A Mathematical Analysis of Digestive Processes in a Model Stomach

Rickett, Lydia (2013) A Mathematical Analysis of Digestive Processes in a Model Stomach. Doctoral thesis, University of East Anglia.

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Abstract

It is of great medical interest to gain a better understanding of digestion in the
human stomach, not least because of the relevance to nutrient and drug delivery. The
Institute of Food Research has developed the Dynamic Gastric Model, a physical, in
vitro model stomach capable of re-creating the physiological conditions experienced in
vivo.
The aim of this thesis is to examine mathematically digestion in the main body (top
section) of the Dynamic Gastric Model, where gentle wall movements and gastric secretions
result in the outside layer of the digesta “sloughing off”, before passing into the
bottom section for further processing. By considering a simplified, local description of
the flow close to the wall, we may gain an insight into the mechanisms behind this behaviour.
This description focuses on the mixing of two layers of creeping fluid through
temporal instability of the perturbed fluid interface. Some attention is also paid to a
more general study of the surrounding flow field.
Linear, two-fluid flow next to a prescribed, sinusoidally moving wall is found to be
stable in all cases. Studies of thin film flow next to such a wall suggest that the same may
be true of the nonlinear case, although in the case of an inclined wall wave steepening
is found to occur for early times. A linear instability is found for small wavenumber
disturbances when the wall is modelled as an elastic beam or when we include a scalar
material field that acts to alter the surface tension at the interface. An examination of
Navier–Stokes flow of a single fluid through a diverging channel (representing a small
strip through the centre of the main body) reveals that the flow loses symmetry at a
lower Reynolds number than flow through a channel of uniform width. Our results are
interpreted in terms of the Dynamic Gastric Model.

Item Type: Thesis (Doctoral)
Faculty \ School: Faculty of Science > School of Mathematics
Depositing User: Mia Reeves
Date Deposited: 11 Mar 2014 11:14
Last Modified: 11 Mar 2014 11:14
URI: https://ueaeprints.uea.ac.uk/id/eprint/48042
DOI:

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