= Surface-reaction-controlled particle growth
{title2=$\dot a\simeq k_s(c_\infty-c_{\rm eq})/c_p$}
When attachment is much slower than exterior <diffusion>, the surface <concentration> stays close to the reservoir value. An attachment coefficient $k_s$ with units of <velocity> gives nearly constant radial growth in the dilute-feed approximation. For a <sphere> the ratio $k_sa/D$ distinguishes attachment control from transport control. A finite attachment rate leads to a <Robin boundary condition> rather than a fixed equilibrium surface concentration.
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