Each grain of NaCl is treated as a shrinking sphere obeying the Noyes-Whitney dissolution law: the mass flux leaving a crystal is proportional to its surface area and to how far the bulk solution sits below saturation, dm/dt = -k·A·(Cs - C). Because A = 4πr² and the crystal volume is (4/3)πr³, the radius itself shrinks at a rate that does not depend on r:
dr/dt = -k(T, stir) · (Cs(T) - C) / rho_NaCl
dC/dt = (sum of dissolved mass) / water mass
Cs(T) is read off the real NaCl solubility curve (about 35.7 g per 100 g water at 0°C, rising only mildly to 39.8 g at 100°C — NaCl is famous for a nearly flat solubility curve, unlike KNO₃ or most other salts). The mass-transfer coefficient k rises with stirring (thinner diffusion boundary layer) and with temperature (faster ion diffusion). As C climbs toward Cs the driving force shrinks, so dissolution slows and eventually stops — any grains still solid at that point simply sit at the bottom, exactly like a real saturated brine.
- Tank — grains sink, shrink and vanish; the water tints blue as ions accumulate.
- Solubility curve — the real Cs(T) curve with a marker at the current temperature; the dot below it is where the bulk concentration C actually sits.
- Saturation trace — C/Cs over time, capped at 100% the moment the brine saturates.