A seed crystal of diameter D (mm) is placed in a solution of dissolved salt, and new crystals are observed to nucleate (form at a constant rate r (crystals/min). Experiments with speed crystals of different sizes show that the rate of nucleation varies with the speed crystal diameter as r(crystals/min) = 200D – 10D2 (D in mm)
(a) What are the units of the constants 200 and 10? Assume the given equation is valid and therefore dimensionally homogeneous).
(b) Calculate the crystal nucleation rate in crystals/s corresponding to a crystal diameter of 0.050 inch.
(c) Derive a formula for r(crystals/s) in terms of D (inches). (See Example 2.6-1) Check the formula using the result of part (b).