A MATHEMATICAL-MODEL FOR DIFFUSION AND EXCHANGE PHENOMENA IN ULTRA NAPKINS

The performance of napkins is nowadays improved substantially by embedding granules of a superabsorbent into the cellulose matrix. In this paper a continuous model for the liquid transport in such an 'ultra napkin' is proposed. Its mean feature is a non-linear diffusion equation strongly coupled with an ODE describing a reversible absorption process. An efficient numerical method based on a symmetrical time splitting and a finite difference scheme of ADI-predictor-corrector type has been developed to solve these equations in a three-dimensional setting. Numerical results are presented that can be used to optimize the granule distribution.