91 research outputs found
The effect of pore-scale contaminant distribution on the reactive decontamination of porous media
A porous material that has been contaminated with a hazardous chemical agent is typically decontaminated by applying a cleanser solution to the surface and allowing the cleanser to react into the porous material, neutralising the agent. The agent and cleanser are often immiscible fluids and so, if the porous material is initially saturated with agent, a reaction front develops with the decontamination reaction occurring at this interface between the fluids. We investigate the effect of different initial agent configurations within the pore space on the decontamination process. Specifically, we compare the decontamination of a material initially saturated by the agent with the situation when, initially, the agent only coats the walls of the pores (referred to as the âagent-on-wallsâ case). In previous work (Luckins et al., European Journal of Applied Mathematics, 31(5):782â805, 2020), we derived homogenised models for both of these decontamination scenarios, and in this paper we explore the solutions of these two models. We find that, for an identical initial volume of agent, the decontamination time is generally much faster for the agent-on-walls case compared with the initially saturated case, since the surface area on which the reaction can occur is greater. However for sufficiently deep spills of contaminant, or sufficiently slow reaction rates, decontamination in the agent-on-walls scenario can be slower. We also show that, in the limit of a dilute cleanser with a deep initial agent spill, the agent-on-walls model exhibits behaviour akin to a Stefan problem of the same form as that arising in the initially saturated model. The decontamination time is shown to decrease with both the applied cleanser concentration and the rate of the chemical reaction. However, increasing the cleanser concentration is also shown to result in lower decontamination efficiency, with an increase in the amount of cleanser chemical that is wasted
Asymptotic solution of a model for bilayer organic diodes and solar cells
Organic diodes and solar cells are constructed by placing together two organic semiconducting materials with dissimilar electron affinities and ionization potentials. The electrical behavior of such devices has been successfully modeled numerically using conventional drift diffusion together with recombination (which is usually assumed to be bimolecular) and thermal generation. Here a particular model is considered and the dark current-voltage curve and the spatial structure of the solution across the device is extracted analytically using asymptotic methods. We concentrate on the case of Shockley-Read-Hall recombination but note the extension to other recombination mechanisms. We find that there are three regimes of behavior, dependent on the total current. For small currents-i.e., at reverse bias or moderate forward bias-the structure of the solution is independent of the total current. For large currents-i.e., at strong forward bias-the current varies linearly with the voltage and is primarily controlled by drift of charges in the organic layers. There is then a narrow range of currents where the behavior undergoes a transition between the two regimes. The magnitude of the parameter that quantifies the interfacial recombination rate is critical in determining where the transition occurs. The extension of the theory to organic solar cells generating current under illumination is discussed as is the analogous current-voltage curves derived where the photo current is small. Finally, by comparing the analytic results to real experimental data, we show how the model parameters can be extracted from the shape of current-voltage curves measured in the dark. © 2012 Society for Industrial and Applied Mathematics
Need a Lift? An Elevator Queueing Problem
Various aspects of the behavior and dispatching of elevators (lifts) were studied. Monte Carlo simulation was used to study the statistics of the several models for the peak demand at uppeak times. Analytical models problems were used to prove or disprove whether schemes were optimal. A mostly integer programming problem was formulated but not studied further
Shape optimization of pressurized air bearings
Use of externally pressurized air bearings allows for the design of mechanical systems requiring extreme precision in positioning. One application is the fine control for the positioning of mirrors in large-scale optical telescopes. Other examples come from applications in robotics and computer hard-drive manufacturing. Pressurized bearings maintain a finite separation between mechanical components by virtue of the presence of a pressurized flow of air through the gap between the components. An everyday example is an air hockey table, where a puck is levitated above the table by an array of vertical jets of air. Using pressurized bearings there is no contact between âmoving partsâ and hence there is no friction and no wear of sensitive components.
This workshop project is focused on the problem of designing optimal static air bearings subject to given engineering constraints. Recent numerical computations of this problem, done at IBM by Robert and Hendriks, suggest that near-optimal designs can have unexpected complicated and intricate structures. We will use analytical approaches to shed some light on this situation and to offer some guides for the design process.
In Section 2 the design problem is stated and formulated as an optimization problem for an elliptic boundary value problem.
In Section 3 the general problem is specialized to bearings with rectangular bases.
Section 4 addresses the solutions of this problem that can be obtained using variational formulations of the problem.
Analysis showing the sensitive dependence to perturbations (in numerical computations or manufacturing constraints) of near-optimal designs is given in Section 5.
In Section 6, a restricted class of âgroove networkâ designs motivated by the original results of Robert and Hendriks is examined.
Finally, in Section 7, we consider the design problem for circular axisymmetric air bearings
Underreamer mechanics
In the oil and gas industry, an underreamer is a tool used to extend and enlarge the diameter of a previously-drilled bore. The problem proposed to the Study Group is to obtain appropriate mathematical models of underreamer dynamics, in forms that will lead to feasible computation. The modes of dynamics of interest are torsional, lateral and axial.
This report describes some initial models, two of which are developed in more detail: one for the propagation of torsional waves along the drill string and their reflection from contact points with the well bore; and one for the dynamic coupling between the underreamer and the drill bit during drilling
Human Decompression Modelling
At present, no decompression algorithm is able to predict safe decompression for all dive scenarios. In practice, empirical adjustments are made by experienced organisations or divers in order to improve decompression profiles for the range of depths and durations needed on any particular dive. Bubble formation and growth in the human body are the fundamental causes of decompression sickness, and it is believed that there is significant scope for incorporating better modelling of these processes into the design of decompression algorithms.
VR Technology is a leading supplier of technical dive computers. The company is interested in expanding upon an existing algorithm (the Variable Gradient Model - VGM), which is used to design ascent profiles/decompression schedules and thereby mitigate the risk of decompression sickness in divers.
The Study Group took the approach of trying to extend the existing Haldane model to account more explicitly for the formation of bubbles. By extending the model to include bubble dynamics it was expected that some physical understanding could be gained for the existing modifications to some of the parameters. The modelling that occurred consisted of first looking at the Haldane model and then considering a single small isolated bubble in each of the compartments and interpreting the predictions of the model in terms of decompression profiles
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