Thesis (MSc)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: Fluid flow through porous media plays an important role in a variety of contexts of which
filtration is one. Filtration efficiency of fibrous filters depends on the micro-structural
characterization of these porous materials and is reflected in the permeability there-of.
Compression of fibrous porous media has a significant effect on the permeability. Experimental
data indicate that the permeability varies generally with more than an order of
magnitude over the narrow porosity range in which the compression takes place. Relative
to the amount of experimental studies regarding this phenomenon, there is a scarcity of
geometric models in the literature that can account for the effect of compression on the
permeability of a fibrous porous medium. Within the context of existing geometric porescale
models based on rectangular geometry, a new model is presented and an existing
model improved to predict the effect of one-dimensional compression in the streamwise
direction. In addition, without compromising on a commitment to mathematical simplicity,
empirical data of a non-woven fibrous porous medium was used to highlight the
effect of model geometry on its predictive capability. Different mathematical expressions
for the relationship between compression and porosity were considered. The permeability
is expressed explicitly in terms of the fibre diameter and the compression fraction and
implicitly in terms of the porosity. The porosity is incorporated through the relationship
between the linear dimensions of the geometric model. The general applicability of the
model(s) was validated by making use of data on airflow through a soft fibrous porous
material as well as through glass and nylon fibres. The permeability predictions fall within
the same order of magnitude as the experimental data. Given the mathematical simplicity
of the model(s), the prediction capability is satisfactory. Attention is drawn to assumptions
made and model restrictions within the analytical modelling procedure. A general
predictive equation is presented for the permeability prediction in which a solid distribution
factor is introduced. The proposed models serve as basis for further adaptation and
refinement towards prediction capability. / AFRIKAANSE OPSOMMING: Vloei van vloeistowwe deur poreuse media speel ’n belangrike rol in ’n verskeidenheid kontekste
waarvan filtrasie een is. Die filtrasie doeltreffendheid van vesel filters hang af van
die mikro-strukturele karakterisering van hierdie poreuse materiale en word gereflekteer
in die permeabiliteit. Kompressie van veselagtige poreuse media het ’n beduidende effek
op die permeabiliteit. Eksperimentele data dui aan dat die verandering in permeabiliteit
gewoonlik oor meer as ’n orde grootte strek oor die klein porositeitsinterval waarin die
kompressie plaasvind. Relatief tot die aantal eksperimentele studies rakende hierdie verskynsel,
is daar ’n tekort aan geometriese modelle in die literatuur wat die effek van
kompressie op die permeabiliteit van veselagtige poreuse media in ag kan neem. Binne
die konteks van bestaande geometriese kanaal-skaal modelle gebasseer op reghoekige geometrie,
is ’n nuwe model voorgestel en ’n bestaande model verbeter om die effek van
een-dimensionele kompressie in die stroomsgewyse rigting te voorspel. Sonder om die
verbintenis tot wiskundige eenvoud prys te gee, is empiriese data van ’n nie-geweefde
veselagtige poreuse medium gebruik om die effek van die geometrie van ’n model op sy
voorspellingsvermo¨e uit te lig. Verskillende wiskundige uitdrukkings is oorweeg vir die
verband tussen kompressie en porositeit. Die permeabiliteit is eksplisiet uitgedruk in
terme van die veseldiameter en die kompressie breukdeel en implisiet in terme van die
porositeit. Die porositeit is ge-inkorporeer deur die verhouding tussen die lineêre dimensies
van die geometriese model. Die algemene toepaslikheid van die model(le) is gestaaf
deur gebruik te maak van data oor lugvloei deur ’n sagte veselagtige poreuse materiaal
sowel as deur glas en nylon vesels. Die voorspellings van die permeabiliteit val binne
dieselfde groote orde as die eksperimentele data. Gegee die wiskundige eenvoud van die
model(le), is die voorspellingsvermoë bevredigend. Aandag is gevestig op aannames wat
gemaak is en modelbeperkings binne die analitiese modellerings prosedure. ’n Algemene
voorspellingsvergelyking is voorgestel vir die voorspelling van die permeabiliteit waarin
’n vaste stof distribusie faktor geinkorporeer is. Die voorgestelde modelle dien as basis
vir verdere aanpassing en verfyning van voorspellingsvermoë.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/86245 |
| Date | 04 1900 |
| Creators | Van Heyningen, Martha Catharina |
| Contributors | Woudberg, Sonia, Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. |
| Publisher | Stellenbosch : Stellenbosch University |
| Source Sets | South African National ETD Portal |
| Language | en_ZA |
| Detected Language | Unknown |
| Type | Thesis |
| Format | 109 p. : ill. |
| Rights | Stellenbosch University |
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