experimental conditions of fixed voltage and current, lead to thermal runaway or to stable conditions. We identify incipient thermal runaway as a necessary condition for the flash event, and hence identify the conditions under which this is likely to occur.
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A new flash (ultra-rapid) spark plasma sintering method applicable to various materials systems, regardless of their electrical resistivity, is developed. A number of powders ranging from metals to electrically insulative ceramics have been successfully densified resulting in homogeneous microstructures within sintering times of 8-35 s. A finite element simulation reveals that the developed method, providing an extraordinary fast and homogeneous heating concentrated in the samples volume and punches, is applicable to all the different samples tested. The utilized uniquely controllable flash phenomenon is enabled by the combination of the electric current concentration around the sample and the confinement of the heat generated in this area by the lateral thermal contact resistance. The presented new method allows: extending flash sintering to nearly all materials, controlling sample shape by an added graphite die, and an energy efficient mass production of small and intermediate size objects. This approach represents also a potential venue for future investigations of flash sintering of complex shapes.
A one dimensional (1-D), isothermal model for a direct methanol fuel cell (DMFC) is presented. This model accounts for the kinetics of the multi-step methanol oxidation reaction at the anode. Diffusion and crossover of methanol are modeled and the mixed potential of the oxygen cathode due to methanol crossover is included. Kinetic and diffusional parameters are estimated by comparing the model to data from a 25 cm2 DMFC. This semi-analytical model can be solved rapidly so that it is suitable for inclusion in real-time system level DMFC simulations.
Background: Experiments have reported low normal tissue toxicities during FLASH radiation, but the mechanism has not been elaborated. Several hypotheses have been proposed to explain the mechanism. The oxygen depletion hypothesis has been introduced and mostly studied qualitatively. Methods: We present a computational model to describe the time-dependent change of oxygen concentration in the tissue. The kinetic equation of the model is solved numerically using the finite difference method. The model is used to analyze the FLASH effect with the oxygen depletion hypothesis, and the brain tissue is chosen as an example. Results: The oxygen distribution is determined by the oxygen consumption rate of the tissue and the distance between capillaries. The change of oxygen concentration with time after radiation has been found to follow a negative exponential function, and the time constant is determined by the distance between capillaries. When the dose rate is high enough, the same dose results in the same change of oxygen concentration regardless of dose rate. The analysis of FLASH effect in the brain tissue based on this model does not support the explanation of the oxygen depletion hypothesis. Conclusions: The oxygen depletion hypothesis remains controversial because oxygen in most normal tissues cannot be depleted by FLASH radiation according to the mathematical analysis with this model and experiments on the expression and distribution of the hypoxia-inducible factors.
In this article, we study the strong well-posedness, stability and optimal control of an incompressible magneto-viscoelastic fluid model in two dimensions. The model consists of an incompressible Navier--Stokes equation for the velocity field, an evolution equation for the deformation tensor, and a gradient flow equation for the magnetization vector. First, we prove that the model under consideration posseses a global strong solution in a suitable functional framework. Second, we derive stability estimates with respect to an external magnetic field. Based on the stability estimates we use the external magnetic field as the control to minimize a cost functional of tracking-type. We prove existence of an optimal control and derive first-order necessary optimality conditions. Finally, we consider a second optimal control problem, where the external magnetic field, which represents the control, is generated by a finite number of fixed magnetic field coils.
Flash sintering phenomena are predominantly associated with ceramics due to thermal runaway of their electric conductivity noticeably represented in materials such as zirconia or silicon carbide. Because of their high electric conductivity, flash sintering of metals is nearly inexistent. In this work, an original metal powder flash sintering method based on a microwave approach is presented. Within the developed approach, an unusually fast (60 s) thermal and sintering runaway of Ti-6Al-4V powder is experimentally revealed under microwave illumination. This phenomenon is simulated based on an electromagnetic-thermal-mechanical (EMTM) model. The developed multiphysics model reveals that the metal powder specimens runaway does not result from its intrinsic material properties, but results from the resonance phenomenon thermally activated by the surrounding tooling material. The EMTM simulation predicts with a very good accuracy the microwave repartition and the resulting densification and powder specimens shape distortions observed experimentally. The comparison of the microwave and conventional sintering kinetics indicates an important acceleration of the sintering behavior under microwave heating. The developed sintering approach has a potential of the implementation for time-effective mass production of small metal parts.
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