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Various hygiene products, notably incontinence pads, bring nonwoven “topsheet” fabrics into contact with individuals’ skin. This contact can damage the skin in various ways, including abrading it by friction, a mechanism enhanced by the presence of moisture. In recent years skin-nonwoven friction has been the subject of significant experimental study in the Continence and Skin Technology Group, UCL, in the course of which methods have been developed which can detect differences in friction between a chosen nonwoven and equivalent skin sites on different individuals under fixed conditions. The reasons for these differences are unknown; their elucidation is one focus of this work. The other is to establish the influence of coarse geometry on the dynamics of a tense nonwoven sheet sliding over a substrate and interacting with it by friction. The first part of this work (“microfriction”) is primarily experimental in nature, and involves two separate experiments. The first involves using a microscope with a shallow depth of field to determine the length of nonwoven fibre in contact with a facing surface as a function of pressure; the second consists of measuring friction between chosen nonwovens and a skin surrogate at a variety of pressures and speeds whilst simultaneously observing the behaviour of the interface down a microscope. Both techniques were extensively validated, and the data from the two experiments were then compared. It had originally been intended to conduct the friction experiment on skin (the other experiment does not require it), and though all equipment was developed with this in mind and all relevant permission was sought and obtained, it was not eventually possible. Instead, a skin friction surrogate (Lorica Soft) established in the literature was used. Data from this show that Amontons’ law (with respect to load) is obeyed to high precision (R2 > 0.999 in all cases), though there is the suggestion of sublinearity at low loads. Detailed consideration of the friction traces suggests that two different friction mechanisms are important, and comparison with the contact data suggests tentatively that they may correspond to adhesion between two different populations of contacts, one “rough” and one “smooth”. Further work applying these techniques to skin is necessary. The second aspect of the work is “geometric friction”; that is, the relationship between the geometry of a surface (on the centimetre scale and upwards) and the friction experienced by a compliant sheet (such as nonwoven topsheet) laid over it in tension. A general equation of motion for slippage between sheet and surface has been derived which in principle allows for both objects to deform and interact according to any plausible friction law. This has then been solved in integral form for Amontons’ law and a low density strip exhibiting no Poisson contraction sliding over any surface with zero Gaussian curvature; closed form solutions for the specific cases of a prism and a circular cone have then been derived and compared. Experimental verification has been provided by a colleague, which shows very good agreement between theory and experiment. It has also been shown that, taking a naïve approach, the classic model for a rigid cylinder can be applied even to a quite extreme cone with experimentally negligible error. NB All prior copyrighted material (diagrams in all cases) has been removed from this edition to facilitate electronic distribution. They have been replaced with boxes of the same size, so pagination is identical with the complete version.

Incontinence represents a costly health problem that affects a person’s quality of life physically, mentally and socially to a greater degree than diabetes, arthritis and many other chronic conditions. Surgery and medication can help improving the symptoms but deposable pads represent the main reliable management solution. In recent years, the disposable products became thinner and more discreet with the introduction of superabsorbent polymers (SAPs). SAPs are in general made of poly-acrylic acid partially neutralised, lightly cross-linked that can take up to 1000 times their weight in water and up to 100 times in urine and hold it under pressure. In order to design and produce reliable absorbent products, there is a need to understand the basic science behind superabsorbent polymers. The literature in this field is vague but basic physics can be applied from literature on soil science and mineralogy. The aim of this project is to develop relevant methods and reliable research methodology to determine properties of superabsorbent polymers such as swelling kinetics, porosity and permeability which could be at use in future mathematical model that would correlate these properties to the product performance. The work comprised in this report is primarily experimental in nature and involves developing several types of testing methods for simulating the interaction of fluid in a pad. More importantly, research methodologies that would lead to determine the porosity of wet gel beds were produced. This included methods for removing the fluid in-between the polymer particles (interstitial) without removing any fluid from within. The final methodology developed is then presented as a liquid porosimetry-based method that integrates swelling kinetics measurements and allows the calculation of the wet gel bed SAP porosity as a function of time and pressure.

In this thesis we examine the behaviour of shells supported by elastic foundations. We begin by critically analysing the existing literature on the study of thin objects such as films, plates, membranes and shells, and we highlight their limitations, validity and present correct formulations when possible. We also do the same for various frictional laws, in particular, Coulomb's law of static friction. Then, we extend the capstan equation to noncircular geometries by modelling membranes supported by rigid foundations in presence of friction. We provide closed-form solutions and compare them to other similar existing models in the literature. Then, we begin the study of shells supported by elastic foundations. We treat the bonded case as a boundary form and prove the existence and the uniqueness of solutions, and thus, prove it is a mathematical theory and not merely a mathematical model. To conclude this case we conduct numerical experiments and compare the results against existing models in the literature. Finally, we introduce a constraint and assert that this condition is analogous to classical frictional laws. This constraint is then used to model shells supported by elastic foundations with friction. As with the previous case, we again prove the existence and the uniqueness of solutions, and conclude by conducting numerical experiments and comparing the results against existing models in the literature. Applications for our work can be found in cable drive electronic systems, curvilinear stretchable electronics and modelling skin abrasion.