A Homogenization Approach for the Roasting of an Array of Coffee Beans

While the processes underlying the roasting of a single coffee bean have been the focus of a number of recent studies, the more industrially relevant problem of roasting an array of coffee beans has not been well studied from a modeling standpoint. Starting with a microscale model for the heat and mass transfer processes within a single bean during roasting, we apply homogenization theory to upscale this model to an effective macroscale model for the roasting of an array of coffee beans. We then numerically simulate this effective model for two caricatures of roasting configurations which are of great importance to industrial scale coffee bean roasting: namely, drum roasters (where the beans are placed in a rotating drum) and fluidized bed roasters (where hot air is blown through the beans). The derivation of the homogenization problem has been carried out in a three-dimensional rectangular geometry. Simulations are presented both for simplified one-dimensional arrays of three-dimensional beans (as these are easier to visualize), as well as cross sections of full three-dimensional arrays of beans (for the sake of verification). We also verify our simulation results against experimental data from the literature. Among the findings is that increasing the air-to-bean volume fraction ratio decreases the drying time for the array of beans in a linear manner. We also find that, in the case of a fluidized bed, an increase in the hot air inflow velocity will decrease the drying time in a nonlinear manner, with diminishing returns observed beyond some point for large enough air inflow velocities

Accounting for cross-immunity can improve forecast accuracy during influenza epidemics

Previous exposure to influenza viruses confers cross-immunity against future infections with related strains. However, this is not always accounted for explicitly in mathematical models used for forecasting during influenza outbreaks. We show that, if an influenza outbreak is due to a strain that is similar to one that has emerged previously, then accounting for cross-immunity explicitly can improve the accuracy of real-time forecasts. To do this, we consider two infectious disease outbreak forecasting models. In the first (the “1-group model”), all individuals are assumed to be identical and cross-immunity is not accounted for. In the second (the “2-group model”), individuals who have previously been infected by a related strain are assumed to be less likely to experience severe disease, and therefore recover more quickly, than immunologically naive individuals. We fit both models to estimated case notification data (including symptomatic individuals as well as laboratory-confirmed cases) from Japan from the 2009 H1N1 influenza pandemic, and then generate synthetic data for a future outbreak by assuming that the 2-group model represents the epidemiology of influenza infections more accurately. We use the 1-group model (as well as the 2-group model for comparison) to generate forecasts that would be obtained in real-time as the future outbreak is ongoing, using parameter values estimated from the 2009 epidemic as informative priors, motivated by the fact that without using prior information from 2009, the forecasts are highly uncertain. In the scenario that we consider, the 1-group model only produces accurate outbreak forecasts once the peak of the epidemic has passed, even when the values of important epidemiological parameters such as the lengths of the mean incubation and infectious periods are known exactly. As a result, it is necessary to use the more epidemiologically realistic 2-group model to generate accurate forecasts. Accounting for cross-immunity driven by exposures in previous outbreaks explicitly is expected to improve the accuracy of epidemiological modelling forecasts during influenza outbreaks

The risk of SARS-CoV-2 outbreaks in low prevalence settings following the removal of travel restrictions

Background Countries around the world have introduced travel restrictions to reduce SARS-CoV-2 transmission. As vaccines are gradually rolled out, attention has turned to when travel restrictions and other non-pharmaceutical interventions (NPIs) can be relaxed. Methods Using SARS-CoV-2 as a case study, we develop a mathematical branching process model to assess the risk that, following the removal of NPIs, cases arriving in low prevalence settings initiate a local outbreak. Our model accounts for changes in background population immunity due to vaccination. We consider two locations with low prevalence in which the vaccine rollout has progressed quickly – specifically, the Isle of Man (a British crown dependency in the Irish Sea) and the country of Israel. Results We show that the outbreak risk is unlikely to be eliminated completely when travel restrictions and other NPIs are removed. This general result is the most important finding of this study, rather than exact quantitative outbreak risk estimates in different locations. It holds even once vaccine programmes are completed. Key factors underlying this result are the potential for transmission even following vaccination, incomplete vaccine uptake, and the recent emergence of SARS-CoV-2 variants with increased transmissibility. Conclusions Combined, the factors described above suggest that, when travel restrictions are relaxed, it may still be necessary to implement surveillance of incoming passengers to identify infected individuals quickly. This measure, as well as tracing and testing (and/or isolating) contacts of detected infected passengers, remains useful to suppress potential outbreaks while global case numbers are high

