When performing a vacuum distillation - is a fine hair capillary necessary? What happens if I perfom the distillation without the capillary?
A capillary would be used, if you have no stirring capabilities. Otherwise, it is not essential.
I think TFSE has something about this, so I'll just give a short answer. If you don't stir (rapidly!) or use a capillary, the liquid will bump bigtime when it boils. Boiling stones DO NOT work under vacuum!
... unless they are vacuum boiling stones. Such exist.
Glass wool can be used instead of capillary or boiling stones. The layer of glass wool must be about 1 cm above than liquid layer in a flask. It gives good results