Nobel P. S., Cui M., Shrinkage of Attached Roots of Opuntia ficus-indica in Response to Lowered Water Potentials — Predicted Consequences for Water Uptake or Loss to Soil, Annals of Botany, 1992, 70(6):485-491, doi: 10.1093/oxfordjournals.aob.a088508
The abstract describes root diameter changes during dehydration. The model analyses water flow through the root, developing air gap and soil.