Raw Egg Spread Simulator (3D)

Hob	Pan ≈	Model, 1 egg, no lid (time to 97 % of white set)
1	100 °C	Barely sizzles. Very slow: over 10 min, and the top may never set without a lid.
2	125 °C	Gentle, ~4½ min. No browning — the pale, tender fried egg.
3	150 °C	Medium, ~3 min. A little colour at the very edge after ~3 min.
4	175 °C	Medium-high, ~2½ min. Edges brown from ~50 s.
5	200 °C	Hot, ~2¼ min. Crisp brown lace from ~30 s.
6	230 °C	Max, ~2 min. Browning from ~25 s; edges burn if left.

In plain terms

When the shell disappears, gravity pulls the egg white outwards and viscosity (the white's "thickness") resists it. Heavier (denser) liquid pushes harder; more viscous liquid moves slower. Two more things stop the spread:

Thick white is a soft gel. It only flows while the push from its own weight is bigger than its strength (a "yield stress"), so it stays piled up round the yolk. Fresher eggs have stronger gel, so it piles higher — that is what the industry's Haugh-unit test measures.
Thin white runs out fast and stops when its edge is so thin that surface tension holds it in place (about 2–3 mm).

The yolk is a liquid in a thin skin (the vitelline membrane). The skin, not viscosity, sets its final shape; the yolk's viscosity only controls how much it wobbles while it settles. The yolk sits in the white, and the thick white clings over it as a clear film wherever the gel is strong enough to hold on the slope.

Several eggs share one sheet of white, so their whites flow into each other and merge. Yolks drift with the white around them and push apart when their skins touch.

Cooking. Heat flows up from the pan through the white. Water stops the white getting hotter than 100 °C, so a hotter pan mostly cooks the bottom faster and browns thin edges sooner. The top loses heat to the air — mostly by evaporation — so the thickest white next to the yolk can stay raw on top; that is why cooks use a lid or baste. Cold eggs also draw heat out of the pan, so more eggs means a cooler pan. White starts to set at about 61–65 °C and is firm by about 80 °C; yolk thickens at about 65 °C and sets at about 70 °C. Set white stops flowing.

How the model works

FLOW Flow per unit width: q = −K ∇P, P = h + (ρ_yolk/ρ_white)·T_yolk (yolk weight acts as extra height) Runny (Newtonian) layer: K = ρ g h³ / (3μ) Gel (Bingham) layer: Y = h − τ_y / (ρ g |∇P|), K = ρ g Y² (3h − Y) / (6μ) Early collapse cap: speed ≤ √(g h) Edge (contact line): a dry spot only wets if the edge is deeper than h_eq = 2·√(γ/ρg)·sin(θ/2) Cooked white: only the unset share of each column can flow Yolks: rest on the white; T(r) = H·√(1 − r²/a²); drift with the white in a ring round them; pushed apart if their footprints overlap White film on yolk: t = τ_y / (ρ g sin α), capped at 1.5 mm HEAT (each grid cell: 5 layers through the white; each yolk: 8 layers through its centre) Conduction: ρc ∂T/∂t = k ∂²T/∂z² (implicit, per column) Pan → white: contact conductance 200 W/m²K (through the oil film) Top → air: 18 W/m²K (convection + radiation) to air warmed by the pan: T_air + 0.15·(T_pan − T_air) Evaporation from the top: q = h_m·L_v·(ρ_v,sat(T) − RH·ρ_v,sat(T_room)), h_m = h_conv/(ρ_air c_p,air·0.9) (heat–mass transfer analogy; Magnus formula for vapour pressure; RH 50 %) Water: no layer above 100 °C (extra heat boils water off) Pan: C·dT/dt = G_hob·(T_element − T) − G_loss·(T − T_room) − (heat into the eggs) C = 1200 J/K, G_hob = 15 W/K, G_loss = 3 W/K; the element level holds an empty pan at the chosen temperature, so cold eggs pull the pan down and it recovers over ~1 min Setting (first order, 4 s): white 0 → ½ over 60–65 °C, ½ → 1 over 65–80 °C yolk 0 → ½ over 64–68 °C, ½ → 1 over 68–72 °C Browning: thin (< 3.5 mm), set white browns at a rate ∝ (T_pan − 140 °C) Start: eggs go into a preheated pan Haugh unit: HU = 100·log₁₀(h_mm − 1.7·W^0.37 + 7.6)

The grid is 128 × 128 cells over 30 cm (2.3 mm cells), solved semi-implicitly with a conjugate-gradient solver. Volume (white on the surface plus the films on the yolks) is conserved to better than 0.001 %. Once nothing has moved for a second, the flow solve is skipped and only re-checked every 0.5 s, which is what makes 10–30× playback possible for cooking.

