A321 Captain reported engine thrust malfunctions caused an unstable approach. The flight crew elected to go-around and troubleshoot the issues. Both windscreens were observed to be clouded with an unknown material. Post flight revealed very fine sand was on the wind screens and the 'AOA was not moving freely.'

Narrative

First Officer (FO) flying arrival and approach RNAVXXR. Storms had passed thru earlier and had left behind clouds; a little wind; and icing conditions on arrival. Wing & engine anti-ice were on. Flying through a cloud layer we both noticed a substance on the front windows. I thought at first it was the clouds and the low visibility associated with it. But the FO stated 'what's on the windows?' We were at approximately 10;000 ft. MSL at this time and stabilized on the RNAV approach path. We were cleared for the approach and the FO could not get the aircraft to slow down. He attempted to go to vertical speed zero and we set the speed at 180 kts. but twice the power advanced for what appeared to be no reason. I suggested we put the gear down - we were at approximately 230-240 kts. Putting the gear down did not help. We now were pretty high for the approach so I asked Tower for an S-turn. He gave us a climb to 9;000 ft. - the controller never stated the word 'go-around' but in essence that was what he was giving us. The FO advanced the power to TOGA and stated such and I stated 'TOGA set' then he went to climb and since we never had the flaps out we went straight to the gear and brought them up. Since the Autopilot was off at the time; the FO started the go-around manually and as I was talking with ATC and slightly heads down reloading the approach the FO stated at least once that he could not get the Autopilot back on. I heard him say a few minutes later that he got it back on. We requested and received the ILS XXL. Came around and flew the aircraft normally to a normal landing. The entire time this film was caked on the front windows. The side windows were clear. We could make out the runway but it was blurry. Landed normally and as I taxied off the runway I realized that the windows were slightly obscuring my view to taxi. This was in daylight hours - had it been at night I am not sure I could have taxied to the gate. Upon arriving at the gate and shutting the engines down; I opened my window and reached my hand out to touch whatever it was on the window. I had tried airborne once to use the wipers but they did not help. The best way I can describe the substance is a white powdery substance that would not come off on my hands but was caked onto the window. I felt the nose of the aircraft and I could feel it on there as well. The aircraft was staying the night in ZZZ so the FO was required to walk-around. I waited until he walked around and he came back and said he did not see anything unusual. I called Maintenance and explained to them what we had - I told him I wasn't even sure how to write this up. He agreed with me that this was a highly unusual thing. The next morning I noticed the aircraft had been very delayed leaving ZZZ and we were scheduled to leave at the gate next to the aircraft. I also noticed in the on-line maintenance log that they had stated that 'due to a sand storm they found the AOA was not moving freely'. Upon arriving at the airport the agent told me that they flew in 6 mechanics on a private jet for that aircraft. When I was doing the walk-around I noticed them and went over and talked with them in detail to give them more of the story. They said the windows had been cleaned by the time they got there but there was still some residue and some on the aircraft itself. They also did not know what it was but were performing a complete flush of the system. The aircraft is back in service now.I am not sure what that substance was nor if it affected the aircraft in a way that made it impossible for us to slow it down. Never seen anything like it. Maybe the act of the go-around put everything 'back in order'??? Just thought some sort of report other than writing it up in the logbook and talking in detail with maintenance should be sent. I would love to find out what the substance was and where it came from!I have nothing to add here from what I already wrote above.