This paper reports a discharge model for lithium sulfur (Li-S) battery cells, supported by a multi-scale description of the composite C/S cathode microstructure. The cathode is assumed to be composed of mesoporous carbon particles with inter-particular pores in-between and the sulfur impregnated into both types of pores. The electrolyte solutes such as sulfur, polysulfides and lithium ions, produced during the discharge, are allowed to exchange between the pores. Furthermore, the model describes the Li 2 S (solid) precipitation and its effects on transport and reduction reaction kinetics. Hereby it provides fundamental insights on the impact on the Li-S discharge curve of practically modifiable manufacturing parameters and operation designs, such as current density, carbon porosity, C/S ratio and sizes of carbon particles and pores. Lithium-ion battery technologies based on dual intercalation electrodes have come to totally dominate the consumer electronics market for mobile devices.1,2 However their capacities still limit the driving ranges and user modes for both electric and hybrid electric vehicles, 3 despite approaching the intrinsic maximum for intercalation reactions. 4,5 With the demand for batteries with even higher capacities, lithium sulfur (Li-S) batteries, 6,7 with a theoretical capacity of 1672 mAh.g −1 based on cathode solid sulfur mass 8 and a potential gravimetric energy density of about 600 Wh.kg −1 , 9 has (re-)gained attention in recent years.10-23 Li-S batteries usually have a lithium metal anode, a porous separator, and a porous C/S composite cathode where the carbon acts as a host and provides electronic wiring for the insulating sulfur, existing as S 8(solid) and Li 2 S (solid) . The pores in both the cathode and the separator are filled with an aprotic electrolyte, e.g. 1 M LiTFSI dissolved in dimethoxyethane (DME): 1,3-dioxolane (DOL) (1:1 volume ratio). 24 There is a general consensus that the reasons behind the theoretical capacity of Li-S batteries not being achieved are short-comings: low sulfur utilization due to poor wiring and soluble polysulfide intermediates giving rise to a parasitic shuttle effect. 25,26 One breakthrough in the last decade was the finding that a host of mesoporous carbon greatly enhanced the active material utilization as compared to a ground C/S mixture. 5 The mesoporous architecture of the cathode primarily assisted in retaining polysulfide intermediates in the cathode. 27Theory and mathematical modeling are powerful tools to assist the optimization of electrochemical devices, by providing insight in operating principles and identifying limitations. [28][29][30] Continuum models applied to Li-S batteries have been successful in simulating various battery operation phenomena. [31][32][33][34][35][36][37] However, most of the continuum models reported so far model the cathode as a homogenous porous medium, described by an effective porosity, not accounting for the * Electrochemical Society Member.h Present address: Institut Charles Gerhardt, CNRS and Univers...

A mathematical model was developed describing the dynamic of the COVID-19 virus over a population considering that the infected can either be symptomatic or not. The model was calibrated using data on the confirmed cases and death from several countries like France, Philippines, Italy, Spain, United Kingdom, China, and the USA. First, we derived the basic reproduction number, R0, and estimated the effective reproduction Reff for each country. Second, we were interested in the merits of interventions, either by distancing or by treatment. Results revealed that total and partial containment is effective in reducing the transmission. However, its duration may be long to eradicate the disease (104 days for France). By setting the end of containment as the day when hospital capacity is reached, numerical simulations showed that the duration can be reduced (up to only 39 days for France if the capacity is 1000 patients). Further, results pointed out that the effective reproduction number remains large after containment. Therefore, testing and isolation are necessary to stop the disease.