Free boundary simulations with moving mesh

Hello,

I am trying to solve a system of PDE to simulate dripping of a water drop from the faucet. These PDEs are quasi-one-dimensional; see equations 17-20 in reference (https://arxiv.org/pdf/physics/0110081.pdf). Could anyone please point me towards a relevant document/example in Fenics to simulate this problem?

Many thanks,
Pallav