1,721,133 research outputs found
A mathematical model for interfacial charge transfer at the semiconductor–dye–electrolyte interface of a dye-sensitised solar cell
No full textA mathematical model for the interfacial charge transfer within dye-sensitised solar cells (DSC) is presented for the semiconductor–dye–electrolyte interface. The model explicitly accounts for each reaction at the interface involving dye molecules, electrolyte species and adsorbed electrons associated with the conduction band surface states of the semiconductor. Additionally, the model accounts for photoelectron injection via singlet and triplet excited dye states. The governing equations can be used to describe the total current produced by the DSC under illuminated and non-illuminated conditions, at steady state. Regular perturbation methods are applied to the model equations to obtain closed form analytic approximations, resulting in approximate solutions that negate the need for numerical solution of the model system. All parameter values associated with the model are obtained from the literature and from experimental data. The presented numerical results and analytic approximations compare favourably to experimental data, capturing the interfacial characteristics of current versus voltage curves of the DSC
The design of microfluidic affinity chromatography systems for the separation of bioanalytes
No full textThe analytical (numerical) design of planar microfluidic affinity chromatography devices, which consist of multiple separation lanes and multiple, different surface-immobilised receptor patterns in each lane, is described. The model is based on the analytical solution of the transport-reaction equations in microfluidic systems of low Gratz number and for injection of small analyte plugs. The results reveal a simple approach for the design of microfluidic affinity chromatography devices tailored to the separation of bioanalytes, where receptors with high binding affinity are available. These devices have been designed for bioanalytical applications in mind, most notably for the proteomics field; the results are illustrated with an example using β-Amyloid binding peptides
Design of novel microfluidic concentration gradient generators suitable for linear and exponential concentration ranges
No full textA novel microfluidic concentration gradient generator is designed where secondary flow, induced via a surface groove, is used to yield a concentration gradient across the output of the microfluidic device. The concentration gradient generator design consists of a single microfluidic channel with two inputs and a single obliquely angled surface groove within the base of the channel to induce the secondary flow and create the concentration gradient. The design allows a concentration gradient to be chosen, either linear or exponential, at the exit of the microfluidic channel with the shape and dimensions of the surface groove within the channel obtained by numerical optimisation. The designed device has a small footprint, suitable for integration within lab-on-a-chip structures for the delivery of a series of an agent to either (i) a single channel and with a concentration gradient or to (ii) a series of reactors with concentrations across a defined range, for bioscience or pharmaceutical screening applications or for chemical reactions
Optimisation of analyte transport in integrated microfluidic affinity sensors for the quantification of low levels of analyte
No full textNew designs for microfluidic channels to be integrated with small-scale affinity sensors for analytical applications are provided. Theoretical approaches demonstrate efficient and uniform mass transfer of the analyte from the bulk flow to small-scale affinity sensors in the base of fluidic channels by (i) active control of the analyte flow speed over the affinity sensor, (ii) non-rectangular channel geometries and (iii) non-uniform distributions of recognition binding sites over the active area of the sensor. The methodology reported provides generic strategies that can be exploited for small-scale sensors in single or multiplex formats
Residual stress generation and necrosis formation in multi-cell tumour spheroids
No full textWe consider how cell proliferation and death generate residual stresses within a multi-cell tumour spheroid (MCTS). Previous work by Jones and co-workers [8] has shown that isotropic growth in a purely elastic MCTS produces growth induced stresses which eventually become unbounded, and hence are physically unrealistic. Since viscoelastic materials show stress relaxation under a fixed deformation we consider the effect of the addition of a small amount of viscosity to the elastic system by examining formation of equilibrium stress profiles within a Maxwell type viscoelastic MCTS. A model of necrosis formation based upon that proposed by Please and co-workers (see [16] [17] [18]) is then presented in which necrosis forms under conditions of adverse mechanical stress rather than in regions of extreme chemical stress as is usually assumed. The influence of rheology on necrosis formation is then investigated, and it is shown that the excessive stress generated in the purely elastic tumour can be relieved either by the addition of some viscosity to the system or by accounting for an inner necrotic interface with an appropriate stress boundary condition
