How Long a Cure Takes to Reach the Middle: Salt Diffusion Times by Thickness, Computed from Fick's Law

Salt preserves meat only where it has arrived. The outside of a curing piece reaches a protective salt concentration quickly, while the centre may wait weeks. This paper computes that wait from Fick's second law for a slab salted on both faces. The stated inputs are a diffusion coefficient for sodium chloride in pork of 2.0e-10 m2/s at 4 °C, an Arrhenius temperature dependence with an activation energy of 25,000 J/mol, a surface held at 10.0 percent water-phase salt, and a required centre concentration of 3.5 percent water-phase salt. At 4 °C the centre reaches the required concentration in 1.57 days for a piece 2 cm thick, 6.29 days at 4 cm, 14.16 days at 6 cm, 25.17 days at 8 cm, and 39.33 days at 10 cm. At 12 °C the corresponding times are 1.16, 4.64, 10.44, 18.57, and 29.01 days. Set against stated spoilage timescales of 14.0 days at 4 °C and 5.0 days at 12 °C, the greatest thickness whose centre is protected in time is 5.97 cm in the refrigerator and 4.15 cm in the cool room. Beyond those thicknesses a surface cure alone, as modelled here, does not protect the centre before the stated spoilage time has passed. Because a constant surface concentration is favourable to the cure, these thicknesses are upper bounds, not safe allowances. SIMULATED, NOT MEASURED.