Abstract
Many multiphase transport problems are characterized by a random mixing of the phases (e.g., transport in porous media). In general, because of this randomness, instrumentation windows are designed such that only averages of field properties over the various phases are measured. In this article we identify an instrument window with a compact distribution. If the field property being filtered lies in the space of tempered distributions, then constraints may be derived on the structure of the filter. Distributional equations are derived which represent transport of a filtered property. The equations are general enough to allow for the use of different instruments to measure different properties. An equation representing the relationship between phase properties and filtered properties is derived when the filter is given by a measure with compact support.
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Cushman, J.H. Multiphase transport based on compact distributions. Acta Appl Math 3, 239–254 (1985). https://doi.org/10.1007/BF00047330
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DOI: https://doi.org/10.1007/BF00047330