Atomized unburned fuel would appear black. White smoke is a very strong indication of coolant entering the cylinders, Check you coolant levers periodically and make sure you aren't consuming any.

Possible explanation, very small crack in cylinder head or head gasket that seals as the engine expands. Had a very similar problem in the TD about 2 years ago now. ended up being the head.

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Current
2006 E320 CDI, 57K bought at 67K "Liesl"
1986 190E 2.3-16, 198K bought at 56K "Brigitta"
1987 300TD (Chuggin Along), 292K "Friedrich"
1995 E320 Wagon, 200K "Louisa"

Past
1987 300SDL, (sold) 125K, bought for 1$ "Kurt"