A many-fibre model of airflow through a fibrous filter

Abstract A model of airflow through a filter is developed, in which the filter is approximated by an array of parallel fibres. The stream function is calculated, not by solving the flow equation, but by finding the functional form, expressed as a double Fourier series, that gives the lowest rate of dissipation of energy due to viscous drag, whilst satisfying the boundary conditions of the system. An explicit form for the stream function is obtained for two symmetrical arrays, and the velocity flow field is calculated for any orientation of airflow to the axis of array, and for any symmetrical shape of fibre. Calculated values of the absolute pressure drop, its variation with flow orientation and its variation with compression of the filter in the direction of airflow, based on this model, agree well with experimental results.