Dialysis is commonly used in medical facilities to aid filtration of the blood for kidney-deficient patients. For these devices, it is useful to have a predictive type of efficiency so that improvement in their performance or a better design can be achieved. This efficiency can be obtained in terms of concentrations of the blood contaminant needed to be removed. Now, the concentration of the waste in the blood can be mathematically modeled through the use of the convective-diffusive transport equations for the dialyzer device. An asymptotic solution is helpful in order to predict such an efficiency.
In this presentation, the authors will analyze the convective-diffusive transport through a semi-permeable cylindrical membrane to determine the effects of the various parameters (i.e. Sherwood number, geometrical dimensions) on the dialyzer performance and efficiency. An asymptotic solution is obtained by assuming a form of the solution to the partial differential equation governing the transport in the dialyzer. This asymptotic solution is validated through the general solution obtained using the Green's function method. Through this comparison, the range of validity of the asymptotic solution can be determined as well as what assumptions in the analysis can be relaxed to acquire a more realistic solution or assess its limitations. This analysis can ultimately aid in the improvement and optimization of dialyzer performance.