PPT Slide
If we take all the baryons in this volume and sweep them up into small dense clouds, the recombination rate increases as the density squared: make them dense enough and they will become neutral.
You could sweep the gas up into a few big neutral clouds or many small neutral clouds. We know, however, that a large fraction of sight-lines though the cluster intercept one of these neutral clouds. Small clouds have higher ratios of cross-sectional area to volume (the square-cube law). To have the gas both neutral and covering most sight-lines through the cluster, we can thus place an upper limit on the size of the neutral clouds: they must be 1kpc or less in width, and have number densities of around 0.1 per cubic cm. The metal line ratios support this model.