How Much Salt a Vegetable Ferment Needs: A Lower Bound from Acidity, and an Upper Bound from the Fermenting Organisms Themselves

Recipes for fermented vegetables state a brine strength, but the organisms in the jar do not experience the brine strength: they experience the salt spread through all the water present, including the water inside the vegetable. This paper computes that distinction and its consequences for a stated batch of 1000 g of cabbage at 92 percent moisture covered with 1000 g of brine at 20 °C. A 2.5 percent brine delivers only 1.30 percent salt in the aqueous phase. Under stated rates for a mixed lactic-acid culture, for salt-sensitive enterobacteria, and for salt-tolerant film yeasts, the days for the ferment to reach pH 4.6 are 3.30 at 1.5 percent brine, 3.58 at 2.0 percent, 3.88 at 2.5 percent, 4.52 at 3.5 percent, and 5.62 at 5.0 percent. The band that acidifies before either spoilage group reaches its stated threshold is 2.0 to 3.5 percent brine (1.04 to 1.82 percent in the aqueous phase). Below the band the enterobacteria arrive first, by 0.27 days at 1.5 percent brine; above the band the film yeasts arrive first, by 0.12 days at 5.0 percent brine, because the extra salt slows the acid producers while leaving the yeasts nearly unaffected. The common claim that more salt is always safer does not hold in this model: the safety margin rises from -0.27 days at 1.5 percent brine to about +0.98 days at 3.5 percent and then falls to -0.12 days at 5.0 percent. SIMULATED, NOT MEASURED.