Membrane filters are used extensively in microfiltration applications. The type of membrane used can vary widely depending on the particular application, but broadly speaking the requirements are to achieve fine control of separation, with low power consumption. The solution to this challenge might seem obvious: select the membrane with the largest pore size and void fraction consistent with the separation requirements. However, membrane fouling (an inevitable consequence of successful filtration) is a complicated process, which depends on many parameters other than membrane-pore size and void fraction; and which itself greatly affects the filtration process and membrane functionality. In this work we formulate mathematical models that can (i) account for the membrane internal morphology (internal structure, pore size and shape, etc.); (ii) describe fouling of membranes with specific morphology; and (iii) make some predictions as to what type of membrane morphology might offer optimum filtration performance.

Pleated membrane filters are widely used in many applications, and offer significantly better surface area to volume ratios than equal-area unpleated membrane filters. However, their filtration characteristics are markedly inferior to those of equivalent unpleated membrane filters in dead-end filtration. While several hypotheses have been advanced for this, one possibility is that the flow field induced by the pleating leads to spatially non-uniform fouling of the filter, which in turn degrades performance. In this paper we investigate this hypothesis by developing a simplified model for the flow and fouling within a pleated membrane filter. Our model accounts for the pleated membrane geometry (which affects the flow), for porous support layers surrounding the membrane, and for two membrane fouling mechanisms: (i) adsorption of very small particles within membrane pores; and (ii) blocking of entire pores by large particles. We use asymptotic techniques based on the small pleat aspect ratio to solve the model, and we compare solutions to those for the closest-equivalent unpleated filter.

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Pleated membrane filters, which offer larger surface area to volume ratios than unpleated membrane filters, are used in a wide variety of applications. However, the performance of the pleated filter, as characterized by a flux-throughput plot, indicates that the equivalent unpleated filter provides better performance under the same pressure drop. Earlier work (Sanaei & Cummings 2016) used a highly-simplified membrane model to investigate how the pleating effect and membrane geometry affect this performance differential. In this work, we extend this line of investigation and use asymptotic methods to couple an outer problem for the flow within the pleated structure to an inner problem that accounts for the pore structure within the membrane. We use our new model to formulate and address questions of optimal membrane design for a given filtration application. *

Cell proliferation within a fluid-filled porous tissue-engineering scaffold depends on a sensitive choice of pore geometry and flow rates: regions of high curvature encourage cell proliferation, while a critical flow rate is required to promote growth for certain cell types. When the flow rate is too slow, the nutrient supply is limited; when it is too fast, cells may be damaged by the high fluid shear stress. As a result, determining appropriate tissue-engineering-construct geometries and operating regimes poses a significant challenge that cannot be addressed by experimentation alone. In this paper, we present a mathematical theory for the fluid flow within a pore of a tissue-engineering scaffold, which is coupled to the growth of cells on the pore walls. We exploit the slenderness of a pore that is typical in such a scenario, to derive a reduced model that enables a comprehensive analysis of the system to be performed. We derive analytical solutions in a particular case of a nearly piecewise constant growth law and compare these with numerical solutions of the reduced model. Qualitative comparisons of tissue morphologies predicted by our model, with those observed experimentally, are also made. We demonstrate how the simplified system may be used to make predictions on the design of a tissue-engineering scaffold and the appropriate operating regime that ensures a desired level of tissue growth.

Flow in the inverted U-shaped tube of a conventional siphon can be established and maintained only if the tube is filled and closed, so that air does not enter. We report on siphons that operate entirely open to the atmosphere by exploiting surface tension effects. Such capillary siphoning is demonstrated by paper tissue that bridges two containers and conveys water from the upper to the lower. We introduce a more controlled system consisting of grooves in a wetting solid, formed here by pressing together hook-shaped metallic rods. The dependence of flux on siphon geometry is systematically measured, revealing behaviour different from the conventional siphon. The flux saturates when the height difference between the two container's free surfaces is large; it also has a strong dependence on the climbing height from the source container's free surface to the apex. A one-dimensional theoretical model is developed, taking into account the capillary pressure due to surface tension, pressure loss due to viscous friction, and driving by gravity. Numerical solutions are in good agreement with experiments, and the model suggests hydraulic interpretations for the observed flux dependence on geometrical parameters. The operating principle and characteristics of capillary siphoning revealed here can inform biological phenomena and engineering applications related to directional fluid transport.

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