Tea and toast” and “beer potomania refer to diets that are severely deficient in solute load but high in free water.
Our kidneys cannot simply excrete free water. There is a minimum osmolality that the fluid has to have for the kidneys to excrete it. Some sources cite a minimum urine osmolality of 60 m Osm/L. If you hold that to be the minimum osmolality, the JASN 2008 article derives the following formula which can be used to estimate how much solute a person needs to consume to excrete a certain number of liters of water.
Free water clearance (cH2O). Uosm = Urinary osmolality. Posm= Plasma osmolality. Solute excretion is the amount of solute consumed which is to be excreted in urine.
They go on to explain that the equation above “not only reflects the well-established fact that as the urinary osmolality (Uosm) decreases the free water clearance commensurately increases but emphasizes that for any given Uosm it is the solute excretion that sets the ceiling as to how much free water will be excreted. Thus, at a urinary osmolality as low as 60 mOsm/kg if solute intake is 900 mOsm/d, 12 L of free water will be excreted. However, if the intake of solutes decreases to 600 mOsm/d, 8 L can be excreted, and in the more extreme setting in which the intake decreases to only 300 mOsm/d, a mere 4 L of free water can be excreted. An intake of fluids that exceeds this volume will culminate in hyponatremia.” JASN 2008.
KTA
The take-home point is that if water ingestion exceeds the amount that can be cleared with the solute excretion at the minimum allowed urinary osmolality, then fluid retention will happen, causing hyponatremia.
This mechanism is true for both “Tea and toast”, “beer potomania”, and primary polydipsia.
Further Reading
J Am Soc Nephrol. 2008 Jun;19(6):1076-8. Impact of solute intake on urine flow and water excretion. https://www.ncbi.nlm.nih.gov/pubmed/18337482