◉ SMOLUCHOWSKI COAGULATION EQUATIONS
COAGULATION KERNEL
Kernel type:
Constant K=1
Additive K=i+j
Multiplicative K=i·j
Brownian K=(1/i+1/j)
Initial clusters:
200
Time step:
0.01
Max cluster size:
30
RESET
STEP
RUN
Total clusters:
—
Mean size ⟨s⟩:
—
Max size:
—
Time t:
0
Smoluchowski (1917):
dnₖ/dt = ½Σᵢ₊ⱼ₌ₖ K(i,j)nᵢnⱼ − nₖΣⱼ K(k,j)nⱼ. For constant kernel: nₖ(t) = 4/(t+2)² × (t/(t+2))^(k-1) — exact scaling solution. Multiplicative kernel: gelation at finite time t*=1 (mass concentrates in infinite cluster). Brownian kernel gives n(s)~s^(-5/2) — same as percolation cluster distribution.