What must happen to the cell volume in order for a prokaryotic membrane to pinch inward and divide the cell in two?

In a prokaryotic division, the cellular reproduction is by binary fission. The bacterial chromosomes replicate then proteins migrate toward the midpoint of the cell and the duplicated chromosomes moves away from each other forming a protein ring at the midpoint. Plasma membrane and cell wall materials will accumulate to add to the cell volume. Then, the protein ring will form a septum that pinch inward and divide the cell in two, forming two daughter cells.