In immobilized algae beads, nutrients such as NH4 and PO4 get adsorbed by the immobilizing matrix (such as alginate), following which they are assimilated by the microalgae via process of photosynthesis. In most research studies, the removal of nutrients by immobilized algae beads is much higher than blank beads. So is the assimilation process faster than the adsorption process?
It more complex then rate perse. When algae (or any living organism) assimilate nutrients they convert simple, small molecules (here NH3 and PO4) to large complex molecules (proteins, nucleic acids etc), and finally to new cells. The absorption on the alginate is a much simpler process. Furthermore, given the above the alginate (or any other absorbing material) will reach saturation much faster as there is no conversion. Thus the rate of alginate (absorption) + micro-algae (assimilation) will be much faster.
And two small correction:
(i) Photosynthesis of micro-algae does not assimilate NO3 or PO4 directly. It provide the cells with a carbon source. The oxygen produced by the water splitting in the photosynthetic could result in oxidation of NO3 to nitrate though.
(ii) The process does no have to go "absorption in alginate --> assimilation". Depending how you make them the alginate beads can be pretty pours.