A model of fluid flow through the detached retina
No full textThe retina is a transparent layer of sensitive tissue which is kept in contact with the choroid (which is responsible in giving nourishment to the retina) inside the eye. When the retina tear develops, it may allow liquefied vitreous humour (VH - a clear gel that fills the space between the lens and the retina) to flow through the retina and push the retina away from the choroids, thus causing a retinal detachment (RD). If the retina remains detached, it will lose the ability to function, vision will become distorted and finally the patient will go permanently blind. A paradigm mathematical model of fluid flow through the detached retina has been developed by considering the lubrication theory limit of the Navier-Stokes equations. In the current study fluid flow between rigid walls has been assumed and we have considered the detached retina to be a thin flap which it is attached to the plain wall (choroid). The detached retina is also assumed to be elastic and deformable; allowing the general theory of beam bending to be applied. In particular, asymptotic analysis has been used in order to calculate and analyze the flow behaviour, the deformation of the detached retina, as well as the fluxes of fluid and the bending moment
Physical modelling of the slow voltage relaxation phenomenon in lithium-ion batteries
Full text linkIn 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
Generic behaviour of nonlinear sound waves near the surface of a star: smooth solutions
No full textWe are interested in the generic behavior of nonlinear sound waves as they approach the surface of a star, here assumed to have the polytropic equation of state P=K??. Restricting to spherical symmetry, and considering only the region near the surface, we generalize the methods of Carrier and Greenspan (1958) for the shallow water equations on a sloping beach to this problem. We give a semiquantitative criterion for a shock to form near the surface during the evolution of generic initial data with support away from the surface. We show that in smooth solutions the velocity and the square of the sound speed remain regular functions of Eulerian radius at the surface
Heterogeneous proliferation within engineered cartilaginous tissue: the role of oxygen tension
No full textThis article investigates heterogeneous proliferation within a seeded three-dimensional scaffold structure with the purpose of improving protocols for engineered tissue growth. A simple mathematical model is developed to examine the very strong interaction between evolving oxygen profiles and cell distributions within cartilaginous constructs. A comparison between predictions based on the model and experimental evidence is given for both spatial and temporal evolution of the oxygen tension and cell number density, showing that behaviour for the first 14 days can be explained well by the mathematical model. The dependency of the cellular proliferation rate on the oxygen tension is examined and shown to be similar in size to previous work but linear in form. The results show that cell-scaffold constructs that rely solely on diffusion for their supply of nutrients will inevitably produce proliferation-dominated regions near the outer edge of the scaffold in situations when the cell number density and oxygen consumption rate exceed a critical level. Possible strategies for reducing such non-uniform proliferation, including the conventional methods of enhancing oxygen transport, are outlined based on the model predictions
Experimental characterization and computational modelling of two-dimensional cell spreading for skeletal regeneration
No full textLimited cell ingrowth is a major problem for tissue engineering and the clinical application of porous biomaterials as bone substitutes. As a first step, migration and proliferation of an interacting cell population can be studied in two-dimensional culture. Mathematical modelling is essential to generalize the results of these experiments and to derive the intrinsic parameters that can be used for predictions. However, a more thorough evaluation of theoretical models is hampered by limited experimental observations. In this study, experiments and image analysis methods were developed to provide a detailed spatial and temporal picture of how cell distributions evolve. These methods were used to quantify the migration and proliferation of skeletal cell types including MG63 and human bone marrow stromal cells (HBMSCs). The high level of detail with which the cell distributions were mapped enabled a precise assessment of the correspondence between experimental results and theoretical model predictions. This analysis revealed that the standard Fisher equation is appropriate for describing the migration behaviour of the HBMSC population, while for the MG63 cells a sharp front model is more appropriate. In combination with experiments, this type of mathematical model will prove useful in predicting cell ingrowth and improving strategies and control of skeletal tissue regeneration
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