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Abstract

A code, MOPOD, has been developed to investigate general relationships between simple porosity growth laws and pore growth phenomena. MOPOD has been formulated as an ‘initial value problem’ and to date, investigations have focused on a very simple porosity growth law of the form dai(t)/dt = vei, where e is the aperture growth rate exponent. A range of qualitatively distinct evolved geometries have been described for porosity growth on 2D and 3D arrays of varying geometries and connectivities as a function of the exponent, e, of the aperture growth-rate law, and the width of the initial aperture distribution, σz. At low growth-rate exponents and moderate values of σz over time there is a homogenization of apertures oriented sub-parallel to the head gradient. At moderate growth-rate exponents these apertures become increasingly heterogeneous in evolved arrays, with planar heterogeneities developing sub-parallel to the head gradient for low values of σz while anastomosing structures develop at higher values of σz. For larger growth-rate exponents preferentially enlarged array-spanning paths develop. No self-organization phenomena have been observed because periodic or cyclic behaviour is not inherent in the simple growth laws investigated to date.

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