Can drag force and lift force be in the same direction in the following case?

In the attached picture, can I say that there is a lift force in the Y-direction, and a drag force too in the same Y-direction?

$F_L$ proportional to $V_fx^2$ ?

$F_D$ proportional to $V_py^2$ ?

Is this equation of motion correct here: $ma = -mg -F_D$ + V$\rho$$g+$ $F_L$ ?

The lift force is because of the horizontal flow which is in fact lifting the particle, and the drag force is the resistance to the particle's upward motion. Is this correct to say.

Please assume that the picture is correct, and such an observation was made.

• I think that you should consider what causes drag. – don_Gunner94 May 2 '16 at 12:44

UPDATE IN RESPONSE TO YOUR COMMENT

I apologise : as you suggest, there might be a lift force on the sphere if there is a shear flow in the fluid (see Discussion in 1st Link). However, this force is likely to be much smaller than the drag on the particle.

http://physics.indiana.edu/~simasgrp/chris/0_Documents/00_Papers/LiftOnSphere/Leighton_85_TheLiftOnASmallSphereTouchingAPlane.pdf

https://www.researchgate.net/publication/232325622_The_Lift_Force_on_a_Small_Sphere_in_the_Presence_of_a_Wall

I do not see any reason for there to be a lift force since the particles do not appear to have an aerodynamic shape. Even if they did, the fact that they are free to rotate means that the 'angle of attack' could be reduced to zero, which would reduce lift to zero.

Possibly the particles could spin which would introduce a force due to the Magnus Effect (see video link). However, if the particles are quite small, viscous drag would quickly wipe out the rotation.

• Hi, when I am using the lift force in the y-direction equation of motion, will be it proportional to (V_fx - V_py)$^2$ or (V_fx$^2$ - V_py$^2$) or something else. I guess this will be the relative velocity for the particle right but not very sure which term is correct in this case? I am sure for drag in the horizontal direction it will be (V_fx - V_px)$^2$ in the motion equation. Thanks a lot for your help. – user2617526 May 5 '16 at 16:02