Functionals in stochastic thermodynamics: how to interpret stochastic integrals

In stochastic thermodynamics standard concepts from macroscopic thermodynamics, such as heat, work, and entropy production, are generalized to small fluctuating systems by defining them on a trajectory-wise level. In Langevin systems with continuous state-space such definitions involve stochastic integrals along system trajectories, whose specific values depend on the discretization rule used to evaluate them (i.e. the 'interpretation' of the noise terms in the integral). Via a systematic mathematical investigation of this apparent dilemma, we corroborate the widely used standard interpretation of heat-and work-like functionals as Stratonovich integrals. We furthermore recapitulate the anomalies that are known to occur for entropy production in the presence of temperature gradients

Computational assessment of the effects of a pulsatile pump on toxin removal in blood purification

<p>Abstract</p> <p>Background</p> <p>For blood purification systems using a semipermeable membrane, the convective mass transfer by ultrafiltration plays an important role in toxin removal. The increase in the ultrafiltration rate can improve the toxin removal efficiency of the device, ultimately reducing treatment time and cost. In this study, we assessed the effects of pulsatile flow on the efficiency of the convective toxin removal in blood purification systems using theoretical methods.</p> <p>Methods</p> <p>We devised a new mathematical lumped model to assess the toxin removal efficiency of blood purification systems in patients, integrating the mass transfer model for a human body with a dialyser. The human body model consists of a three-compartment model of body fluid dynamics and a two-compartment model of body solute kinetics. We simulated three types of blood purification therapy with the model, hemofiltration, hemodiafiltration, and high-flux dialysis, and compared the simulation results in terms of toxin (urea and beta-2 microglobulin) clearance and the treatment dose delivered under conditions of pulsatile and non-pulsatile pumping. <it>In vivo </it>experiments were also performed to verify the model results.</p> <p>Results</p> <p>Simulation results revealed that pulsatile flow improved the convective clearance of the dialyser and delivered treatment dose for all three types of therapy. Compared with the non-pulsatile pumping method, the increases in the clearance of urea and beta-2 microglobulin with pulsatile pumping were highest with hemofiltration treatment (122.7% and 122.7%, respectively), followed by hemodiafiltration (3.6% and 8.3%, respectively), and high-flux dialysis (1.9% and 4.7%, respectively). EKRc and std Kt/V averaged 28% and 23% higher, respectively, in the pulsatile group than in the non-pulsatile group with hemofiltration treatment.</p> <p>Conclusions</p> <p>The pulsatile effect was highly advantageous for all of the toxins in the hemofiltration treatment and for β₂-microglobulin in the hemodiafiltration and high-flux dialysis treatments.</p

Development and testing of a Jatropha fruit shelling process for shell-free kernel recovery in biodiesel production

Achieving shell-free kernel recovery from Jatropha fruits is important to improve oil yield and oil quality during oil extraction in biodiesel production. A shelling process with two stages of cracking and separation to remove the shells completely and husks partially was designed. Both stages used double-level cracking rollers and a blower with ducting as a separation unit. For the first, the performance was evaluated using five different roller clearances (9.5 mm, 10.0 mm, 10.5 mm, 11.0 mm and 11.5 mm) with a combination of five blower air speeds (8.5 ± 0.5 m s−1, 9.0 ± 0.6 m s−1, 9.5 ± 0.5 m s−1, 10.0 ± 0.4 m s−1 and 10.5 ± 0.5 m s−1). A roller clearance of 10.5 mm and air speed of 10.0 ± 0.4 m s−1 were selected as the optimal conditions with the highest separation efficiency between kernels and shells at 94.59%. The shells and husks achieved 95.88% and 12.20% removal respectively while kernel recovery achieved 98.65%. For the second stage, the performance was evaluated using five different roller clearances (5.0 mm, 5.5 mm, 6.0 mm, 6.5 mm and 7.0 mm) with a combination of five blower air speeds (6.5 ± 0.4 m s−1, 7.0 ± 0.2 m s−1, 7.5 ± 0.4 m s−1, 8.0 ± 0.2 m s−1 and 8.5 ± 0.5 m s−1). At the optimal conditions, with a roller clearance of 6.0 mm and air speed of 7.5 ± 0.4 m s−1, the maximum separation efficiency was 97.69%. Total shell and husk removal achieved for the stages were 100.00% and 45.46% respectively. A total of 2.40% kernels were lost