Infection, inflammation and intervention: mechanistic modelling of epithelial cells in COVID-19

While the pathological mechanisms in COVID-19 illness are still poorly understood, it is increasingly clear that high levels of pro-inflammatory mediators play a major role in clinical deterioration in patients with severe disease. Current evidence points to a hyperinflammatory state as the driver of respiratory compromise in severe COVID-19 disease, with a clinical trajectory resembling acute respiratory distress syndrome, but how this ‘runaway train’ inflammatory response emerges and is maintained is not known. Here, we present the first mathematical model of lung hyperinflammation due to SARS-CoV-2 infection. This model is based on a network of purported mechanistic and physiological pathways linking together five distinct biochemical species involved in the inflammatory response. Simulations of our model give rise to distinct qualitative classes of COVID-19 patients: (i) individuals who naturally clear the virus, (ii) asymptomatic carriers and (iii–v) individuals who develop a case of mild, moderate, or severe illness. These findings, supported by a comprehensive sensitivity analysis, point to potential therapeutic interventions to prevent the emergence of hyperinflammation. Specifically, we suggest that early intervention with a locally acting anti-inflammatory agent (such as inhaled corticosteroids) may effectively blockade the pathological hyperinflammatory reaction as it emerges

Optimisation of Fluid Mixing in a Hydrosacc⃝ Growing Module

A mathematical model is sought for the flow of nutrients in the Hydrosac⃝c growing module being developed by Phytoponics. The basic operation involves long fluid-filled bags with periodic growing zones from which root systems emerge into the bulk fluid. The system is periodically perturbed via two main processes: partial drainage and refilling of each bag with nutrient infused water, with inlet and outlet at opposite ends of the bag; and a more violent oxygenation of the water through bubbles that rise from the pores of an aeration tube that runs underneath the central long axis of the bag. The aim of the modelling is to determine the key parameters and fluid regimes underlying the nutrient mixing process, to ensure that required nutrient levels are maintained through- out the root zones, and to enable optimal scheduling of the nutrient and bubble flow. Simple experiments were performed via the injection of dye into an operating Hydrosac⃝c that contained semi-mature plants. This enabled a basic understanding of the time and lengthscales of nutrient flow, and also the extent to which mixing occurs in different zones within the bag. Four different flow regimes are identified. At the scale of a single root, a Stokes-flow approximation may be used. At the scale of the individual plant, a so-called Brinkman flow regime may be employed which is describes a transition between slow porous- medium flow and fast channel flow. These equations may be homogenised into a 1D model that can be used to estimate the macro-scale flow of nutrients along the length of the bag. A shear flow model is used to predict the extent to which this flow permeates into regions dominated by plant roots. This leads to the requirement to model the bubble-driven flow within a bag cross-section containing a plant. Simplified two-phase flow equations are de- rived and solved within the software COMSOL. The results suggest that the bubble flow is sufficient to drive recirculating flow, which is also found to be consistent with previous literature. The overall conclusion is that both the periodic flow of nutrients and the aeration are re- quired in order to enable even nutrient spread in the Hydrosac⃝c . Wave effects can be ignored, as can the effect of stagnated nutrient diffusion. The longitudinal nutrient flow enables the whole sack to be reached on the time scale of several cycles of the main inlet flow, while the recirculation from the bubble flow enables enables nutrients to spread within the plant roots. Nevertheless, regions of stagnation can occur via this process near any sharp corners of the bag. It is recommend that the various analyses are combined into a a reduced-order mathemat- ical model that can be used to optimise the dynamic operation of the Hydrosac⃝c , which can also be adaptable to other geometries and growing conditions