Particulate matter from exhaust gases emitted by power plant boilers in particular (if you’ll pardon the pun) is primarily removed via the use of electrostatic precipitators or by baghouses.
A precipitator is a large chamber through which the exhaust gases all travel on their way to the stack. The precipitator is filled with steel curtains designed to baffle and slow the gases somewhat, but their primary function is to attract the particles in the gas by virtue of the electrostatic charges imparted through them via high-powered capacitors on the roof of the precipitator building. This sets up the curtains to be electrically charged, which attracts the particles to bind to them – in a manner similar to what happens when you rub a balloon on your head, and the charged balloon then attracts other objects to it. At regular intervals a hammer device pounds on the hanger rods holding the curtains in place, and the particles then drop into ash hoppers at the base of the building, where they are removed, generally on conveyor belts, to the rest of the ash handling system.
Baghouses are used in place of precipitators in some applications (I don’t know of any plants using both baghouse and precipitator) where a series of fabric bags (think “gigantic vacuum cleaner bags”) hang from the top of the chamber, and induced cyclonic motion in the flue gases causes them to funnel through the bags just like a vacuum cleaner, which accumulate the ash for automated disposal (through hoppers and into the same type of conveyor system as described above).
These things are a lot more effective than you would think. When you pass a power plant, the largest plumes of steam – easily recognized as steam – come from the cooling towers that many plants have. However, the “smoke” often cited from the “smoke stack” also contains a lot of steam. Most coals burned at utility power plants have up to (and sometimes even more than) 30% water, and that also goes up the stack with the exhaust gases. You can see the finest ash and “smoke” from a power plant (properly maintained and operated, that is) if you look closely, but a lot of what comes from the stack is just “more steam”.
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But you had asked about scrubbers. In a power plant application, “scrubbers” refer generally to “flue gas desulpherization” (FGD) devices, which function downstream of the precipitator / baghouse, and which utilize various chemical and physical means (sometimes involving water spray, and sometimes “dry”) to extract the SO2 (sulphur dioxide) created as part of the combustion process. These operate downstream of the particulate removal devices, because excess ash and soot particles would render them less effective, degrading their performance and shortening their effective working lives.
Scrubbers also refer to CO2 scrubbers, which work in human breathing atmosphere applications such as submarines and other atmospheres (like space capsules, for example – maybe some long haul planes, too, I think) which require the constant reuse of a contained atmosphere. It’s not “lack of oxygen” that hampers most such living environments, but “buildup of CO2”, so the scrubbers effectively extract exhaled CO2 from such limited, closed environments so the air can be reused by the people who depend upon it. (I don’t know much about CO2 scrubbers except to know that the “limited, closed atmosphere” is key – there are no effective CO2 scrubbers yet devises, as far as I know that can handle the volumes of flue gases given off by even a fairly small power plant.)
Scrubbers of these types do not remove much particulate matter at all, except coincidentally, as every passage of flue gas leaving the furnace of a coal-fired boiler contains – and drops – some ash through its entire traverse as the gas loses heat and speed and encounters obstacles in the flow.