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Free flow channel confined by porous walls is a feature of many of the natural and industrial settings. Viscous flows adjacent to saturated porous medium occur in cross-flow and dead-end filtrations employed primarily in pharmaceutical and chemical industries for solid-liquid or gas-solid separations. Various mathematical models have been put forward to describe the conjugate flow dynamics based on theoretical grounds and experimental evidence. Despite this fact, there still exists a wide scope for extensive research in numerical solutions of these coupled models when applied to problems with industrial relevance. The present work aims towards the numerical analysis of coupled free/porous flow dynamics in the context of industrial filtration systems. The free flow dynamics has been expressed by the Stokes equations for the creeping, laminar flow regime whereas the flow behaviour in very low permeability porous media has been represented by the conventional Darcy equation. The combined free/porous fluid dynamical behaviour has been simulated using a mixed finite element formulation based on the standard Galerkin technique. A nodal replacement technique has been developed for the direct linking of Stokes and Darcy flow regimes which alleviates specification of any additional constraint at the free/porous interface. The simulated flow and pressure fields have been found for flow domains with different geometries which represent prototypes of actual industrial filtration equipment. Results have been obtained for varying values of permeability of the porous medium for generalised Newtonian fluids obeying the power law model. A series of numerical experiments has been performed in order to validate the coupled flow model. The developed model has been examined for its flexibility in dealing with complex geometrical domains and found to be generic in delivering convergent, stable and theoretically consistent results. The validity and accuracy of the simulated results has been affirmed by comparing with available experimental data.

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Transdermal drug delivery using microneedles depends on the rate of drug transport through the viable epidermis. Therefore minimizing the distance between the drug loaded surface and the microcirculation in the dermis where the drug is absorbed into the body is significant in improving drug delivery efficiency. A quantifiable relationship between microneedle design parameters and skin diffusion properties is therefore desirable, which is what this study aims to achieve. A framework is presented to quantitatively determine the effects of design parameters on drug diffusion through skin, where the effects of compressive strain on skin due to insertion of microneedle are considered. The model is then used to analyse scenarios of practical importance. For all scenarios analysed, predicted steady state flux was found to be lower when effect of microneedle strain on diffusion coefficient was accounted for. For example simulations results indicated increasing tip radius from 5μm to 20μm flux increased from 6.56x10 -6 mol/m 2 /s to 7.02x10 -6 mol/m 2 /s for constant diffusion coefficient. However if the effect of strain on diffusion coefficient is considered, the calculated flux increases from 5.30x10 -6 mol/m 2 /s to a peak value of 5.32x10 -6 mol/m 2 /s (at 10μm) and decreases to 5.29x10 -6 mol/m 2 /s. This paper contributes by reporting a framework to relate microneedle geometry to permeability with inclusion of the possible effects the microneedle design may pose on the diffusion coefficient.

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