A new spray-painting system is being evaluated for the auto industry. The paint is delivered via an atomizer that produces \(10 \mu \mathrm{m}\) particles and propels them toward the surface at a velocity of \(10 \mathrm{~m} / \mathrm{s}\). The particles are a dilute suspension of pigment agents in a solvent and for modeling purposes can be assumed to be pure solvent. To form a good coating, the particles must arrive at the surface with \(75 \%\) by volume of the solvent remaining. The free stream concentration of the solvent is effectively zero and the solvent has a specific gravity of 0.85 and a molecular weight of 100 . The whole system operates at atmospheric pressure and at the temperature of deposition, the vapor pressure of the solvent is \(250 \mathrm{~mm} \mathrm{Hg}\). The diffusivity of the solvent in air was measured to be \(1 \times 10^{-9} \mathrm{~m}^{2} / \mathrm{s}\) and the Schmidt number for the solvent is 500 . How far away from the surface can the painting nozzle be located?