During fast lithium-metal plating, the anode surface roughens: any point that sticks out slightly sees a locally higher ionic flux (the electric field concentrates at protrusions), so it grows faster than its neighbors — a positive-feedback instability that produces needle-like dendrites. Left unchecked, a dendrite eventually bridges the gap to the counter-electrode and shorts the cell.
This model deposits lithium onto a grid of surface sites. Each step it picks a site with probability weighted by how far its height sits above the local average:
P(site i) ∝ exp( k · (hᵢ − h̄) )
k = k₀ · (J / J_ref) · (1 − 0.85 · additive/100)
Higher current density J raises k, sharpening the feedback and producing thin, fast-growing fingers — this mirrors the real dependence of dendrite onset on applied current. Electrolyte additives (e.g. FEC, LiNO₃-type film formers) build a more uniform, mechanically robust SEI that evens out local flux, lowering k and pushing growth back toward smooth, "mossy" deposition. Applied stack pressure mechanically resists protrusions: in the model, a tall site under high pressure has its next atom redirected to its lowest neighbor instead, physically flattening the front — consistent with experiments showing external pressure suppresses dendrite propagation.
The time-to-short estimate follows the scaling of Sand's time (Chazalviel's space-charge model for the onset of dendritic growth in a binary electrolyte):
τ_Sand = π D (e C₀ / (2 J t₊))² ⇒ τ ∝ 1 / J²
The panel's readout keeps that J⁻² scaling and applies directionally correct multipliers for additive and pressure suppression; treat the number as an illustrative, relatively-scaled estimate rather than a lab-calibrated prediction. Growth stops and the cell "shorts" when the tallest column reaches the fixed counter-electrode plane.