Growth by Collision and Coalescence Questions and Answers

Answer: A

Correct answer: a difference in fall speed between the droplets

Collision requires one droplet to overtake another, and that requires them to fall at different speeds - which in turn requires them to differ in size. A population of identical droplets falls together and never collides, however dense it is, which is why the initial breadth of the droplet spectrum matters so much.

Answer: B

Correct answer: Both A and R are true, and R is the correct explanation of A

Both are true and the reason gives the mechanism. Terminal velocity depends on size, so a narrow spectrum gives nearly uniform fall speeds and almost no relative motion between droplets. Broadening the spectrum - by giant nuclei, by turbulence, by entrainment - is what starts collection going.

Answer: C

Stokes drag balanced against weight gives a fall speed proportional to the square of the radius for droplets below about forty micrometres. Above that the relationship flattens and eventually approaches a square root dependence.

Answer: D

Doubling the radius quadruples the fall speed while the Stokes regime holds. That widening gap in fall speed with size is exactly what makes larger droplets effective collectors. The advantage compounds as the collector continues to grow.

Answer: A

Correct answer: False

The square law comes from Stokes flow, which holds only while the drop is small and the Reynolds number low. As the drop grows the flow separates behind it and the drag rises far faster, so the terminal velocity levels off at about 9 metres a second and increases hardly at all beyond a few millimetres.

Answer: B

Correct answer: the fraction of droplets in its path that actually strike it

Not every droplet in the geometric path is struck: the airflow round the falling collector carries the smaller ones aside. The collision efficiency is that fraction, and it is quite separate from the coalescence efficiency, which asks what proportion of the strikes actually merge.

Answer: C

Correct answer: A-2, B-4, C-1, D-3

The four quantities build on one another. Collision efficiency is the fraction of droplets in the path that strike; coalescence efficiency the fraction of strikes that unite; collection efficiency the product of the two; and the collection kernel the rate at which volume is swept multiplied by that collection efficiency.

Answer: D

Correct answer: Both A and R are true, and R is the correct explanation of A

Both are true and the reason gives the mechanism. As two droplets approach, the air between them must drain away, and if it cannot do so quickly enough the film holds them apart and they rebound. Coalescence efficiency is generally high for small droplets and falls for large ones, where the impact energy is greater.

Answer: A

Correct answer: the airflow deflects small droplets around such a collector

A small collector displaces very little air and the streamlines close round it smoothly, carrying the tiny droplets past without contact. Only when the collector reaches about twenty micrometres does its inertia become sufficient for droplets to cross the streamlines and strike it - which is the Hocking limit.

Answer: B

The first two are correct and describe the runaway character of the process. The third ignores the collision efficiency threshold that governs when collection can begin at all. Below that size a drop sweeps almost nothing from its path.