A simple model for the desulphurisation of flue gas using reactive filters

Desulphurisation of flue gas is essential before it can be released safely into the atmosphere. One way of removing sulphur dioxide is to use a purification device incorporating a reactive filter, in which the flue gas stream passes in front of a porous-catalyst-filled structure which converts the gaseous sulphur dioxide into liquid sulphuric acid. In this paper, we build and solve a simple mathematical model to describe the operation of a paradigm reactive filter. Our model captures the transport of sulphur dioxide through the device via advection in the main “outer” flow and diffusion through the catalyst structure along with the production of sulphuric acid. This sulphuric acid gradually accumulates in the filter rendering it less efficient. We determine the clogging time for an individual channel (that is, the time at which the entrance to the channel becomes completely filled with liquid) and explore how the concentrations of sulphur dioxide and oxygen and the thickness of the sulphuric acid layer change as the key dimensionless parameters are varied, comparing numerical and asymptotic results where appropriate. We then turn our attention to the device scale and solve our model numerically to determine the overall lifetime of the device. We vary the key dimensionless parameters and explore how they affect the efficiency of the device. In the physically relevant parameter regime, we find an explicit solution to the outer flow problem which agrees well with numerical solutions and provides a formula for the lifetime of the device. Finally, we propose a formula for determining the catalyst reaction rate, given data on the concentration of sulphur dioxide exiting the device

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

The effect of polar lipids on tear film dynamics.

In this paper, we present a mathematical model describing the effect of polar lipids, excreted by glands in the eyelid and present on the surface of the tear film, on the evolution of a pre-corneal tear film. We aim to explain the interesting experimentally observed phenomenon that the tear film continues to move upward even after the upper eyelid has become stationary. The polar lipid is an insoluble surface species that locally alters the surface tension of the tear film. In the lubrication limit, the model reduces to two coupled non-linear partial differential equations for the film thickness and the concentration of lipid. We solve the system numerically and observe that increasing the concentration of the lipid increases the flow of liquid up the eye. We further exploit the size of the parameters in the problem to explain the initial evolution of the system

The Extent of Voluntariness in Plea Bargaining for Economic and Financial Crimes in Nigeria

A two-phase model is presented to describe avascular tumour growth. Conservation of mass equations, including oxygen-dependent cell growth and death terms, are coupled with equations of momentum conservation. The cellular phase behaves as a viscous liquid, while the viscosity of the extracellular water manifests itself as an interphase drag. It is assumed that the cells become mechanically stressed if they are too densely packed and that the tumour will try to increase its volume in order to relieve such stress. By contrast, the overlapping filopodia of sparsely populated cells create short-range attractive effects. Finally, oxygen is consumed by the cells as it diffuses through the tumour. The resulting system of equations are reduced to three, which describe the evolution of the tumour cell volume fraction, the cell speed and the oxygen tension. Numerical simulations indicate that the tumour either evolves to a travelling wave profile, in which it expands at a constant rate, or it settles to a steady state, in which the net rates of cell proliferation and death balance. The impact of varying key model parameters such as cellular viscosity, interphase drag, and cellular tension are discussed. For example, tumours consisting of well-differentiated (i.e. viscous) cells are shown to grow more slowly than those consisting of poorly-differentiated (i.e. less viscous) cells. Analytical results for the case of oxygen-independent growth are also presented, and the effects of varying the key parameters determined (the results are in line with the numerical simulations of the full problem). The key results and their biological implications are then summarised and future model refinements discussed

Kinetics of surfactant desorption at an air-solution interface.

The kinetics of re-equilibration of the anionic surfactant sodium dodecylbenzene sulfonate at the air-solution interface have been studied using neutron reflectivity. The experimental arrangement incorporates a novel flow cell in which the subphase can be exchanged (diluted) using a laminar flow while the surface region remains unaltered. The rate of the re-equilibration is relatively slow and occurs over many tens of minutes, which is comparable with the dilution time scale of approximately 10-30 min. A detailed mathematical model, in which the rate of the desorption is determined by transport through a near-surface diffusion layer into a diluted bulk solution below, is developed and provides a good description of the time-dependent adsorption data. A key parameter of the model is the ratio of the depth of the diffusion layer, H(c), to the depth of the fluid, H(f), and we find that this is related to the reduced Péclet number, Pe*, for the system, via H(c)/H(f) = C/Pe*(1/2). Although from a highly idealized experimental arrangement, the results provide an important insight into the "rinse mechanism", which is applicable to a wide variety of domestic and industrial circumstances