the nerd zone · /ˌkɑː.məˈnɛt/

We named the company after the math that says the bucket is about to overflow.

In 1939, a Soviet physicist named David Albertovich Frank-Kamenetskii wrote down the equation for the moment a chemical reaction stops being boring and starts being a fire. We dropped the "Frank-" and kept the rest. Kamenet is his name. This page is what it means.

Зельдович, Я. Б. & Франк-Каменецкий, Д. А. — "Theory of thermal explosion," Acta Physicochimica URSS, 1939

step 1 · the idea

A thermal explosion is a race between two things.

That's the whole theory in one sentence. Inside a charging lithium cell, two clocks are running against each other — heat going in vs heat going out. When one starts outpacing the other, the cell heats up. When it stops being able to catch up, the cell vents, then burns, then takes the rack with it.

Frank-Kamenetskii's contribution was to write down exactly when the race tips. Not a vibe. An equation. We watch the same race, in real rooms, with sensors instead of chalk.

step 2 · the bucket and the hole

Pour water in. Watch the hole try to keep up.

Slide the temperature dial. The faucet ("heat creation") opens exponentially with temperature — that's the Arrhenius law. The hole ("heat escape") only opens linearly. Past the tipping point, you cannot pour fast enough to lose.

Heat creation · faucet 0.0 W

Heat escape · hole 0.0 W

Cell temperature 25 °C

Net heat (in − out) +0.0 W

Verdict nominal

Heat creation: Q_in = A·e^−Eₐ/RT
Heat escape: Q_out = h·(T − T_amb)

Cell temperature 25 °C ………………………………………………… 180 °C

Push past ≈ 95 °C and the faucet wins. Past ~135 °C a real cell vents. Past ~150 °C, runaway.

step 3 · the two curves

A picture Frank-Kamenetskii drew on a chalkboard.

Plot heat against temperature. Heat creation curves up like a hockey stick. Heat escape goes up like a ramp. They can cross twice, kiss once, or never meet. Each case is a different fate for the cell.

δ = q·ρ·A·L²·E_a λ·R·T_a²·e^E_a/RT_a

The Frank-Kamenetskii parameter. If δ > δ_cr, the geometry of the cell can no longer shed heat fast enough. For an infinite slab, δ_cr ≈ 0.878. For a sphere, 3.32. For a cylinder, 2.00. These are the famous three numbers.

step 4 · the circle of doom

Why it runs away. It's a loop, not a slope.

A normal warm thing equilibrates: heat in, heat out, settle. A thermal-runaway thing doesn't, because the rate of the reaction itself depends on temperature. The output of the loop is also its input.

For a lithium cell, "the reaction" is the cathode breaking down, the electrolyte oxidizing, then the anode reducing oxygen, then the separator melting. Each step lights the next. By the time you see smoke you are watching a chain of reactions that started ten or twenty minutes earlier — quietly, at 60 or 70 °C, deep inside a pack that still looked fine from outside.

Our sensor watches for the early loop, not the smoke. That's the whole product, and the whole reason for the name.

David A. Frank-Kamenetskii, Soviet theoretical physicist (1910–1970).

Д. А. Франк-Каменецкий 1910 – 1970

step 5 · the man

A theoretical physicist, working through a war.

Frank-Kamenetskii was born in 1910 in Vilna — today's Vilnius — and trained at the Tomsk Technological Institute. He spent his career at the Institute of Chemical Physics in Moscow as a student of Nikolay Semenov (Semenov got a Nobel for adjacent work; Frank-Kamenetskii arguably deserved one too). His book Diffusion and Heat Exchange in Chemical Kinetics — written largely during the Second World War — is the book every combustion engineer still owns.

He worked on rockets, on nuclear reactors, on stars. But the piece we love is the small one: the moment a smoldering pile of damp hay becomes a fire, the moment a battery becomes a problem, both have the same equation. He wrote it down. We watch it.

"A thermal explosion is the loss of stability of a stationary state."

— D. A. Frank-Kamenetskii

end of the nerd zone

Catch the loop early enough and the equation doesn't get to finish.

That's the job. Heat plus off-gas plus tamper, a fixed rule on the device, the relay drops, the room stays a room. The math Frank-Kamenetskii wrote down 87 years ago, watched by a thing on a wall.

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