Numerical investigations of traveling singular sources problems via moving mesh method

This paper studies the numerical solution of traveling singular sources problems. In such problems, a big challenge is the sources move with different speeds, which are described by some ordinary differential equations. A predictor-corrector algorithm is presented to simulate the position of singular sources. Then a moving mesh method in conjunction with domain decomposition is derived for the underlying PDE. According to the positions of the sources, the whole domain is splitted into several subdomains, where moving mesh equations are solved respectively. On the resulting mesh, the computation of jump $[\dot{u}]$ is avoided and the discretization of the underlying PDE is reduced into only two cases. In addition, the new method has a desired second-order of the spatial convergence. Numerical examples are presented to illustrate the convergence rates and the efficiency of the method. Blow-up phenomenon is also investigated for various motions of the sources

Emergent behavior in active colloids

Active colloids are microscopic particles, which self-propel through viscous fluids by converting energy extracted from their environment into directed motion. We first explain how articial microswimmers move forward by generating near-surface flow fields via self-phoresis or the self-induced Marangoni effect. We then discuss generic features of the dynamics of single active colloids in bulk and in confinement, as well as in the presence of gravity, field gradients, and fluid flow. In the third part, we review the emergent collective behavior of active colloidal suspensions focussing on their structural and dynamic properties. After summarizing experimental observations, we give an overview on the progress in modeling collectively moving active colloids. While active Brownian particles are heavily used to study collective dynamics on large scales, more advanced methods are necessary to explore the importance of hydrodynamic and phoretic particle interactions. Finally, the relevant physical approaches to quantify the emergent collective behavior are presented.Comment: 31 pages, 14 figure

Development of predictive models of flow induced and localized corrosion

Corrosion is a serious industrial concern. According to a cost of corrosion study released in 2002, the direct cost of corrosion is approximately $276 billion dollars in the United States – approximately 3.1% of their Gross Domestic Product. Key influences on the severity of corrosion include: metal and electrolyte composition, temperature, turbulent flow, and location of attack. In this work, mechanistic models of localized and flow influenced corrosion were constructed and these influences on corrosion were simulated.A rigourous description of mass transport is paramount for accurate corrosion modelling. A new moderately dilute mass transport model was developed. A customized hybrid differencing scheme was used to discretize the model. The scheme calculated an appropriate upwind parameter based upon the Peclet number. Charge density effects were modelled using an algebraic charge density correction. Activity coefficients were calculated using Pitzer’s equations. This transport model was computationally efficient and yielded accurate simulation results relative to experimental data. Use of the hybrid differencing scheme with the mass transport equation resulted in simulation results which were up to 87% more accurate (relative to experimental data) than other conventional differencing schemes. In addition, when the charge density correction was used during the solution of the electromigration-diffusion equation, rather than solving the charge density term separately, a sixfold increase in the simulation time to real time was seen (for equal time steps in both simulation strategies). Furthermore, the charge density correction is algebraic, and thus, can be applied at larger time steps that would cause the solution of the charge density term to not converge.The validated mass transport model was then applied to simulate crevice corrosion initiation of passive alloys. The cathodic reactions assumed to occur were crevice-external oxygen reduction and crevice-internal hydrogen ion reduction. Dissolution of each metal in the alloy occurred at anodic sites. The predicted transient and spatial pH profile for type 304 stainless steel was in good agreement with the independent experimental data of others. Furthermore, the pH predictions of the new model for 304 stainless steel more closely matched experimental results than previous models.The mass transport model was also applied to model flow influenced CO2 corrosion. The CO2 corrosion model accounted for iron dissolution, H+, H2CO3, and water reduction, and FeCO3 film formation. The model accurately predicted experimental transient corrosion rate data.Finally, a comprehensive model of crevice corrosion under the influence of flow was developed. The mass transport model was modified to account for convection. Electrode potential and current density in solution was calculated using a rigourous electrode-coupling algorithm. It was predicted that as the crevice gap to depth ratio increased, the extent of fluid penetration also increased, thereby causing crevice washout. However, for crevices with small crevice gaps, external flow increased the cathodic limiting current while fluid penetration did not occur, thereby increasing the propensity for crevice corrosion

Study of the Chemical Fabrication Process of NSOM Probes and the Modification of the Probe Surface

