I am wondering how does an extended slat generate drag because I often read that slots agument lift by increasing critical angle of attack, but they do generate some extra drag. I am curious what is the cause of this drag.
Friction drag is proportional to the speed gradient right at the wall. This gradient is highest when the boundary layer is thin, and every boundary layer starts at zero thickness, with thickness increasing downstream.
Slots on purpose allow a fresh boundary layer to form on the wing or flap downstream of them because this fresh boundary layer can overcome steeper pressure rises downstream.
The downside of this fresh boundary layer is a lot more friction drag compared to the retracted state where the boundary layer of the slat becomes the (now much thicker) boundary layer of the wing. The same is happening again with the flaps: Slotted flaps allow the highest lift increases, but at the cost of much increased drag. However, would there be no new boundary layer on the flap, the flow would separate much earlier, at much lower flap angles and angles of attack.
Another effect are higher speeds of the flow around the wing at high lift coefficients. Low pressure means high speed, so the flow speed outside of the boundary layer is higher when local pressure is lower. This increases the speed gradient in the boundary layer, thus adding another drag increment,
The slat projects downward increasing frontal area, and forms a convergent duct leading from below to above the LE, that forces air to go around sharp corners to move up through the slot. Plenty of turbulence, extra frontal area, and air forced to make sharp changes in direction. Of course it's going to be draggier than a clean leading edge.
The effect is so strong that on the CRJs, the landing technique is completely different from the 200, with no slats, to the slightly larger 700, with slats. The 200 just coasts when you pull off the thrust, and you go to idle at 50 ft.
The 700, you have to keep the power on into the flare and ease it off at 10-20 ft, or else you will come down like a brick as the speed rapidly bleeds off. Using 200 technique on a 700 will guarantee a hard landing.
All passive High Lift devices (e.g. nothing that uses active flow control) increase the Lift Coefficient by increasing the overall camber of the wing system (the wing + slats + flaps).
If the wing stays at the same angle of attack, and the slats + flaps are extended, the increased camber is going to increase the lift coefficient. The benefit of this is that the aircraft can now fly slower and produce the same amount of lift to maintain level flight. The detriment of this configuration is the increase in induced drag.
As we know from the induced drag relationship, the induced drag coefficient scales with the square of the lift coefficient, and so the extra lift generated by slats + flaps comes at a significant expense of drag.
Vorticity is shed at any point that we have a spanwise change in circulation, including at the edge of slats & flaps. Therefore even modern wingtip winglets do not minimize the induced drag penalty that comes from these high lift devices.