Nathan

I see other replies have alerted you to a blocked AC drain. However, there is another possibility I suggest you may want to investigate.

Air is drawn into the Heater/AC unit from within a plenum in front of the windscreen. There is a plastic cowl under your wipers that covers this plenum. Volvo have hidden a couple of drains (well, at least they did no my 96 model 850R) inside this plenum. When they block, water accumulates in here and then sloshes across to the passenger side as you describe. When the water gets here it floods over the "seal" and falls into (and around) the heater asesembly. From here it can get into the passengar side footwell.

I had this happen to me recently and confirm the "sloshing" sound coming from what appears to be the upper reaches of the dash. This is prominent after rain or washing the car.

To access these drains you need to:
(1) undo the wiper retaining nuts and pull wipers off
(2) remove 5 retaining screws across the front of the plastic cowl
(3) disconnect the two external drains - in the engine bay - from the cowl
(4) pull the cowl forward to disengage it from the bottom lip of the screen, and then lift out.

When you are to this point, one drain will be apparent adjacent to the air inlet to the heater. The second will be partly hidden by the fuse box on the other side. Clean both and gently rinse through to confirm they are flowing freely.

While you are in there, you can directly remove any debris from the inlet to the fan. If you don't have a pollen filter, this is also the perfect time to fit one!

Note your AC drain is posibly also blocked or has come adrift from the point where it passes through the floor, but I suggest it would be prudent to also look at these plenum drains. Unfortunately, even if the AC drain is not blocked, it will not prevent leakage from the water that floods over from the plenum into the heater air inlet opening.

Hopefully you have not soaked your carpets (front/rear) as it can be a messy job to get them dried out.

Nathan, most surely it is your air conditioning drain pipe that is clogged. With time a lot of debris will accumulate in the evaporator case. This will cause the symtoms you describe as condensation that is generated by the use of AC will not be able to flow out. To clean this drain you will have to remove the passenger side under panel plate. Also you will have to pull back the carpet on passenger side. You will see the drain which is a black rubber pipe about half an inch in diameter that connects the air conditioning case to a hole on the center of the floor tunnel. In order to clean it, first protect the surrounding area with plastic and rags. Then pull it from the floor. Probably some water will come out of it so it might be handy to have some recipient to colect it. If nothing comes out then the clogging is inside the pipe or even in the lower part of the AC case. Pull the pipe from the AC case and have rags to collect the dirty water that will flow out. After the flow stops, clean the plastic tube under the AC case carefully with a piece of wire. Then clean the rubber pipe, and make sure it is totally unclogged before you put it back. That is it. After you remove the lower panel plate and pull back the carpet, make sure you identify clearly the drain pipe, and where and how it connects to the AC case and to the drain hole on the floor. And make sure you dry everything very well before putting the carpet back in place. Might be a good idea to leave the car in the sun for sometime to dry the carpet. Good luck, and post if you have any trouble.

your drain plug is clogged.. remove the passenger side kickplate and you will see a short rubber hose going to the floor. Have something like a pop bottle to collect the water that will drain out when you pull the hose off.
Clear out the blockage (usually a leaf) and put back togetter.
dry your carpets