Values used

Property	Default	Basis
Egg white density	1040 kg/m³	measured Thick white 1.046 g/cm³ [5]; whole egg contents 1.031 g/cm³ [4]. One study lists hen white at 1134 kg/m³ [1] — an outlier, not used.
Yolk density	1030 kg/m³	measured 1027 [1] to 1034 kg/m³ [5]
Thin white viscosity	0.012 Pa·s	measured Liquid egg white 0.0116 Pa·s at 25 °C [3]
Thick white viscosity	2 Pa·s	measured Whole white ≈2000× water at 1 s⁻¹; power-law n = 0.31, k = 2.1 Pa·sⁿ [2]
Yolk viscosity	1.0 Pa·s	measured 0.51 Pa·s at 25 °C falling to 0.12 Pa·s at 60 °C [3]; Herschel–Bulkley K = 1.5, n = 0.90 [1]. The temperature trend from [3] scales the slider value.
Thick white yield stress	12 Pa	calibrated Gives ≈5.7 mm thick white and ≈76 HU, in line with measured 5.6–6.3 mm and 73–78 HU [6]. Stirred white measures below 0.8 Pa [2]; the intact gel is much stronger, so this is a model fit.
Egg make-up	58 g; 58 % white, 31 % yolk, 11 % shell	measured Average hen egg ≈57 g; 17 % inner thin / 57 % thick / 23 % outer thin white [7]
Yolk index	0.40	measured Good egg 0.32–0.40 [8]; farm 0.45, retail ≈0.35 [9]
Thermal conductivity / diffusivity	white 0.52 W/m·K, 1.7×10⁻⁷ m²/s; yolk 0.34 W/m·K, 1.3×10⁻⁷ m²/s	measured Coimbra et al. (2006), as tabulated in [15]
Setting temperatures	white 60–80 °C; yolk 64–72 °C	measured White starts to set 62–65 °C (ovotransferrin, 12 % of white); ovalbumin (54 %) at ~80 °C; yolk thickens ~65 °C, sets ~70 °C [14]. The smooth ramps between these points are assumed.
Hob 1–6 → pan °C	100 / 125 / 150 / 175 / 200 / 230	approximate Manuals: 1 = low, 2–5 = medium, 6 = high, depends on pan [11]. Mapped onto published low/medium/high pan ranges of roughly 93–135 / 135–180 / 180–230 °C [12] (a general cooking-guide source, not a standard). A pale, tender fried egg needs a pan of about 120 °C [13].
Pan → egg contact	200 W/m²K	calibrated Chosen so hob 3 (≈150 °C) sets the white in ≈3 min, matching recipe times for an uncovered sunny-side-up egg: 3–4 min at medium [16], 2–3 min at medium-low [17]
Air loss, warm air over the pan, humidity, pan heat capacity and coupling, setting time, browning onset	18 W/m²K; 0.15; 50 %; 1200 J/K, 15 & 3 W/K; 4 s; 140 °C	assumed Engineering estimates; no egg-specific source found
Film cap over the yolk	1.5 mm	assumed
Surface tension / contact angle	0.050 N/m; plate 60°, oiled non-stick pan 70°, glass 35°	assumed

Limits — read before relying on numbers

Thin-film theory is approximate for the first ~0.1 s while the egg is still tall.
Each white uses one "average" viscosity plus a yield stress; real white is shear-thinning and slightly elastic.
Heat only flows up and down within each cell, not sideways, and moving white carries its heat with it. Hot oil spitting onto the top is not modelled, so at high heat real eggs may set on top a little sooner than shown.
The evaporation formula is the standard dilute-vapour analogy; near 100 °C (a boiling surface) it is only approximate. Water lost by evaporation is not removed from the white's volume.
The pan is one lumped temperature: the patch under each egg cools no more than the rest of the pan, which slightly understates the local dip.
The yolk is heated through one column at its centre; its sides are not modelled separately. There is no lid or basting, so the film on top of the yolk stays raw.
Browning is an empirical rate, not chemistry. Set times in the hob table come from this model, tuned against recipe times (which vary by cook and pan), not lab measurements.
Theory items (lubrication flow, Bingham films, Lamb damping, capillary puddle height, 1-D conduction) are standard textbook results and were not re-checked against sources in this build.

Raw egg on a flat surface

Eggs

Cooking (hob setting)

Egg freshness preset

Density

Viscosity

Gel strength & shape

Surface

View