Congratulations on this interesting piece of work. Of course the problem you faced in this research is the complete lack of any known silicon (silicic acid) biochemistry. The only biologically available form of silicon is silicic acid which is a small neutral molecule. You at least did not get this confused with silicate which does not exist in natural waters below pH 10. So, your method needs to apply to a system in which there is essentially no binding or at least nothing stronger than hydrogen bonds. It is most likely that silicic acid follows water into the diatom and the uptake of water is both osmotically but also importantly 'hydraulically' driven. Think of the diatom like a small water pump taking up and expelling water. The silicic acid follows the water at rates depending upon the individual water channels and potentially other components capable of supporting constrained environments. How might this then fir with your modelling exercise?
Best wishes
Chris Exley