Using Stokes' law $v = \frac{g d^2 (\rho_s - \rho_f)}{18 \mu}$, if unhomogenized milk has fat globules of average diameter $d_1 = 4.0\;\mu\text{m}$, and two-stage homogenization reduces the diameter to $d_2 = 1.0\;\mu\text{m}$, the creaming rate of the fat globules in homogenized milk is reduced by a factor of ________ (answer in integer).
Answer Key:
16
Step-by-Step Solution & Explanation
From Stokes' law, creaming velocity $v \propto d^2$:
$\frac{v_1}{v_2} = \left(\frac{d_1}{d_2}\right)^2 = \left(\frac{4.0}{1.0}\right)^2 = 4^2 = 16$
Thus, the creaming velocity decreases by a factor of 16.