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Paper-based microfluidic devices are popular for their ability to automate multistep assays for chemical or biological sensing at a low cost, but the design of paper microfluidic networks has largely relied on experimental trial and error. A few mathematical models of flow through paper microfluidic devices have been developed and have succeeded in explaining experimental flow behavior. However, the reverse engineering problem of designing complex paper networks guided by appropriate mathematical models is largely unsolved. In this article, we demonstrate that a two-dimensional paper network (2DPN) designed to sequentially deliver three fluids to a test zone on the device can be computationally designed and experimentally implemented without experimental trial and error. This was accomplished by three new developments in modeling flow through paper networks: (i) coupling of the Richards equation of flow through porous media to the species transport equation, (ii) modeling flow through assemblies of multiple paper materials (test membrane and wicking pad), and (iii) incorporating limited-volume fluid sources. We demonstrate the application of this model in the optimal design of a paper-based signal-enhanced immunoassay for a malaria protein, PfHRP2. This work lays the foundation for the development of a computational design toolbox to aid in the design of paper microfluidic networks. ©

Microfluidic paper-based analytical devices (μPADs) are simple but powerful analytical tools that are gaining significant recent attention due to their many advantages over more traditional monitoring tools. These include being inexpensive, portable, pump-free, and having the ability to store reagents. One major limitation of these devices is slow flow rates, which are controlled by capillary action in the hydrophilic pores of cellulosic paper. Recent investigations have advanced the flow rates in μPADs through the generation of a gap or channel between two closely spaced paper sheets. This multilayered format has opened up μPADs to new applications and detection schemes, where large gap sizes (>300 μm) provide at least 169× faster flow rates than single-layer μPADs, but do not conform to established mathematical models for fluid transport in porous materials, such as the classic Lucas-Washburn equation. In the present study, experimental investigations and analytical modeling are applied to elucidate the driving forces behind the rapid flow rates in these devices. We investigate a range of hypotheses for the systems fluid dynamics and establish a theoretical model to predict the flow rate in multilayered μPADs that takes into account viscous dissipation within the paper. Device orientation, sample addition method, and the gap height are found to be critical concerns when modeling the imbibition in multilayered devices.

In this paper a simplified network model for mechano-sorptive creep is presented, which is a further development of an earlier paper [Strömbro, J., Gudmundson, P., 2008. Mechano-sorptive creep under compressive loading – a micromechanical model. International Journal of Solids and Structures 45 (9), 2420–2450.]. It is assumed that the anisotropic hygroexpansion of the fibres leads to large stresses at the fibre bonds when the moisture content changes. The resulting stress state will accelerate creep if the fibre material obeys a constitutive law that is non-linear. Fibre kinks are included in order to capture experimental observations of larger mechano-sorptive effects in compression than in tension. Moisture dependent material parameters and anisotropy in the fibre distribution have been introduced. Theoretical predictions based on the model are compared to experimental results for an anisotropic paper both under tensile and compressive loading at varying moisture content and it is found that the important features in the experiments are captured by the model. Different kinds of drying conditions have also been examined.

The creep of paper is accelerated by moisture cycling, an effect known as mechano-sorptive creep. It has also been observed that the mechano-sorptive effects are larger in compression than in tension. In this paper a simplified network model for mechano-sorptive creep is presented. It is assumed that the anisotropic hygroexpansion of the fibres leads to large stresses at the fibre–fibre bonds when the moisture content changes. The resulting stress state will accelerate creep if the fibre material obeys constitutive laws that are non-linear in stress. Geometrical fibre effects are included in the model in order to capture experimental observations of the differences between paper loaded in tension and compression. Theoretical predictions based on the developed model are compared to experimental results for paper both under tensile and compressive loading at varying moisture content. The important features in the experiments are captured by the model, i.e. the creep is accelerated by the moisture cycling and the mechano-sorptive effects are larger in compression than in tension.

The increasing costs associated with water supply and the disposal of wastewater has stimulated industries to seek more efficient water management systems. Mathematical modelling and simulation can be a very valuable tool for the study of the multiple alternatives available whilst assessing optimum solutions for water management in industry. This study introduces a new steady state model library able to reproduce industrial water circuits. It has been implemented in a novel software framework for the representation, simulation and optimization of industrial water networks. A water circuit representing a paper mill has been modelled and simulated showing the capability to reproduce real case studies. Alternative scenarios for the water network have also been tested to assess the capability of the models to optimize water circuits minimizing total cost.

The migration of components from paper into Tenax® was studied to determine the influence of molecular size and chemical character of the migrant and the influence of paper characteristics in the migration process. The Weibull model was applied because Fick's 2nd law of diffusion gave poor fits in some cases. The migration pattern depended on the migrants molecular size and was independent of temperature in the studied range. The migration rate decreased with the migrant molecular size. The influence of the migrants character (polarity and vapour pressure) on the migration behaviour was also studied: nonpolar migrants with high vapour pressure presented low relative migration values and polar migrants presented high values of relative migration. Results indicated that the apparent partition coefficient between paper and the simulant Tenax® increased with the migrant vapour pressure and with both the paper grammage and the recycled pulp content.

In this thesis, the focus has been on micro-mechanical mechanisms in polymer-based materials and structures. The first part of the thesis treats length-scale effects on polymer materials. Experiments have showed that the smaller the specimen, the stronger is the material. The length-scale effect was examined experimentally in two different polymers materials, polystyrene and epoxy. First micro-indentations to various depths were made on polystyrene. The experiments showed that length-scale effects in inelastic deformations exist in polystyrene. It was also possible to show a connection between the experimental findings and the molecular length. The second experimental study was performed on glass-sphere filled epoxy, where the damage development for tensile loading was investigated. It could be showed that the debond stresses increased with decreasing sphere diameter. The debonding grew along the interface and eventually these cracks kinked out into the matrix. It was found that the length to diameter ratio of the matrix cracks increased with increasing diameter. The experimental findings may be explained by a length-scale effect in the yield process which depends on the strain gradients. The second part of the thesis treats mechano-sorptive creep in paper, i.e. the acceleration of creep by moisture content changes. Paper can be seen as a polymer based composite that consists of a network of wood fibres, which in its turn are natural polymer composites. A simplified network model for mechano-sorptive creep has been developed. It is assumed that the anisotropic hygroexpansion of the fibres leads to large stresses at the fibre-fibre bonds when the moisture content changes. The resulting stress state will accelerate creep if the fibre material obeys a constitutive law that is non-linear in stress. Fibre kinks are included in order to capture experimental observations of larger mechano-sorptive creep effects in compression than in tension. Furthermore, moisture dependent material parameters and anisotropy are taken into account. Theoretical predictions based on the developed model are compared to experimental results for anisotropic paper both under tensile and compressive loading at varying moisture content. The important features in the experiments are captured by the model. Different kinds of drying conditions have also been examined. QC 20100910

A mathematical model for fibrous structures using a direction dependent scaling law is presented. The orientation of fibrous nets (e.g. paper) is analysed with a method based on the curvelet transform. The curvelet-based orientation analysis has been tested successfully on real data from paper samples: the major directions of fibrefibre orientation can apparently be recovered. Similar results are achieved in tests on data simulated by the new model, allowing a comparison with ground truth. peerReviewed