Drying Fish Before It Spoils: A Thickness Bound from the Race Between Water Loss and Bacterial Growth

Sun-drying fish is a race. The centre of a piece must lose enough water to reach a safe water activity before bacteria multiplying on and in the fish reach a spoilage level. This paper computes that race from stated assumptions: exponential bacterial growth from an initial count of 1000 colony-forming units per gram to a stated spoilage threshold of 10,000,000 per gram (13.29 doublings, at doubling times of 0.67 hours at 35 C, 0.80 hours at 32 C and 1.67 hours at 25 C), and a slab diffusion model for drying, with effective diffusivities of 2.0, 1.2 and 0.8 x 10-9 m2/s in three climates and a safe centre target of water activity 0.85, corresponding to a centre moisture of 24.6 percent dry basis under a stated sorption relation for fish. The greatest full thickness that wins the race is 14.2 mm in hot-arid conditions, 10.5 mm in hot-humid coastal conditions and 13.6 mm in temperate conditions. The bound is severe because drying time grows with the square of thickness while growth time does not depend on thickness at all: a 20 mm piece needs 17.6 hours for its centre to reach the target in hot-arid air against a spoilage time of 8.9 hours, and 38.3 hours in hot-humid air against 10.6 hours. A 40 mm piece, representative of a thick whole fish laid out unsplit, needs 70.5 hours in hot-arid air and 153.0 hours in hot-humid air, exceeding the spoilage time by factors of about eight and fourteen. Under the stated assumptions, drying thick whole fish unsplit in humid coastal conditions cannot produce a safe product; splitting or filleting to about 10 mm is the change that alters the outcome. SIMULATED, NOT MEASURED.