Near-field scanning optical microscopy (NSOM) merges scanning probe technology with the power of high-resolution optical microscopy and provides a natural view into the nanoworld. NSOM requires tapered probes with subwavelength optical apertures and wide cone angles to efficiently channel the illumination light to the tip apex so that it can acquire optical images beyond the diffraction limit. Tapered probes with a range of cone angles can be fabricated through chemical etching of optical fibers using hydrofluoric acid (HF) by varying the etching time. Apart from their use for NSOM imaging, such optical probes can also be transformed into nanosensors by attaching sensing elements to the NSOM probe surface. This work seeks to identify the maximum obtainable cone angle in an NSOM probe fabricated by chemical etching of an optical fiber and to create a nanosensor using this kind of probe. We investigate the progression of cone angles with etching time and propose a model of the etching process. We find that the variation of cone angle as a function of etching time does not follow the expected exponential plateau curve and we compare the experimental result to simulations with multiphysics models of the etching process of an optical fiber. Additionally, functionalization of NSOM probes with different fluorescent molecules is investigated and a fluorescent nanosensor is developed. We observe that the nanosensor is able to detect concentration changes of Cu^(2+) and Fe^(3+) ions in a droplet of sample solution

Continuum and discrete approach in modeling biofilm development and structure: a review

The scientific community has recognized that almost 99% of the microbial life on earth is represented by biofilms. Considering the impacts of their sessile lifestyle on both natural and human activities, extensive experimental activity has been carried out to understand how biofilms grow and interact with the environment. Many mathematical models have also been developed to simulate and elucidate the main processes characterizing the biofilm growth. Two main mathematical approaches for biomass representation can be distinguished: continuum and discrete. This review is aimed at exploring the main characteristics of each approach. Continuum models can simulate the biofilm processes in a quantitative and deterministic way. However, they require a multidimensional formulation to take into account the biofilm spatial heterogeneity, which makes the models quite complicated, requiring significant computational effort. Discrete models are more recent and can represent the typical multidimensional structural heterogeneity of biofilm reflecting the experimental expectations, but they generate computational results including elements of randomness and introduce stochastic effects into the solutions

Advances in catalysis for fuel cells

Imperial Users onl

Microfabricated Reference Electrodes and their Biosensing Applications

Over the past two decades, there has been an increasing trend towards miniaturization of both biological and chemical sensors and their integration with miniaturized sample pre-processing and analysis systems. These miniaturized lab-on-chip devices have several functional advantages including low cost, their ability to analyze smaller samples, faster analysis time, suitability for automation, and increased reliability and repeatability. Electrical based sensing methods that transduce biological or chemical signals into the electrical domain are a dominant part of the lab-on-chip devices. A vital part of any electrochemical sensing system is the reference electrode, which is a probe that is capable of measuring the potential on the solution side of an electrochemical interface. Research on miniaturization of this crucial component and analysis of the parameters that affect its performance, stability and lifetime, is sparse. In this paper, we present the basic electrochemistry and thermodynamics of these reference electrodes and illustrate the uses of reference electrodes in electrochemical and biological measurements. Different electrochemical systems that are used as reference electrodes will be presented, and an overview of some contemporary advances in electrode miniaturization and their performance will be provided

Numerical simulation of slug flow with high viscosity liquid

Slug flow is one of the most common flow patterns in multiphase oil/gas transport in pipelines. Due to its complexity, it poses numerous challenges to model development. Industrial slug flow models are one-dimensional and can give poor predictions in situations where the associated closures and simplifications are no longer valid. Computational Fluid Dynamics (CFD) facilitates high-resolution studies of slug flow dynamics by implementing multi-dimensional models. Understanding the physics of slug flow would help identify the main flow mechanisms to be modelled and enable the development of mechanistic slug flow models for commercial software. In this thesis, a computational approach is developed. The front tracking method (FTM) (Tryggvason et al. 2001) and the phase field method (PFM) (Ding et al. 2007) are used to model long bubbles in slug flows. Results of the validation study show good agreement with DeBisschop et al. (2002), who performed simulations of long bubbles in two-dimensional channels in the creeping-flow limit. Their work is extended here to moderate Archimedes numbers (10 < Ar < 200). The effects of inertia, surface tension, viscosity and inclination angle on the terminal velocity and the shape of a long bubble in different flow conditions are investigated. Furthermore, the FTM is coupled with a discrete bubble tracking method (DBTM), which has resulted in a robust hybrid method to model small and large bubbles simultaneously in an Eulerian-Lagrangian fashion. The method allows the study of the interaction of the small bubbles with a long bubble. The work is extended further to three dimensions using the PFM. The validation study shows good agreement with the present two-dimensional numerical work. The geometry is converted from a square channel to a pipe to facilitate a more realistic simulation of slug flow in pipelines. This work will provide a rigorous basis for developing simplified models.Open Acces