\(\mathrm{NaCl}\) is crystallizing from an aqueous (water) liquid solution onto a crystal particle of pure \(\mathrm{NaCl}\) at \(18^{\circ} \mathrm{C}\). Assume particle growth is controlled by mass transfer, and the particle is spherical. The aqueous solution is supersaturated at a mass fraction of \(\mathrm{NaCl}\) \(=0.30\). If the initial particle diameter is \(D=0.1 \mathrm{~mm}\), find \(D\) after \(3600 \mathrm{~s}\).

Data: Solubility of \(\mathrm{NaCl}\) in water at \(18^{\circ} \mathrm{C}=0.2647\) mass fraction.

Density pure solid \(\mathrm{NaCl}=2.163 \mathrm{~g} / \mathrm{cm}^{3}\). Molecular weight \(\mathrm{NaCl}=58.45\).

Density of aqueous solution of \(\mathrm{NaCl}=1.20 \mathrm{~g} / \mathrm{cm}^{3}\) (assume constant).

Density of pure water \(=1.0 \mathrm{~g} / \mathrm{cm}^{3}\). Molecular weight pure water \(=18\).

\(D_{\mathrm{NaCl}-\text { water }}\) at \(18^{\circ} \mathrm{C}=1.24 \times 10^{-9} \mathrm{~m}^{2} / \mathrm{s}\). Mass transfer coefficient \(\mathrm{k}=2.0 \times 10^{-6} \mathrm{~m} / \mathrm{s}\).