Turbulent shear layers in confining channels

We present a simple model for the development of shear layers between parallel flows in confining channels. Such flows are important across a wide range of topics from diffusers, nozzles and ducts to urban air flow and geophysical fluid dynamics. The model approximates the flow in the shear layer as a linear profile separating uniform-velocity streams. Both the channel geometry and wall drag affect the development of the flow. The model shows good agreement with both particle-image-velocimetry experiments and computational turbulence modelling. The low computational cost of the model allows it to be used for design purposes, which we demonstrate by investigating optimal pressure recovery in diffusers with non-uniform inflow

Predicting drug pharmacokinetics and effect in vascularized tumors using computer simulation

In this paper, we investigate the pharmacokinetics and effect of doxorubicin and cisplatin in vascularized tumors through two-dimensional simulations. We take into account especially vascular and morphological heterogeneity as well as cellular and lesion-level pharmacokinetic determinants like P-glycoprotein (Pgp) efflux and cell density. To do this we construct a multi-compartment PKPD model calibrated from published experimental data and simulate 2-h bolus administrations followed by 18-h drug washout. Our results show that lesion-scale drug and nutrient distribution may significantly impact therapeutic efficacy and should be considered as carefully as genetic determinants modulating, for example, the production of multidrug-resistance protein or topoisomerase II. We visualize and rigorously quantify distributions of nutrient, drug, and resulting cell inhibition. A main result is the existence of significant heterogeneity in all three, yielding poor inhibition in a large fraction of the lesion, and commensurately increased serum drug concentration necessary for an average 50% inhibition throughout the lesion (the IC50 concentration). For doxorubicin the effect of hypoxia and hypoglycemia (“nutrient effect”) is isolated and shown to further increase cell inhibition heterogeneity and double the IC50, both undesirable. We also show how the therapeutic effectiveness of doxorubicin penetration therapy depends upon other determinants affecting drug distribution, such as cellular efflux and density, offering some insight into the conditions under which otherwise promising therapies may fail and, more importantly, when they will succeed. Cisplatin is used as a contrast to doxorubicin since both published experimental data and our simulations indicate its lesion distribution is more uniform than that of doxorubicin. Because of this some of the complexity in predicting its therapeutic efficacy is mitigated. Using this advantage, we show results suggesting that in vitro monolayer assays using this drug may more accurately predict in vivo performance than for drugs like doxorubicin. The nonlinear interaction among various determinants representing cell and lesion phenotype as well as therapeutic strategies is a unifying theme of our results. Throughout it can be appreciated that macroscopic environmental conditions, notably drug and nutrient distributions, give rise to considerable variation in lesion response, hence clinical resistance. Moreover, the synergy or antagonism of combined therapeutic strategies depends heavily upon this environment

Crack propagation in a geothermal energy reservoir

We consider the problem of the opening of pre-existing cracks with high pressure fluid in the case where changes in the fluid pressure are balanced predominantly by stresses due to the local crack asperity deformations. A model is proposed for this process using a particular choice of 'crack law' and 'flow law' which leads to a free boundary problem. A singular perturbation analysis reveals that, in the boundary layer, the motion of the free boundary is governed by a singular integro-differential equation

A two-phase model for evaporating solvent-polymer mixtures

Evaporating solvent-polymer mixtures play an important role in a number of modern industrial applications. We focus on developing a two-phase model for a fluid composed of a volatile solvent and a non-volatile polymer in a thin-film geometry. The model accounts for density differences between the phases as well as evaporation at a fluid-air interface. We use the model in one dimension to explore the interplay between evaporation and compositional buoyancy; the former promotes the growth of a polymer-rich skin at the free surface while the latter tends to pull the denser polymeric phase to the substrate. We also examine how these mechanisms influence the drying time of the film. In the limit of dilute polymer, the model can be reduced to a single nonlinear boundary value problem. The non-dilute problem has a rich asymptotic structure. We find that the shortest drying times occur in the limit of strong gravitational effects due to the rapid formation of a bilayer with a polymer-rich lower layer and a solvent-rich upper layer. In addition, gravity plays a key role in inhibiting the formation of a skin and can prevent substantial increases in the drying time of the film

Physical modelling of the slow voltage relaxation phenomenon in lithium-ion batteries

