Dust Grain Growth Barriers 2D: Size-Velocity Phase Diagram

Disk Conditions

Turbulence strength α 1.0×10⁻³

Fragmentation velocity v_frag 1.0 m/s

Bounce-onset size (aggregate porosity) 5 mm

Simulation speed 1.0×

Live Readouts

Mean grain size

1.0 µm

Largest ever (barrier)

1.0 µm

Simulated time

0.0 s

Collisions/s (sampled)

stick 0% bounce 0% fragment 0%

How it works

This is the 2D counterpart to the 3D dust-grain-growth simulation — a genuinely different numerical model, not a flattened version of its particle box. The 3D model tracks individual aggregates drifting in a spatial patch and merging on physical contact. This one instead plots the population directly in the space where the growth barriers actually live: aggregate size vs. collision velocity, exactly as these barriers are presented in the real dust-coagulation literature (Zsom et al. 2010; Güttler et al. 2010).

Same-size collision velocity (zero drift term when both grains share a Stokes number):
  v(r) = c_s·√(α·St(r))            St(r) = r/r₀,  r₀ ≈ 1 m,  c_s ≈ 500 m/s

Growth-timescale law (dm/dt = ρ_dust·π(2r)²·v ⇒ the r² cancels):
  dr/dt = K·v(r)                    K = local dust-to-bulk density ratio (pacing only)

Each tracer grows along this curve until:
  v(r) ≥ v_frag  → fragmentation barrier: reset to a fresh monomer
  r ≥ bounce-onset size → bouncing barrier: growth halts, aggregate stays parked

The curve you see traced on the top panel is v(r) itself — every dust tracer's dot sits exactly on it, at whatever size it has currently grown to. The dashed red line is your fragmentation threshold; the dashed yellow line is your bounce-onset size. Whichever the growing curve reaches first is the barrier that actually stalls growth — raise v_frag or lower α to push the red line out of the way and let the yellow line dominate, or the reverse.

The stick / bounce / fragment percentages below the readouts come from a separate, independent check: every frame, random pairs are drawn from the current tracer population and classified with the exact same velocity formula and thresholds used for growth — this is the same event statistic the 3D sim shows, just computed by sampling pairs in a well-mixed patch instead of detecting spatial contact.

Time is heavily compressed for visibility (as in most of these barrier demos) — the bottom panel's histogram shows the live size distribution piling up right at whichever barrier line is currently the tighter constraint.

Stick zone (grows) Bounce zone (stalls) Fragment zone (resets)