Spin-coating on nanoscale topography and phase separation of diblock copolymers

CRANN researchers are interested in mathematical modelling of all aspects of the process of spin-coating of diblock copolymers, with the aim of removing expensive trial and error design cycles. Of particular interest is the flow of the polymer during spin-coating, and also during the subsequent annealing process. Also of considerable interest is the chemical process of phase-separation and self-assembly of the diblock copolymer. Existing models in the literature rely heavily on computationally expensive Monte-Carlo simulation methods. The modelling work performed during the study group in summarized in this report. The report is split into four main sections, with discussion and suggestions for experiments in the concluding section. The content of the sections is as follows: Section 0.2: Mathematical modelling of spin-coating onto a flat substrate; no annealing considered. Section 0.3: Modelling of spin-coating onto a substrate with topography (i.e. trenches); no annealing considered. Section 0.4: Flow of polymer during annealing. Section 0.5: Models for self-assembly of polymers into nanostructures. Sections 0.2 to 0.4 are focussed on the fluid flow problems for the polymer, and go some way to providing useful answers to Problem 1. On the other hand, Problem 2 was found to be extremely challenging, and the efforts described in section 0.5 represent only a relatively modest impact on this problem

A Coupled Electrochemical and Hydrodynamical Two-Phase Model for the Electrolytic Pickling of Steel

In industrial electrolytic pickling, a steel strip with oxidized surfaces is passed through an aqueous electrolyte between a configuration of electrodes, across which a potential difference is applied. The strip is thereby indirectly polarized, and electrochemical reactions at the strip surface result in the dissolution of the oxide layer and the evolution of hydrogen and oxygen bubbles. In this paper, we extend an earlier mathematical model for the electrochemical aspects of the process, which took account only of the liquid phase, to include the effect of the gas phase. The model is two-dimensional, steady-state and isothermal, and comprises five ionic species, the mixture velocity, pressure, and the gas fraction; numerical solutions of this model are then obtained. The results of the single and two-phase models are compared, and their implications for the actual pickling process are discusse

Asymptotic analysis of drug dissolution in two layers having widely differing diffusivities

This paper is concerned with a diffusion-controlled moving-boundary problem in drug dissolution, in which the moving front passes from one medium to another for which the diffusivity is many orders of magnitude smaller. The classical Neumann similarity solution holds while the front is passing through the first layer, but this breaks down in the second layer. Asymptotic methods are used to understand what is happening in the second layer. Although this necessitates numerical computation, one interesting outcome is that only one calculation is required, no matter what the diffusivity is for the second laye

Numerical Simulation of Brazing Aluminium Alloys with Al–Si Alloys

Joining parts using low-melting temperature alloys has long been used for manufacturing complex components such as heat exchangers made of aluminium alloys. Investigations of the process have shown that core/ clad interaction during heating and brazing can lead to a significant decrease in the amount of liquid available for joint formation. This study presents a transient one-dimensional model for the process that takes into account the diffusion of silicon and the movement of the core/clad interface, with the model equations being implemented in the finite element software COMSOL Multiphysics; the results are compared to literature experimental data. Silicon profiles in the core are well described, while there appears a significant difference between predicted and experimental values of remaining clads which suggest a strong effect of silicon diffusion and liquid penetration at core grain boundaries

Laser Welding of a Stent

We consider the problem of modelling the manufacture of a cylindrical Stent, in which layers of a plastic material are welded together by a Laser beam. We firstly set up the equations for this system and solve them by using a Finite Element method. We then look at various scalings which allow the equations to be simplified. The resulting equations are then solved analytically to obtain approximate solutions to the radial temperature profile and the averaged axial temperature profile

A finite difference technique for solving a time strain separable K-BKZ constitutive equation for two-dimensional moving free surface flows

This work is concerned with the numerical solution of the K-BKZ integral constitutive equation for two-dimensional time-dependent free surface flows. The numerical method proposed herein is a finite difference technique for simulating flows possessing moving surfaces that can interact with solid walls. The main characteristics of the methodology employed are: the momentum and mass conservation equations are solved by an implicit method; the pressure boundary condition on the free surface is implicitly coupled with the Poisson equation for obtaining the pressure field from mass conservation; a novel scheme for defining the past times is employed; the Finger tensor is calculated by the deformation fields method and is advanced in time by a second-order Runge–Kutta method. This new technique is verified by solving shear and uniaxial elongational flows. Furthermore, an analytic solution for fully developed channel flow is obtained that is employed in the verification and assessment of convergence with mesh refinement of the numerical solution. For free surface flows, the assessment of convergence with mesh refinement relies on a jet impinging on a rigid surface and a comparison of the simulation of a extrudate swell problem studied by Mitsoulis (2010) [44] was performed. Finally, the new code is used to investigate in detail the jet buckling phenomenon of K-BKZ fluids.Indisponível

Lives saved with vaccination for 10 pathogens across 112 countries in a pre-COVID-19 world.

BackgroundVaccination is one of the most effective public health interventions. We investigate the impact of vaccination activities for Haemophilus influenzae type b, hepatitis B, human papillomavirus, Japanese encephalitis, measles, Neisseria meningitidis serogroup A, rotavirus, rubella, Streptococcus pneumoniae, and yellow fever over the years 2000-2030 across 112 countries.MethodsTwenty-one mathematical models estimated disease burden using standardised demographic and immunisation data. Impact was attributed to the year of vaccination through vaccine-activity-stratified impact ratios.ResultsWe estimate 97 (95%CrI[80, 120]) million deaths would be averted due to vaccination activities over 2000-2030, with 50 (95%CrI[41, 62]) million deaths averted by activities between 2000 and 2019. For children under-5 born between 2000 and 2030, we estimate 52 (95%CrI[41, 69]) million more deaths would occur over their lifetimes without vaccination against these diseases.ConclusionsThis study represents the largest assessment of vaccine impact before COVID-19-related disruptions and provides motivation for sustaining and improving global vaccination coverage in the future.FundingVIMC is jointly funded by Gavi, the Vaccine Alliance, and the Bill and Melinda Gates Foundation (BMGF) (BMGF grant number: OPP1157270 / INV-009125). Funding from Gavi is channelled via VIMC to the Consortium's modelling groups (VIMC-funded institutions represented in this paper: Imperial College London, London School of Hygiene and Tropical Medicine, Oxford University Clinical Research Unit, Public Health England, Johns Hopkins University, The Pennsylvania State University, Center for Disease Analysis Foundation, Kaiser Permanente Washington, University of Cambridge, University of Notre Dame, Harvard University, Conservatoire National des Arts et Métiers, Emory University, National University of Singapore). Funding from BMGF was used for salaries of the Consortium secretariat (authors represented here: TBH, MJ, XL, SE-L, JT, KW, NMF, KAMG); and channelled via VIMC for travel and subsistence costs of all Consortium members (all authors). We also acknowledge funding from the UK Medical Research Council and Department for International Development, which supported aspects of VIMC's work (MRC grant number: MR/R015600/1).JHH acknowledges funding from National Science Foundation Graduate Research Fellowship; Richard and Peggy Notebaert Premier Fellowship from the University of Notre Dame. BAL acknowledges funding from NIH/NIGMS (grant number R01 GM124280) and NIH/NIAID (grant number R01 AI112970). The Lives Saved Tool (LiST) receives funding support from the Bill and Melinda Gates Foundation.This paper was compiled by all coauthors, including two coauthors from Gavi. Other funders had no role in study design, data collection, data analysis, data interpretation, or writing of the report. All authors had full access to all the data in the study and had final responsibility for the decision to submit for publication