How centrifugation can be explained in an inertial frame? I am reading about centrifugation and I can't understand what forces are responsible for the sedimentation and how the motion of particle can be explained in an inertial frame. I can understand sedimentation in a stationary fluid. All the explanations I have found are the following:

Inbalance in centrifugal, drag and buoyant force.

But I would like an explanation based in an inertial frame. My current explanation is that the forces that a particle "feels" are not enough to keep it in circular motion. But then I can't understand why it must move vertically (sedimentation) and not horizontally. I have drawn also a free body diagram but still can't grasp why a particle settles down. I am not even sure if the direction of buoyant force is correct or it should be in the direction of drag.
                                      
 A: An explanation in the inertial frame is annoying and unnecessarily complicated. This is exactly the sort of situation where non-inertial frames are best used: they simplify the calculation immensely. However, it is possible to do the unnecessarily complicated analysis in the inertial frame. To simplify the analysis a little we will put the centrifuge in space so that there is no gravity. Sedimentation will still occur.
First, consider a small parcel of the fluid. The fluid parcel moves in uniform circular motion so it is subject to a centripetal force. The only force acting on that parcel is the pressure. That means that the pressure cannot be uniform, but rather must be greater on the outside than on the inside. Specifically, the difference in pressure force is equal to the mass of the parcel times the centripetal acceleration. This keeps the fluid in uniform circular motion.
Now, consider a chunk of sediment the same volume as the parcel. The pressure gradient is the same for the chunk as it is for the fluid, and it’s volume is the same too. So the force acting on the sediment chunk is the same as the force acting on the fluid parcel. But since it’s mass is larger, this force is insufficient for uniform circular motion at the radius of the centrifuge. This means that it does not accelerate inwards sufficiently to stay at the same radius, and therefore it moves to a larger radius. This continues until the chunk reaches the wall of the tube which can exert a force sufficient to provide the centripetal acceleration necessary for uniform circular motion at the radius of the centrifuge.
Now that we have understood the pressure gradient, or buoyancy, in the inertial frame then the drag and other forces can be added unchanged from the standard non-inertial analysis.
A: There are many applications of centrifugation, they all have this in common: the device is pulling G's.
Here on Earth the Earth's gravity is pulling 1 G.
Let's say that you have boarded some carnival ride, and the angular velocity and diameter are such that the centrepetal acceleration is pulling 1 G too.
Inertial mass and gravitational mass are equivalent. Here the two directions of pulling G's are perpendicular so you can calculate the resultant amount of G's that is being pulled with Pythagoras' theorem.
More generally, since inertial mass and gravitational mass are equivalent: the direction in which buoyancy force acts is opposite to the direction in which G's are being pulled
