INTERACTIVE MODELFIELD NOTEHEAT TRANSFER
The Two-Bath Egg Bench
- Study
- Field note
- Review
- Peer-edited by the club review board
- Article
- 14 sectionsabout 20 min
- Files
- LaTeX source22 kB
Two models below. The first is a simplified stand-in for the paper's real finite-element simulation: it tracks two lumped temperatures, one for the albumen and one for the yolk, and runs the paper's own reported Arrhenius rate law on each to estimate how “done” they are. It is not the paper's spatial model — it is a two-node cartoon of it, built so you can feel the shape of the mechanism. The second model strips away the egg entirely and just shows you the rate law itself, because that curve is the reason any of this works.
Model 1. Two nodes, one egg
The albumen node tracks whichever bath it is currently in fairly quickly (it sits right against the water). The yolk node tracks it much more slowly, because it is buried under a centimetre or two of albumen. Both nodes then feed the paper's own reported rate constants for their region into k = A·exp(−Ea/RT), and a cooking fraction accumulates from 0 to 100% for each. This is a linear lumped model: it will always converge, on average, to the plain midpoint of whatever two bath temperatures you choose, which is a real limitation the field note discusses — the paper's own nonlinear finite-element model finds the yolk two degrees above that midpoint, something this toy cannot reproduce.
- Total time
- 32.0 min
- Time in hot bath
- 16.0 min
- Time in cold bath
- 16.0 min
- Naive mean bath temp
- 65.0°C
- Albumen cooked at end
- —
- Yolk cooked at end
- —
Both nodes obey the same rate law with the paper's own reported yolk and albumen parameters (Ea and A) and an assumed gas constant R = 8.314 J mol-1 K-1, the value implied by the equation's form but not stated explicitly in the paper. “Cooked” here means the rate-law fraction X reaching close to 1, not a texture judgement.
Model 2. The rate law itself
Everything above rides on one curve: how fast egg proteins denature as a function of temperature, using the paper's own Arrhenius parameters for yolk and albumen. Drag the dial and watch both rate constants, plotted on a logarithmic scale because they span more than seventy orders of magnitude across this range.
Move the dial from 65°C to 100°C: the yolk's rate constant does not double or triple, it jumps by roughly five orders of magnitude. That single fact is why the yolk has to be shielded by the egg's own geometry rather than protected by the recipe — at the bath's own hot-phase temperature, an unshielded yolk would be overcooked before the two-minute hot phase was a tenth over.
What the toggling does and does not prove
Neither model reproduces the paper. Di Lorenzo and colleagues solved a real finite-element heat-conduction problem over an actual ellipsoid geometry, coupled to the same two Arrhenius equations used here, and validated the result against real cooked eggs. What is here is the kinetic engine underneath their result, with two lumped nodes standing in for a full spatial temperature field, and the arithmetic left where you can check it against your own dragging.