Subtopic: Concentration and drying of liquid foods – evaporators, tray, drum and spray dryers
Question Statement:
In spray drying of liquid milk, droplet drying kinetics in the constant-rate drying period follow the classical $D^2$-law of droplet evaporation ($d^2 = d_0^2 - K t$). If a rotary atomizer is adjusted such that the initial Sauter mean diameter of milk droplets is halved from $120\,\mu\text{m}$ to $60\,\mu\text{m}$, the required drying time of an individual droplet is reduced by a factor of:
Options:
(A) 2
(B) 4
(C) 8
(D) 16
Answer Key:
B
Step-by-Step Solution & Explanation
According to the $D^2$-law for droplet evaporation:
$t_{\text{dry}} \propto d_0^2$
When diameter is reduced from $120\,\mu\text{m}$ to $60\,\mu\text{m}$:
$\frac{t_{\text{dry}, 1}}{t_{\text{dry}, 2}} = \left(\frac{120}{60}\right)^2 = 2^2 = 4$
Therefore, the drying time decreases by a factor of 4.