There are few English language research papers on the effect of surface roughness. As I recall, the Russian hydraulic mining papers consistently state that a smooth surface is necessary for a coherent jet. And I vaguely recall one (French?) paper that said even short rough patches can have a noticeable effect. This is why I have not tried to 3D print nozzles. A CNC lathe or mill with some smoothing/polishing after cutting probably would be ideal.
I didn't notice that typo in Theobald's paper, so thanks for pointing it out. I think there are some other problems with some of his range plots, and his breakup length data seems odd when plotted with other similar data too.
I'm interested in seeing how well the 3D printed nozzle works. But I think a fairly sudden large contraction (diameter ratio greater than 10 if possible) with a very short orifice is most likely to be better. The contraction should be smooth if possible, but as I recall some of the data I have suggests that even non-smooth instantaneous contractions can do really well.
Here's a plot with the only data I have on the effect of the contraction.
This is from a hard to find Russian book
. Not much detail is given in the text, unfortunately, but the plot is the diameter ratio vs. the fraction of maximum breakup length you can get. Larger ratios clearly are better, but the effect saturates.
Also, I'm not sure whether Theobald's shape is entirely valid if the proportions aren't maintained, but it should still be good if you scale it with different proportions.
Edit: In terms of minimizing the effect of the roughness, a large contraction should help. First, the contraction usually has a turbulence reduction effect (this is why it improves breakup length). Second, a large contraction necessarily means a large diameter pipe, which would make the relative roughness smaller.