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Title: Mathematical modelling of membrane filtration
Author: Krupp, Armin Ulrich
ISNI:       0000 0004 7430 5595
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 2017
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In this thesis, we consider four different problems in membrane filtration, using a different mathematical approach in each instance. We account for the fluid-driven deformation of a filtercake using nonlinear poroelasticity in Chapter 2. By considering feeds with very high and very low particle concentrations, we introduce a quasi-static caking model that provides a suitable approximation to the full model for the physically realistic concentration regimes. We illustrate the agreements and differences between our model and the existing conventional cake-filtration law. In Chapter 3, we introduce a stochastic model for membrane filtration based on the quantised nature of the particles and show how it can be applied for feeds with different particle types and membranes with an interconnected pore structure. This allows us to understand the relation between the effects of clogging on the level of an individual pore and on the macroscopic level of the entire membrane. We conclude by explaining the transition between the discrete and continuous model based on the Fokker--Planck equation. In Chapter 4, we consider the inverse problem of determining the underlying filtration law from the spreading speed of a particle-laden gravity current. We first couple the theory of gravity currents with the stochastic model developed in Chapter~3 to determine a filtration law from a given set of experiments. We then generalise this idea for the porous medium equation, where we show that the position of the front follows a power law for the conventional filtration laws, which allows us to infer the clogging law in certain instances. We conclude the thesis by showing in Chapter 5 how we can combine experimental measurements for the clogging of a depth filter and simple fluid dynamics to accurately predict the pressure distribution in a multi-capsule depth filter during a filtration run.
Supervisor: Please, Colin ; Griffiths, Ian Sponsor: Engineering and Physical Sciences Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Mathematics ; Porous Media ; Porous Medium Equation ; Membrane Filtration ; Gravity Current ; Mathematical Modelling