In the lithium-ion battery literature, discharges followed by a relaxation to equilibrium are frequently used to validate models and their parametrizations. Good agreement with experiment during discharge is easily attained with a pseudo-two-dimensional model such as the Doyle-Fuller-Newman (DFN) model. The relaxation portion, however, is typically not well-reproduced, with the relaxation in experiments occurring much more slowly than in models. In this study, using a model that includes a size distribution of the active material particles, we give a physical explanation for the slow relaxation phenomenon. This model, the Many-Particle-DFN (MP-DFN), is compared against discharge and relaxation data from the literature, and optimal fits of the size distribution parameters (mean and variance), as well as solid-state diffusivities, are found using numerical optimization. The voltage after relaxation is captured by careful choice of the current cut-off time, allowing a single set of physical parameters to be used for all C-rates, in contrast to previous studies. We find that the MP-DFN can accurately reproduce the slow relaxation, across a range of C-rates, whereas the DFN cannot. Size distributions allow for greater internal heterogeneities, giving a natural origin of slower relaxation timescales that may be relevant in other, as yet explained, battery behavior

Planned experiments for mechanical assemblies

For experiments on mechanical products, conventional methods for reducing the experimental effort that is needed to extract information, such as those of Taguchi, can be infeasible because components with the dimensions needed for a standard factorial plan can be prohibitively expensive. Also, many factors for investigation are not directly measurable, as they are derived from the properties of several components and their assembly. Methods are described for finding optimal plans for such experiments from a minimal sample of measured components, and are illustrated through a pilot investigation of a hydraulic pump. Important issues are addressed of the robustness of the plans to possible missing data, for example due to product failure, and the need to ensure that the influences of the various different factors can be clearly extracted from the experimental results. On-going work in the aeronautical industry on products for low-volume manufacturing is also described, where experiments are run on-line so that information can be swiftly obtained without delay in the manufacturing process

Multiscale modelling and analysis of lithium-ion battery charge and discharge

A microscopic model of a lithium battery is developed, which accounts for lithium diffusion within particles, transfer of lithium from particles to the electrolyte and transport within the electrolyte assuming a dilute electrolyte and Butler-Volmer reaction kinetics. Exploiting the small size of the particles relative to the electrode dimensions, a homogenised model (in agreement with existing theories) is systematically derived and studied. Details of how the various averaged quantities relate to the underlying geometry and assumptions are given. The novel feature of the homogenisation process is that it allows the coefficients in the electrode-scale model to be derived in terms of the microscopic features of the electrode (e. g. particle size and shape) and can thus be used as a systematic way of investigating the effects of changes in particle design. Asymptotic methods are utilised to further simplify the model so that one-dimensional behaviour can be described with relatively simpler expressions. It is found that for low discharge currents, the battery acts almost uniformly while above a critical current, regions of the battery become depleted of lithium ions and have greatly reduced reaction rates leading to spatially nonuniform use of the electrode. The asymptotic approximations are valid for electrode materials where the OCV is a strong function of intercalated lithium concentration, such as Li xC 6, but not for materials with a flat discharge curve, such as LiFePO 4. © 2011 Springer Science+Business Media B.V

Stochastic modelling of membrane filtration

Membrane fouling during particle filtration occurs through a variety of mechanisms, including internal pore clogging by contaminants, coverage of pore entrances, and deposition on the membrane surface. In this paper we present an efficient method for modelling the behaviour of a filter, which accounts for different retention mechanisms, particle sizes, and membrane geometries. The membrane is assumed to be composed of a series of, possibly interconnected, pores. The central feature is a conductivity function, which describes the blockage of each individual pore as particles arrive, which is coupled with a mechanism to account for the stochastic nature of the arrival times of particles at the pore. The result is a system of ordinary differential equations based on the pore-level interactions. We demonstrate how our model can accurately describe a wide range of filtration scenarios. Specifically, we consider: a case where blocking via multiple mechanisms can occur simultaneously, which have previously required the study through individual models; the filtration of a combination of small and large particles by a track-etched membrane; and particle separation using interconnected pore networks. The model is significantly faster than comparable stochastic simulations for small networks, enabling its use as a tool for efficient future simulations.</p