Rub is used after these nouns:
back, spice

hard, vigorously
He rubbed his face vigorously with the towel.

well
Put a little cream onto each hand and rub it in well.

gently, lightly
He gently rubbed his swollen nose.

slowly
She rubbed her chin thoughtfully.

absently (esp. AmE)
in, together
He began to rub his hands together in glee.

begin to

against
The cat rubbed against my legs.

at
She stood up, rubbing at her back.

into
Rub the cream well into your skin.

on
She rubbed her hands on her apron.

with
I rubbed my glasses with my handkerchief.

Rub is used with these nouns as the object:
back, beard, belly, butter, cheek, chin, dirt, eye, forehead, hand, head, jaw, neck, nose, oil, palm, penis, shin, stomach, temple, tummy, wrist