Modeling and simulation of heat of mixing in lithium ion batteries

poster abstractHeat generation is a major safety concern in the design and development of lithium ion batteries (LIBs) for large scale applications, such as electric vehicles. The total heat generation in LIBs includes entropic heat, enthalpy, reaction heat, and heat of mixing (1-3). The heat of mixing will be released during relaxation of Li ion concentration gradient. For instance, after the drivers turn off their vehicles, the generation of entropy, enthalpy and reaction heat in LIBs will stop, but the heat of mixing is still being generated. Thomas and Newman derived methods to compute heat of mixing in LIB cells and investigated the heat of mixing on a Li|LiPF6 in ethylene carbonate:dimethyl carbonate|LiAl0.2Mn1.8O4-δF0.2 cell (4). The objective of this study is to investigate the influence of heat of mixing on the LIBs with different materials, porosities, particle sizes, and charge/discharge rate and to understand whether it is necessary to consider heat of mixing during the design and development of LIBs. In this study, a mathematical model was built to simulate heat generation of LIBs using COMSOL Multiphysics. The LIB model was based on Newman’s model. LiCoO2 was applied as the cathode materials, and LiC6 was applied as the anode material. The results of heat of mixing were compared with the other heat sources to investigate the weight of heat of mixing in the total heat generation. Table 1 shows the heat of mixing, irreversible heat, and reversible heat in anode and cathode electrodes at 5 min during a 2 C discharge process. As shown in Table 1, the heat of mixing in cathode is smaller than the heat of mixing in anode, mainly due to the lower Li ion diffusivity and larger particle size of LiC6. The heat of mixing is not as much as the irreversible heat and reversible heat, but it cannot be neglected for this operating condition. The heat of mixing in different LIB cells and under different operating conditions will be reported. The mathematical model: Mathematical model equations: = ( − ) + + Σ Δ + Σ Σ ( − ) = [ 1 2 ∙ ( − ,∞)] =

Simulation of Heat Generation in a Reconstructed LiCoO2 Cathode during Galvanostatic Discharge

A three dimensional numerical framework with finite volume method was employed to simulate heat generation of a semi lithium ion battery (LIB) cell during isothermal galvanostatic discharge processes. The microstructure of the LIB cathode electrode was experimentally determined using X-ray nano computed tomography technology. Heat generation in the semi LIB cell during galvanostatic discharge processes from different mechanisms, such as electronic resistive heat, ionic resistive heat, contact resistive heat, reaction heat, entropic heat and heat of mixing, was investigated. The spatial distribution of heat generation rates from different mechanisms was also studied. The simulation results demonstrate that the magnitude of heat generation rates spans a wide range in the electrode due to structural inhomogeneity. The simulation results of heat generation from the three dimensional model and the porous-electrode theory model were compared in this study. It is found that the typical Bruggeman coefficient, 1.5, underestimated ionic resistance in the electrolyte and overestimated electronic resistance in the cathode particles. In general, the three dimensional model predicted more heat generation than the porous-electrode theory model at large discharge rates due to the wider distribution of physical and electrochemical properties

Polarization Analysis Based on Realistic Lithium Ion Battery Electrode Microstructure Using Numerical Simulation

poster abstractThe performance of lithium ion battery (LIB) is limited by the inner polarization and it is important to understand the factors that affect the polarization. This study focuses on the polarization analysis based on realistic 3D electrode microstructures. A c++ software was developed to rebuild and mesh the microstructure of cathode and anode electrodes through Nano-CT and Micro-CT scanned images respectively. As a result, the LIB model was composed of electrolyte, cathode and anode active materials and current collectors. By employing 3D finite volume method (FVM), another c++ code was developed to simulate the discharge and charge processes by solving coupled model equations. The simulation revealed the distribution of physical and electrochemical variables such as concentration, voltage, current density, reaction rate, et al. In order to explore the correlation of local effects and electrode structural heterogeneity, the cathode electrode were divided equally into 8 sub-divisions, of which the porosity, tortuosity, specific surface area were calculated. We computed the polarizations in the sub-divisions due to different sub-processes, i.e., the activation of electrochemical reactions and charge transport of species. As shown in Fig. 1, the tortuosity is very irregular because of unevenly distributed cathode particle size and packing pattern with low porosity. There are no exact and direct relations among porosity, tortuosity and specific surface area. Fig. 2 shows that the polarizations are related to the porosity in sub-divisions. The knowledge from the study will help to figure out the mechanism of polarization and power loss in LIB, which could be useful to improve LIB design and manufacturing. Acknowledgments: This work was supported by US National Science Foundation under Grant No. 1335850. Fig. 1 Porosity and tortuosity in sub-divisions of a cathode electrode Fig. 2 Intercalation reaction polarization and ionic conduction polarization of sub-divisions at 120 sec during a 5 C charging proces