N. robusta feeds on and builds its tube out of particles it gathers from the neighborhood. When feeding, the worm extends its tentacles out over the bottom for a distance several times the length of its body.  Each tentacle forms a long groove.  Sediment with food particles is  transferred to the groove.  It is then carried down the groove by thousands of moving hairs (cilia) to lips in the mouth region.

Some particles are eaten, others form, and still others are tube building material, or rejected.

Terebellid in vertical burrow.

Our species lives in horizontal tubes.

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Figure from Barnes, R.D. 1987. Invertebrate Zoology. CBS College, New York, NY

Close up and cross section of a terebellid tentacle.

B.  Particles in tentacle groove;

C. Cross section of tentacle showing cilia in the groove.

Figure from Dales, R.P. 1955 Feeding and Digestion in Terrebellid Polychaetes.

J. Mar. Biol. Assoc., U.K.