I have had the vacuum pump diaphragm fail on the 1972 220D and not notice it while on the highway. When I stopped the car disappeared in a cloud of the thickest white smoke you can imagine. I think the color of the smoke is related to the quality of the combustion as well as the "fuel."

When you have water leaking into the combustion chamber, you don't burn it like a fuel, you make water vapor which comes out the exhaust pipe. The water vapor consists of small droplets that will quickly evaporate once they are surrounded by air of a lower relative humidity, and then they really disappear. This is apparent in the winter when the water vapor produced by combustion meets up with cold air that cannot support the moisture content of the hot exhaust. The white steam ("smoke") that you see quickly evaporates as the exhaust mixes with the winter air, raising its temperature and lowering its relative humidity and the evidence of combustion disappears.

Oil smoke, on the other hand is only less visible as it is mixed with enough air to make the concentration of particlulate produced by combustion reflect less light than we need to see it. In a white smoke I believe you have oil droplets from incomplete combustion of the unusually high concentrations of oil in the combustion chamber coming out the exhaust pipe. The white appearance results from much the similarity of the oil droplet size and other characteristics compared to the water droplets of the steam. The high oil content in the intake reduces combustion temperatures to the point that much of the oil never reaches the temperature needed to ignite. The result is a longer lasting white fog that smells nothing like anti-freeze or steam. It is long lasting because it does not ever actually evaporate like water droplets.

So, if the oil level in the car is going down and the water level is not, I suspect the white smoke is coming from the oil. Just my opinion.....Jim

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Own:
1986 Euro 190E 2.3-16 (291,000 miles),
1998 E300D TurboDiesel, 231,000 miles -purchased with 45,000,
1988 300E 5-speed 252,000 miles,
1983 240D 4-speed, purchased w/136,000, now with 222,000 miles.
2009 ML320CDI Bluetec, 89,000 miles

Owned:
1971 220D (250,000 miles plus, sold to father-in-law),
1975 240D (245,000 miles - died of body rot),
1991 350SD (176,560 miles, weakest Benz I have owned),
1999 C230 Sport (45,400 miles),
1982 240D (321,000 miles, put to sleep)