a rush on (something)
A large, sudden, and widespread demand for something. I'm sorry, we had a rush on the chocolate cheesecake this afternoon, so I'm afraid we're out. There's always a rush on bed linens when the college students move back into town for a new semester.
rush on something
and run on somethinga large demand for something. There was a rush on bottled water during the drought. During the hot summer, there was a run on air conditioners.