How do I lower the surface tension of water without using a detergent? For many years I've used a Rainbow vacuum, which uses a reservoir of water as the filter.   While I'm quite pleased with it, I've found that when trying to vacuum cement dust or wood ash not all of the  particles are captured in the water.   I believe a remedy to this would be to lower the surface tension of the water.  Yes, I can always be sure to use hot water, but I'd like to go further.  Obviously I can't use a suds-producing detergent because the vacuum produces lots of turbulence in the reservoir.   

What commonly available chemicals could I use that would give me the greatest reduction of surface tension? So far I've tried to research trisodium phosphate, sodium carbonate, and a product called Haemo-Sol which is a non-ionic surfactant... but I can't find surface tension numbers for any of these much less the concentration to use.

The manufacturer suggests adding a tablespoon of vinegar, which I think is
rather lame.

Can anyone make a good guess or point me in the right direction?
Your goal is to reduce the surface tension of the water so that it does not support the formation of large bubbles or inhibit the whetting of the dirt particles.  

When the bubbles are small, the dust inside will be more likely to make contact with the liquid surface of the bubble within the lifetime of the bubble. Also, when it does make contact, it will be much more likely to irreversibly adhere to the water if you have reduced the surface tension.  

The word "surfactant" is a blend of "surface active agent"$^1$, and this is what you need to interfere with the surface tension of your water.  I believe that you may have written off detergents too hastily. I think the best solution will be to add a small amount of laundry detergent, or possibly non-foaming carpet cleaner. Each of these products are designed to foam to a lesser degree than, say, dishwashing detergent or most hand soaps.  

I suspect that you will have to experiment a bit, but that something on the order of a single cc per liter may be sufficient to increase the effectiveness of dust removal without causing excessive suds. Your goal should be to see how much detergent you can add without adversely affecting your vacuum, and decide whether this has resulted in a decreased throughput of dust particles.  

As to your title question, "How do I lower the surface tension of water without using a detergent?", what I'm really saying is 1) that most anything that does what you want could probably be deemed a detergent and 2) that a detergent is likely the most practical solution to your problem.

1) Surfactants and Interfacial Phenomena, Fourth Edition, Rosen and Kunjappu, John Wiley and Sons, Inc., 2012