Why Droplet Still Fall at Terminal Velocity ?

Force balance Equation for terminal velocity of a freely falling droplet or particle

Force balance : Drag force + Buoyancy force = Gravity force

Lets take the case of freely falling droplet in a gas liquid separator, gas is flowing upwards and droplet is falling down now my, fundamental doubt is

1. When all the force acting on the droplet get balanced (cancel out together), how the droplet can still fall ?
2. Terminal velocity by definition is relative velocity of gas and droplet ?

A metal ball is held and once release in the air...

FORCE BALANCE
Drag force + Buoyancy force + External force + Gravity force = 0
Upward direction, Fd + Fb + Fe +(-Fg) = 0
==> Fd + Fb + Fe = Fg

Event at 0- second...
When the ball is at static condition (metal ball is held),
==> Fd is function of velocity and . As velocity is zero ==> Fd = 0
==> Fb is function of relative density between ambient and ball. Ball density (say metal ball is approx. 3000 kg/m3) relative to air (~1.3 kg/m3), it is almost negligible. ==> Fb=0

==> Thus, Fe= Fg, V=0 m/s


Event at 0+ second...
When the ball is just released (o+ second),
==> Fe = 0
==> Fb negligible. ==> Fb=0
==> Fg maintain with no change
==> Fd is function begin to increasing...

Net Force (Fg > Fd) will drive the ball downward. Ball velocity begin to increase.


Event at t second...
When the ball velocity increase upto terminal velocity (relative velocity between ball and gas),
==> Fe = 0
==> Fb negligible. ==> Fb=0
==> Fg maintain with no change
==> Fd increase upto terminal velocity

Terminal velocity
Ball velocity is increased upto a velocity where Fg = Fd, this velocity is called terminal velocity. At this velocity, net force = 0 as Fd = Fg ==> No further increase in velocity. Constant velocity.

Metal ball vs Droplet

Ball as compare to droplet, same principle applied. The differences area the droplet shape may change from time to time and drag coefficient (C_d) will change from time to time. From engineering perspective, the change (too small) is negligible.

Reference :
i) Gas liquid Separator Sizing Using GPSA
ii) Two Suction Nozzles on Drum for Two Pumps Operation...