text: also diffuse over the substrate (conserved dynamics). The conserved part is treated along the lines 
  
  developed above for the nanoparticles. For the non-conserved part we assume a standard form 
  
  [85], i.e., the change in time of ρl is proportional to −(µsurf(r, t) − µ) = −δF [ρn, ρl]/δρl(r) 
  
  where µsurf(r, t) is the local chemical potential of the liquid at the point r on the surface at time t. 
  
  This gives the evolution equation for the liquid density 
  (cid:21)  (cid:20) 
  
  ∂ρl 
  ∂t 
  δF [ρn, ρl] 
  δρl  δF [ρn, ρl] 
  δρl 
  M c  − M nc  = ∇ · 
  l ρl∇ 
  , 
  l 
  
  where we assume that the coefﬁcients M c 
  l and M nc 
  l 
  are constants. 
  
  16 