D-optimal designs for sorption kinetic experiments: Cylinders

This project extends prior research in D-optimal design for sorption kinetics in a slab to cylindrical geometry. Combining Fick’s second law of diffusion and a convective mass transfer boundary condition at the surface of the cylinder with D-optimal theory provides the experimental design which results in the best estimates of the model parameters: the material’s diffusivity and the convective mass transfer coefficient. The results show that for a wide range of diffusivities and convective mass transfer coefficients, the D-optimal support points can be expressed in terms of the dimensionless Biot number and Fourier modulus. Furthermore, it is shown that when the Biot number is between 0.10 and 10.0, both the diffusivity and the convective mass transfer coefficient can be simultaneously estimated. Outside of this range, only one model parameter can be determined, and which one can be determined depends on the magnitude of the Biot number.