Dust Grain Growth Barriers in a Protoplanetary Disk

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 orbits

Collisions/s

stick 0% bounce 0% fragment 0%

How it works

Each sphere is a dust aggregate drifting and being stirred inside a small patch of a protoplanetary disk. Its coupling to the gas is set by the Stokes number St = r / r₀ (r₀ ≈ 1 m), which controls two independent collision-velocity sources:

Radial drift (Weidenschilling 1977):
  v_drift(St) = 2·St / (1+St²) · v_hw     [v_hw ≈ 50 m/s headwind]

Turbulent stirring (Ormel & Cuzzi 2007, tightly-coupled limit):
  v_turb ≈ c_s·√(α·St_max)                [c_s ≈ 500 m/s]

Collision speed:
  v_rel = √(v_turb² + Δv_drift²)

Every collision is classified from the physics, not chance:

Stick (green) — v_rel is below v_frag and the merged size stays under the bounce-onset size. Mass is conserved: r_new = (r₁³+r₂³)^⅓.
Bounce (yellow) — v_rel is still below v_frag, but the merged aggregate would cross the bounce-onset size. Real compacted aggregates rebound instead of sticking past roughly mm–cm sizes — this is the observationally-motivated bouncing barrier (Zsom et al. 2010) — so no growth occurs.
Fragment (red) — v_rel exceeds v_frag; both aggregates shatter and are reset toward monomer size, returning mass to the small end of the distribution.

Raise turbulence α or lower v_frag to make the fragmentation barrier bite earlier; lower the bounce-onset size to make the bouncing barrier dominate instead. Particle motion in the box is illustrative of stirring and drift direction; the size/velocity numbers driving each collision's outcome are the real formulas above. This is the same size bottleneck (roughly mm to m) that real coagulation models struggle to cross without invoking streaming instability or pebble accretion.

Small dust / ice Pebble aggregate Near barrier size

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