what should I cover beams in the ceiling with?

[Missjoberg]

Having trouble with sawdust leaking out between the ceiling and the beams in the ceiling as well as between the beams. It was used as insulation but now I've exposed the beams and plan to stain them dark. What can I use to seal it so the dirt doesn't fall down?

 

[eviljava]

Chemical wood in the beams and then some trim between the ceiling and beams?

 

[dsub]

Soft joint between beam and ceiling. Between the beams, probably the same but in the intended final color of the stain since the stain will not cover the joint.